GRADE 3 MATHEMATICS
CURRICULUM GUIDE
Loudoun County Public Schools 2016-2017
Overview, Scope and Sequence, Unit Summaries, The First 20 Days Classroom Routines, Curriculum Framework, Learning Progressions
(additional attachments: Intervention Ideas, NCSM Great Tasks SOL alignment, Math Literature Connections)
Additional resources (including FLIPCHARTS based on VDOE ESS lessons) may be found on the
Elementary Math Resources VISION site: http://loudounvision.net/. Search: Math—Elementary Resources; Enrollment key: MATH (all caps)
LCPS Grade 3 Mathematics Curriculum Guide 2016-2017
INTRODUCTION TO LOUDOUN COUNTY’S MATHEMATICS CURRICULUM GUIDE
This CURRICULUM GUIDE is a merger of the Virginia Standards of Learning (SOL) and the
Mathematics Achievement Standards for Loudoun County Public Schools. The CURRICULUM GUIDE includes excerpts from documents published by the Virginia Department of Education. Other statements, such as
suggestions on the incorporation of technology and essential questions, represent the professional consensus of Loudoun’s teachers concerning the implementation of these standards.
This CURRICULUM GUIDE is the lead document for planning, assessment, and curriculum work.
NAVIGATING THE LCPS MATHEMATICS CURRICULUM GUIDE
The Curriculum Guide is created to link different components of the guide to related information from the Virginia Department of Education, resources created by Loudoun County Public Schools, as well as vetted outside resources.
To navigate the curriculum guide, click on the hyperlink (if in MSWord, hold the [ctrl] button and left click with the mouse on the hyperlink). It will direct you to either another resource within the curriculum guide, or to a website resource.
If you’re directed to a resource within the curriculum guide, to “go back,” hold the [alt] key and press the left arrow button. Mathematics Internet Safety Procedures 1. Teachers should review all Internet sites and links prior to using it in the classroom. During this review, teachers need to ensure the appropriateness of the content on the site, checking for broken links, and paying attention to any inappropriate pop-ups or solicitation of information. 2. Teachers should circulate throughout the classroom while students are on the internet checking to make sure the students are on the appropriate site and are not minimizing other inappropriate sites. 3. Teachers should periodically check and update any web addresses that they have on their LCPS web pages. 4. Teachers should assure that the use of websites correlates with the objectives of the lesson and provide students with the appropriate challenge.
LCPS Grade 3 Mathematics Curriculum Guide 2016-2017
2009 Virginia SOL Testing Blueprint: Test Items by Strand Dates of LCPS Quarters SOL Reporting
Category Grade 3 SOL Number of Test
Items (CAT) Number of Test
Items
(Traditional)
Number and Number Sense
3.1a-c, 3.2, 3.3a-c 7 10
Computation and
Estimation 3.4, 3.5, 3.6, 3.7 7 10
Measurement and
Geometry
3.8, 3.9a-d, 3.10a-b,
3.11a-b, 3.12, 3.13, 3.14,
3.15, 3.16
8 11
Probability, Statistics,
Patterns, Functions,
and Algebra
3.17a-c, 3.18, 3.19, 3.20a-b
6 9
2016 – 2017 School Calendar
Starts Ends
First Quarter August 29 November 4
Second Quarter November 9 January 26
Third Quarter January 30 April 6
Fourth Quarter April 17 June 9
Quarter 1 Quarter 2 Quarter 3 Quarter 4
P = Teacher Workday/Planning Day H = Holiday/ No School F = First Day of School TI = Teacher Institute for new professionals NH = New Hire Workday SD = In School Staff Development days CS = County Wide Staff Development Days
LCPS Grade 3 Mathematics Curriculum Guide 2016-2017
Grade 3 Nine Weeks Overview 1st Quarter 2nd Quarter 3rd Quarter 4th Quarter
Unit 1-Classroom Routines: “The First 20 Days Classroom Routines” NUMBER TALKS 3.11 Time/Elapsed Time 3.12 Equiv. Periods of Time 3.13 Temperature 3.17 Data and Graphs
Unit 2-Place Value 3.1 Place Value, Round, Compare
Unit 3-Computation With Whole Numbers (addition/subtraction)
3.2 Related Facts to Solve Problems 3.4 Single- & Multistep Problems (add/subtract) 3.20 Identity/Commutative Properties (addition)
Unit 4-Money 3.8 Count & Compare Money, Making Change
Unit 1-Classroom Routines: NUMBER TALKS 3.11 Time/Elapsed Time 3.12 Equiv. Periods of Time 3.13 Temperature 3.17 Data and Graphs
Unit 5-Computation With Whole Numbers (multiplication/division) 3.5 Multiplication & Division Facts 3.6 Model Multiplication & Division, Create & Solve Story Problems 3.19 Patterns (see unit summary) 3.20 Identity/Commutative Properties (multiplication)
Unit 6-Patterns and Data 3.17 Collect, Display, & Interpret Data 3.19 Patterns
Unit 7-Geometry 3.14 Plane & Solid Geometric Figures 3.15 2D Geometry 3.16 Congruent/Non-congruent Geometric Figures
Unit 1-Classroom Routines: NUMBER TALKS 3.11 Time/Elapsed Time 3.12 Equiv. Periods of Time 3.13 Temperature 3.17 Data and Graphs
Unit 8-Fractions, Probability, and Measurement (length) 3.3 Model, Name, & Compare Fractions 3.18 Probability 3.9ad Length to Nearest ½ Inch, Area/Perimeter
Unit 9-Computation with Fractions 3.7 Add/Subtract Fractions With Like Denominators
Unit 10-Elapsed Time and Temperature 3.11 Time/Elapsed Time 3.12 Equiv. Periods of Time 3.13 Temperature
Unit 1-Classroom Routines: NUMBER TALKS 3.11 Time/Elapsed Time 3.12 Equiv. Periods of Time 3.13 Temperature 3.17 Data and Graphs
Unit 11-Measuring My World 3.9 Measure Length, Weight, Liquid Volume, Area/Perimeter 3.10 Area/Perimeter
Review for SOL Assessment & Post SOL Topics
48 days 45 days 48 days 39 days
LCPS Grade 3 Mathematics Curriculum Guide 2016-2017
Grade 3 Scope & Sequence Quarter 1: 48 days
Days UNIT Standard Content Strand Topic
All year Unit 1-Classroom
Routines
“The First 20 Days Classroom Routines”
& NUMBER TALKS, Time/Elapsed Time, Equiv. Periods of Time, Temperature, Data/Graphs
12 Unit 2-Place Value 3.1 Number and Number
Sense Place Value, Round, Compare
22 Unit 3-Computation With
Whole Numbers (addition/subtraction)
3.2 Number and Number
Sense Related Facts to Solve Problems
3.4 Computation and
Estimation Single- and Multistep Problems (add/subtract)
3.20 Patterns, Functions,
and Algebra Identity/Commutative Properties (addition)
10 Unit 4-Money 3.8 Measurement Count and Compare Money, Make Change
4 Assessment, Review, and Intervention
LCPS Grade 3 Mathematics Curriculum Guide 2016-2017
Quarter 2: 45 days
Days UNIT Standard Content Strand Topic
All year Unit 1-Classroom
Routines NUMBER TALKS, Time/Elapsed Time, Equiv. Periods of Time, Temperature, Data/Graphs
21 Unit 5-Computation With
Whole Numbers (multiplication/division)
3.5 Computation and
Estimation Multiplication and Division Facts
3.6 Computation and
Estimation Model Multiplication and Division, Create and
Solve Story Problems
3.19 Patterns, Functions,
and Algebra Patterns (see unit summary)
3.20 Patterns, Functions,
and Algebra Identity/Commutative Properties (multiplication)
10 Unit 6-Patterns & Data
3.17 Probability and
Statistics Collect, Display, and Interpret Data
3.19 Patterns, Functions,
and Algebra Patterns
10 Unit 7-Geometry
3.14 Geometry Plane and Solid Geometric Figures
3.15 Geometry 2D Geometry
3.16 Geometry Congruent/Non-congruent Geometric Figures
4 Assessment, Review, and Intervention
LCPS Grade 3 Mathematics Curriculum Guide 2016-2017
Quarter 3: 48 days
Days UNIT Standard Content Strand Topic
All year Unit 1-Classroom
Routines
NUMBER TALKS, Time/Elapsed Time, Equiv. Periods of Time, Temperature,
Data/Graphs
22 Unit 8-Fractions, Probability, and
Measurement (length)
3.3 Number and Number
Sense Model, Name, and Compare Fractions
3.18 Probability and
Statistics Probability
3.9ad Measurement Length to Nearest ½ inch, Area/Perimeter
12 Unit 9-Computation
With Fractions 3.7
Computation and Estimation
Add/Subtract Fractions With Like Denominators
10 Unit 10-Elapsed Time &
Temperature
3.11 Measurement Time/Elapsed Time
3.12 Measurement Equivalent Periods of Time
3.13 Measurement Temperature
4 Assessment, Review, and Intervention
LCPS Grade 3 Mathematics Curriculum Guide 2016-2017
Quarter 4: 39 days
Days UNIT Standard Content Strand Topic
All year Unit 1-Classroom
Routines
NUMBER TALKS, Time/Elapsed Time, Equiv. Periods of Time, Temperature,
Data/Graphs
18 Unit 11-Measuring My
World
3.9 Measurement Measure Length, Weight, Liquid Volume,
Area/Perimeter
3.10 Measurement Area/Perimeter
21 Assessment, Review, and Intervention
SOL Tests
LCPS MATH Unit Summary Grade 3 2016-2017
Unit: 1 Quarters 1-4
Classroom Routines
VDOE Standards of Learning:
1st quarter: The First 20 Days Classroom Routines 3.11 The student will
a) tell time to the nearest minute, using analog and digital clocks
3.12 The student will identify equivalent periods of time, including relationships among days, months, and years, as well as minutes and hours.
3.13 The student will read temperature to the nearest degree from a Celsius thermometer and a Fahrenheit thermometer. Real thermometers and physical models of thermometers will be used.
3.17 The student will a) collect and organize data, using observations, measurements, surveys, or
experiments; b) construct a line plot, a picture graph, or a bar graph to represent the
data; and c) read and interpret the data represented in line plots, bar graphs, and
picture graphs and write a sentence analyzing the data.
VDOE Process Goals: Problem Solving, Communication, Connections, Reasoning, Representations
Learning Targets:
I can tell time to the nearest minute using different clock models.
I can identify equivalent periods of time and recognize the relationships between the different periods of time.
I can read and write temperatures to the nearest degree using Celsius and Fahrenheit thermometers and pictorial models.
I will collect data, and represent the data in graphs to write a sentence explaining the results.
Big Ideas Essential Questions
Classroom routines (about 10 minutes each day) can be used to introduce, support, and extend topics throughout the yearly curriculum in order to provide students with regular practice in important mathematical ideas.
Can you compare and contrast analog and digital clocks?
Can you explain and justify how to determine time on an analog clock? elapsed time?
How is a calendar organized to measure time?
Can you describe the relationships that exist among periods of time within a calendar year?
When and why do we have a leap year?
What the purpose of a thermometer?
How is temperature related to everyday activities?
How do you explain strategies that can be used to collect, organize, and represent data?
How does the type of data and the questions to be answered influence the choice of graph?
Can you compare and contrast the key elements needed when constructing line plots and graphs?
How do you collect, organize, display, and interpret data to provide different kinds of information?
LCPS MATH Unit Summary Grade 3 2016-2017
Prerequisite Skills Vocabulary
VDOE Vertical Alignment document K-3 VDOE Vertical Alignment document 3-6
2.12 The student will tell and write time to nearest 5 min 2.13 The student will a) determine past/future days of the week b) identify days/dates on calendar 2.14 The student will read temperature on thermometer in Celsius and Fahrenheit to nearest 10 degrees 2.17 The student will construct picture/picto/bar graphs
VDOE Vocabulary Word Wall Cards data half-hour days of the week categories quarter hour months of the year survey hours minutes bar graph hour hand time data point minute hand equivalent relationships increments analog clock picture graph digital clock scale a.m. temperature horizontal axis p.m. elapsed time vertical axis Celsius Fahrenheit title thermometer labels legend/key line plot prediction
Achievement Criteria How to Assess Achievement
“The content of the mathematics standards is intended to support the following five process goals for students:
• becoming mathematical problem solvers • communicating mathematically • reasoning mathematically • making mathematical connections and • using mathematical representations to model and
interpret practical situations.” -2009 Mathematics Standards of Learning
Click here for a brief audio PowerPoint slide with more information about the Process Goals
Pre and Post Unit Assessments for each standard
can be found in PowerSchool Assessment (formerly Interactive Achievement)
Sample Math Tasks are available in VISION:
Search: LCPS-Math: K-12 Math Tasks Enrollment key: MATH
NCSM Great Tasks
(available in all LCPS Elementary Schools—click link)
Classroom Routines
1st quarter: The First 20 Days Classroom Routines NUMBER TALKS: Number Talks sample flipcharts available on the Elementary Math Resources VISION site Example: http://www.mathsolutions.com/videopage/videos/Final/Classroom_NumberTalk_Gr3.swf INVESTIGATIONS: Mathematical Thinking at Grade 3 Calendar Math p. 87/Exploring Data p. 89
Create an interactive bulletin board. The clock faces will need to be laminated or placed in plastic sleeves so that students will be able to draw hands on them and then erase the hands. In the middle section, the elapsed time will change daily or even during the day. Students will be given a digital start time written on the board. A student will go to the bulletin board and record the digital time on the start time clock face by drawing the hands. The student will then check the elapsed time and determine the end time to draw on the end time clock face. (Note: A geared clock needs to be available for students’ use at this bulletin board. Be careful when giving out start times and elapsed times that the end time does not need to cross over between a.m. and p.m.)
Have students work together in groups of two or three to create, exchange, and solve five word problems dealing with the temperature changes that they have observed over a period of time.
Display graphs around the classroom, and have students keep their individual graphs in binders or folders. Additional resources (including FLIPCHARTS based on VDOE ESS lessons) may be found on the Elementary Math Resources VISION site: http://loudounvision.net/ Search: Math—Elementary Resources Enrollment key: MATH (all caps)
LCPS MATH Unit Summary Grade 3 2016-2017
Unit: 2 Quarter 1
Place Value
VDOE Standards of Learning:
3.1 The student will a) read and write six-digit numerals and identify the place value and value of each digit; b) round whole numbers, 9,999 or less, to the nearest ten, hundred, and thousand; and c) compare two whole numbers between 0 and 9,999, using symbols (>, <, or = ) and words (greater than, less than, or equal to).
VDOE Process Goals: Problem Solving, Communication, Connections, Reasoning, Representations
Learning Targets:
I can read, write, and model six-digit numerals and identify the place value positions, value of each digit, and the relationship of each place value position to the next.
I can round whole numbers, 9,999 or less, to the nearest ten, hundred, and thousand and represent my thinking using pictures, numbers, and words.
I can compare two whole numbers between 0 and 9,999, using symbols (>, <, or = ) and words (greater than, less than, or equal to).
Big Ideas Essential Questions
• Understand that knowledge of place value is essential when comparing numbers. • Understand the relationships in the place value system, where each place is ten times the value of the place to its right. • Understand that rounding gives an estimate to use when exact numbers are not needed for the situation. • Understand the relative magnitude of numbers by comparing numbers. • Understand how to use manipulatives such as base 10 blocks, Digiblocks, etc. • Use patterns in the place value system to read and write numbers.
Can you explain the relationship in the place value system using a six-digit numeral?
Can you compare and contrast written formats for whole numbers (standard, written, and expanded notation)?
What is the magnitude of each 4 in the number 4,444?
Can you explain strategies for comparing two whole numbers?
Can you explain the use of an inequality symbol in an equation?
Why are numbers rounded? Are there other strategies for estimation?
Can you demonstrate and explain how to round a four-digit number using a variety of strategies?
Prerequisite Skills Vocabulary
VDOE Vertical Alignment document K-3 VDOE Vertical Alignment document 3-6
2.1 The student will a) read/write/ID place value in 3‐digit numeral b) round 2‐digit numbers to nearest ten c) compare two whole numbers 0 – 999 with symbols and/or words. 2.4 The student will a) count by 2/5/10 to 100, starting at multiples of 2,5,10 b) count backward by 10 from 100 c) recognize even/odd numbers 2.2 The student will a) ID ordinal positions w/numbers 1st ‐ 20th b) write ordinal numbers
VDOE Vocabulary Word Wall Cards
digit place value number numeral standard form expanded form place value rounding estimation greater than less than equal to compare ones tens hundreds thousands ten thousands hundred thousands
LCPS MATH Unit Summary Grade 3 2016-2017
Achievement Criteria How to Assess Achievement
“The content of the mathematics standards is intended to support the following five process goals for students:
• becoming mathematical problem solvers • communicating mathematically • reasoning mathematically • making mathematical connections and • using mathematical representations to model and
interpret practical situations.” -2009 Mathematics Standards of Learning
Click here for a brief audio PowerPoint slide with more information about the Process Goals
Pre and Post Unit Assessments for each standard
can be found in PowerSchool Assessment (formerly Interactive Achievement)
Sample Math Tasks are available in VISION:
Search: LCPS-Math: K-12 Math Tasks Enrollment key: MATH
NCSM Great Tasks
(available in all LCPS Elementary Schools—click link)
Differentiation Resources
Use place value mats to reinforce the concept of place values. Use base-10 blocks to model place values.
Have students demonstrate understanding of place value by changing numbers from standard form into expanded form, and from expanded form into standard form.
Use a number line graphic organizer.
Use color coding and/or underlining to identify the place value position to be rounded.
Use colored markers to emphasize numbers when writing on a number line.
Have students create a human number line to demonstrate how to round a number.
Have students create a set of number cards with various place values underlined, indicating that the number is to be rounded to this place. Then, have students create a second set of number cards that are the rounded numbers matching the first set of cards. Have students play a matching game with the cards.
Have students underline specific place value to look at when determining whether a number is greater than, less than, or equal to another number (e.g., 2,567 > 2,308)
Have students formulate their own “greater than,” “less than,” and “equal to” statements about the location of specific places on a map, using symbols and terms.
Intervention Ideas (available in all LCPS Elementary Schools—click link)
ELL Model Performance Indicators (click to link)
Investigations: Mathematical Thinking at Grade 3 Investigation 1: What is a Hundred? Session1: How Much is 100? Session 2 and 3: Working with 100 Landmarks in the Hundreds Investigation 3: Constructing a 1000 Chart ESS lessons: 3.1a Place Value 3.1 b Rounding Whole Numbers 3.1 c Comparing Numbers Learn Zillion: 3.1a Understand the Value of a Digit in a Multi-Digit Number 3.1b Round to the Nearest Ten Using a Number line 3.1b Round to the Nearest Ten Using Base Ten Blocks 3.1b Round to the Nearest Ten or Hundred Using Real World Situations Brain POP 3.1b Rounding Math Literature Connections (click link) Additional resources (including FLIPCHARTS based on VDOE ESS lessons) may be found on the Elementary Math Resources VISION site: http://loudounvision.net/ Search: Math—Elementary Resources Enrollment key: MATH (all caps)
LCPS MATH Unit Summary Grade 3 2016-2017
Unit: 3 Quarter 1
Computation with Whole Numbers (add/subtract)
VDOE Standards of Learning:
3.2 The student will recognize and use the inverse relationships between addition/subtraction and multiplication/division to complete basic fact sentences. The student will use these relationships to solve problems.
3.4 The student will estimate solutions to and solve single-step and multistep problems involving the sum or difference of two whole numbers, each 9,999 or less, with or without regrouping.
3.20 The student will a) investigate the identity and the commutative properties for addition and
multiplication; and b) identify examples of the identity and commutative properties for
addition and multiplication.
VDOE Process Goals: Problem Solving, Communication, Connections, Reasoning, Representations
Learning Targets:
I can use inverse relationships between addition/subtraction and multiplication/division to complete basic fact sentences and solve problems.
I can estimate answers and solve problems involving one or more steps in which I will need to add and/or subtract numbers that are 9,999 or less.
I can investigate the identity and commutative properties for addition and multiplication and identify examples of the properties.
Big Ideas Essential Questions
Understand, model, and explain how addition and subtraction are related.
Equal emphasis should be placed on the structure of problems in solving single- and multi-step practical problems (ie: a part plus a part equals a whole in addition and a whole minus a part equals a part in subtraction).
Recognize that estimation skills are valuable, time-saving tools particularly in practical situations when exact answers are not required or needed and determining the reasonableness of the sum or difference.
Develop and use strategies to estimate whole number sums and differences, while utilizing flexible methods of combining numbers, to determine the reasonableness of an exact answer.
Know that mathematical relationships can be expressed using number sentences. Represent the equals sign as “the same as” by varying the location of the equals sign in number sentences. (ie: 50 = 25 + 25)
Investigate the identity and commutative property for addition.
Include patterns as a connection (ie: 25 + 25 = 50, 26 + 24 = 50, 27 + 23 = 50, etc.)
How do you use the inverse relationships between addition/subtraction to solve related basic fact sentences? For example, 5 + 3 = 8 and 8 – 3 = __
How do you write three related basic fact sentences when given one basic fact sentence for addition/subtraction?
(ie: Given 3+7=10, then solve the related facts: __+ 3 = 10, 10- 7= __, and 10- 3= __.
How do you determine whether an estimate or an exact answer is an appropriate solution for practical addition and subtraction problems?
How do you solve problems involving the sum of two whole numbers, with or without regrouping, paper and pencil, mental computation, or using calculators?
How do you solve problems involving the difference of two whole numbers, with or without regrouping, paper and pencil, mental computation, or using calculators,?
What is the identity property in addition when a number is added to zero? (ie: 0 + 2 = 2, 5 + 0 = 5)
What is the commutative property for addition?
How do you write number sentences to represent equivalent mathematical relationships? (e.g., 4 x 3 = 14 - 2).
LCPS MATH Unit Summary Grade 3 2016-2017
Prerequisite Skills Vocabulary
VDOE Vertical Alignment document K-3 VDOE Vertical Alignment document 3-6
2.6 The student when given two whole numbers whose sum is 99 or less will a) estimate the sum 2.7 The student when given two whole numbers each 99 or less will b) find the difference 2.8 The student will create and solve one and two‐step addition and subtraction problems with data from tables and picture or bar graphs.
VDOE Vocabulary Word Wall Cards
inverse add addend relationship subtract sum factor difference array number sentence estimate factor related facts regroup product addend property identity identity property commutative property
equal part whole
Achievement Criteria How to Assess Achievement
“The content of the mathematics standards is intended to support the following five process goals for students:
• becoming mathematical problem solvers • communicating mathematically • reasoning mathematically • making mathematical connections and • using mathematical representations to model and
interpret practical situations.” -2009 Mathematics Standards of Learning
Click here for a brief audio PowerPoint slide with more information about the Process Goals
Pre and Post Unit Assessments for each standard
can be found in PowerSchool Assessment (formerly Interactive Achievement)
Sample Math Tasks are available in VISION:
Search: LCPS-Math: K-12 Math Tasks Enrollment key: MATH
NCSM Great Tasks
(available in all LCPS Elementary Schools—click link)
Differentiation Resources
Write number sentences both horizontally and vertically so that students may use multiple strategies for computation.
Have students use grid paper to assist them in lining up columns of numbers vertically when adding and subtracting.
Allow students with designated accommodation to use calculators.
Have students create example and non-example cards for the identity property for addition. Then, have them exchange cards with partners and sort the cards into the correct columns on the Example/Non-Example mat. Have partners check for accuracy.
Intervention Ideas (available in all LCPS Elementary Schools—click link)
ELL Model Performance Indicators (click to link)
Investigations: Mathematical Thinking at Grade 3 Investigation 2: Doubles and Halves Investigation 4: Exploring Odds and Evens Combining and Comparing
Investigation 1: Comparisons with Record Numbers
Investigation 3: Adding with Money, Inches, and Time
(Also SOLs 3.8, 3.11)
Investigation 4: Working With Hundreds
ESS lessons: 3.2 Inverse Relationships (Related to SOL 3.4, 3.5) 3.4 Addition and Subtraction (Related to 3.1a)
3.20 Array for the Commutative Property for
Multiplication!
3.20 My Identity Is in My Pocket
3.20 Property Commute
LCPS MATH Unit Summary Grade 3 2016-2017
Learn Zillion: 3.2 Solve Addition Problems Using Complements of Ten 3.2 Use Addition and Subtraction Fact Families to Solve for Unknown Amounts 3.2 Identify Addition and Subtraction Patterns Using a Hundreds Chart 3.2 Find Number Patterns by Using “In” and “Out” Boxes Brain POP Jr.: Adding with Regrouping Subtracting with Regrouping BrainPOP: Commutative Property Math Literature Connections (click link) Additional resources (including FLIPCHARTS based on VDOE ESS lessons) may be found on the Elementary Math Resources VISION site: http://loudounvision.net/ Search: Math—Elementary Resources Enrollment key: MATH (all caps)
LCPS MATH Unit Summary Grade 3 2016-2017
Unit: 4 Quarter 1
Money
VDOE Standards of Learning:
3.8 The student will determine, by counting, the value of a collection of bills and coins whose total value is $5.00 or less, compare the value of the bills and coins, and make change.
VDOE Process Goals: Problem Solving, Communication, Connections, Reasoning, Representations
Learning Targets:
I can count the value of a collection of coins ($5.00 or less), compare the value of bills and coins, and use multiple strategies to make change.
Big Ideas Essential Questions
A collection of coins and bills has a value that can be counted (counting on, beginning with the highest value, and/or by grouping the coins and bills)
Determine the change after a purchase ($5.00 or less), including counting on, using coins and bills, i.e., starting with the amount to be paid (purchase price), counting forward to the next dollar, and then counting forward by dollar bills to reach the amount from which to make change; and mentally calculate the difference.
Can you demonstrate how to count the value of collections of coins and bills up to $5.00.?
How do you compare the values of two sets of coins or bills, up to $5.00, using the terms greater than, less than, and equal to?
Can you show how to make change from $5.00 or less?
Prerequisite Skills Vocabulary
VDOE Vertical Alignment document K-3 VDOE Vertical Alignment document 3-6
2.10 The student will a) count/compare collection of coins with values of $2.00 or less b) use cent/dollar symbols and decimal points
VDOE Vocabulary Word Wall Cards
money coin bill value change skip counting collection
Achievement Criteria How to Assess Achievement
“The content of the mathematics standards is intended to support the following five process goals for students:
• becoming mathematical problem solvers • communicating mathematically • reasoning mathematically • making mathematical connections and • using mathematical representations to model and
interpret practical situations.” -2009 Mathematics Standards of Learning
Click here for a brief audio PowerPoint slide with more information about the Process Goals
Pre and Post Unit Assessments for each standard
can be found in PowerSchool Assessment (formerly Interactive Achievement)
Sample Math Tasks are available in VISION:
Search: LCPS-Math: K-12 Math Tasks Enrollment key: MATH
NCSM Great Tasks
(available in all LCPS Elementary Schools—click link)
LCPS MATH Unit Summary Grade 3 2016-2017
Differentiation Resources
Allow students to use calculators.
Allow students to use grid paper to line up numbers vertically when showing their work.
Have students work with larger amounts when making change.
Discuss which human resources need to know how to calculate money and make change. List types of capital and natural resources they may choose to spend their money on.
Use Coin Box on the Illuminations website to count, collect, exchange, and make change with virtual coins.
Intervention Ideas (available in all LCPS Elementary Schools—click link)
ELL Model Performance Indicators (click to link)
Investigations: Landmarks in the Hundreds Investigation 2: Using Landmarks to Solve Problems Session 4: Solving Problems with Money
Things That Come in Groups: Investigation 5: Problems with Larger Numbers Session 1: Calculate Savings ESS lessons: 3.8 Money Counts BrainPOP Jr.: Counting Coins Dollars and Cents Equivalent Coins Math Literature Connections (click link) Additional resources (including FLIPCHARTS based on VDOE ESS lessons) may be found on the Elementary Math Resources VISION site: http://loudounvision.net/ Search: Math—Elementary Resources Enrollment key: MATH (all caps)
LCPS MATH Unit Summary Grade 3 2016-2017
Unit: 5 Quarter 2
Computation with Whole Numbers (multiply/divide)
VDOE Standards of Learning:
3.5 The student will recall multiplication facts through the twelves table, and the corresponding division facts.
3.6 The student will represent multiplication and division, using area, set, and number line models, and create and solve problems that involve multiplication of two whole numbers, one factor 99 or less and the second factor 5 or less.
3.19 The student will recognize and describe a variety of patterns formed using numbers, tables, and pictures, and extend the patterns, using the same or different forms.
3.20 The student will a) investigate the identity and the commutative properties for addition and
multiplication; and b) identify examples of the identity and commutative properties for
addition and multiplication.
VDOE Process Goals: Problem Solving, Communication, Connections, Reasoning, Representations
Learning Targets:
I can understand models and patterns of multiplication in order to recall multiplication facts and relate them to division facts.
I can create and use models (area, set, and number lines) of multiplication to create and solve multiplication problems (one factor 99 or less and the second factor 5 or less).
I can investigate the identity and commutative properties for addition and multiplication and identify examples of the properties.
Big Ideas Essential Questions
Understand and explain how multiplication and division are related.
Recognize that estimation skills are valuable, time-saving tools particularly in practical situations when exact answers are not required or needed. They are also valuable in determining the reasonableness of the product or quotient.
Investigate the identity and commutative property for multiplication.
Know that mathematical relationships can be expressed using number sentences. Represent the equals sign as “the same as” and not a symbol that gives an answer by varying the location of the equals sign in number sentences. (ie: 50 = 25 + 25)
Numerical patterns can be incorporated into the unit through skip counting on a number line, skip counting on a hundred chart, etc.
Partial products and partial quotients are strategies that allow for students to engage in number sense while using computation.
(ie: 57 x 8 = (50 x 8) + (7 x 8) = 400 + 56 = 456)
How do you use the inverse relationships between multiplication/division to solve related basic fact sentences?
How do you write three related basic fact sentences when given one basic fact sentence for multiplication/division?
How do you determine whether an estimate or an exact answer is an appropriate solution for practical multiplication and division problems?
How do you solve problems involving the product of two whole numbers, with or without regrouping, using calculators, paper and pencil, or mental computation?
How do you solve problems involving the quotient of two whole numbers, with or without regrouping, using calculators, paper and pencil, or mental computation?
What is the identity property in multiplication?
What is the commutative property?
How do you write number sentences to represent equivalent mathematical relationships? (e.g., 4 x 3 = 14 - 2).
LCPS MATH Unit Summary Grade 3 2016-2017
Prerequisite Skills Vocabulary
VDOE Vertical Alignment document K-3 VDOE Vertical Alignment document 3-6
2.5 The student will recall addition and subtraction facts w/sums to 20 or less 2.9 The student will recognize and describe related facts and inverse relationship between addition and subtraction
VDOE Vocabulary Word Wall Cards numeral factor fact family area number sentence linear array set multiply skip counting product quotient divide dividend equal divisor quotient commutative property identity property
Achievement Criteria How to Assess Achievement
“The content of the mathematics standards is intended to support the following five process goals for students:
• becoming mathematical problem solvers • communicating mathematically • reasoning mathematically • making mathematical connections and • using mathematical representations to model and
interpret practical situations.” -2009 Mathematics Standards of Learning
Click here for a brief audio PowerPoint slide with more information about the Process Goals
Pre and Post Unit Assessments for each standard
can be found in PowerSchool Assessment (formerly Interactive Achievement)
Sample Math Tasks are available in VISION:
Search: LCPS-Math: K-12 Math Tasks Enrollment key: MATH
NCSM Great Tasks
(available in all LCPS Elementary Schools—click link)
Differentiation Resources
Provide multiplication charts, calculators, and additional math aids for students with memory difficulties.
Supply scrap paper/grid paper for students to draw arrays.
Include multistep problems for students (ie: 2 × 3 × 4 or 3 × 6 + 2).
Distribute sheets of grid paper. Brainstorm with students how they could use the grid paper to model the commutative property for multiplication. Ask students what the product of 3 × 5 is. Then, have students shade a 3 × 5 area of blocks on the grid paper and cut out the shaded area. Next, ask students what the product of 5 × 3 is, and have students shade a 5 × 3 area of blocks and cut out the shaded area. Have students compare their two cutouts by placing one on top of the other, and identify that the two cutouts are congruent. Ask why the two shapes are congruent. Write the 3 × 5 = 5 × 3 on the board, and ask students whether they agree or disagree with
Investigations: Things that Come in Groups Landmarks in the Hundreds
Investigation 2: Using Landmarks to Solve Problems
Sessions 5, 6: Real – World Multiplying and Dividing
ESS lessons: 3.5 Multiplication and Division 3.6 Multiplication and Division Representations
3.20 Array for the Commutative Property for
Multiplication!
3.20 My Identity Is in My Pocket
3.20 Property Commute
Learn Zillion: 3.5 Understanding Multiplication and Division Relationships 3.5 Understand Multiplication Using Equal Groups 3.5 Solve Multiplication Using Arrays 3.5 Division Using a Number Line
LCPS MATH Unit Summary Grade 3 2016-2017
what you just wrote. Have them justify their reasoning. Ask students how the congruence of the two cutouts demonstrates the commutative property for multiplication. The students’ justification must include the fact that the order of the factors does not change the product. Give students an opportunity to work in groups to come up with other examples for the commutative property for multiplication, using the grid paper. (Note: Students could use the “equation mat” to place the grids on the mat and the Commutative Property Model recording sheet to record their examples. (ESS lessons)
Have students create example and non-example cards for the identity property of multiplication. Then, have them exchange cards with partners and sort the cards into the correct columns on the Example/Non-Example mat. Have partners check for accuracy.
Quotient Café activity on the Illuminations site.
Intervention Ideas (available in all LCPS Elementary Schools—click link)
ELL Model Performance Indicators
(click to link)
3.5 Solve Division by Drawing Pictures 3.5 Solve Division by Subtracting Equal Groups 3.5 Solve Multiplication and Division Problems Using a Diagram 3.5 Find Number Patterns by Using “In” and “Out” Boxes to 3.5 Solve Multiplication and Division 3.6 Understand Multiplication Problems Representing as
Areas
3.6 Find a Missing Quotient in a Division Problem BrainPOP Jr.: Multiply by 0 and 1 Arrays Making Equal Groups Repeated Addition Repeated Subtraction Dividing with Remainders BrainPOP: Multiplication Division Commutative Property Math Literature Connections (click link) Additional resources (including FLIPCHARTS based on VDOE ESS lessons) may be found on the Elementary Math Resources VISION site: http://loudounvision.net/ Search: Math—Elementary Resources Enrollment key: MATH (all caps)
LCPS MATH Unit Summary Grade 3 2016-2017
Unit: 6 Quarter 2
Patterns and Data
VDOE Standards of Learning:
3.17 The student will a) collect and organize data, using observations, measurements, surveys, or
experiments; b) construct a line plot, a picture graph, or a bar graph to represent the
data; and c) read and interpret the data represented in line plots, bar graphs, and
picture graphs and write a sentence analyzing the data.
3.19 The student will recognize and describe a variety of patterns formed using numbers, tables, and pictures, and extend the patterns, using the same or different forms. *see Big Ideas
VDOE Process Goals: Problem Solving, Communication, Connections, Reasoning, Representations
Learning Targets:
I will collect data, and represent the data in graphs to write a sentence explaining the results.
I can recognize, describe, and extend numeric and geometric patterns (repeating or growing) using concrete objects, numbers, tables, and pictures and identify mathematical relationships that exist within patterns.
Big Ideas Essential Questions
Develop methods of collecting, organizing, describing, displaying, and interpreting data to answer questions they have posed about themselves and their world.
Make connections between data represented in different ways (ie: how data in a bar graph compares and contrasts to the same data in a line plot).
Numerical patterns can be tied into this graphing unit by skip counting by various increments on the scale of the graph and/or by using the key of a picture graph (ie: a symbol stands for 2 votes—if there are 5 symbols in the graph, you would count 2, 4, 6, 8, 10).
How do you explain strategies that can be used to collect, organize, and represent data?
How does the type of data and the questions to be answered influence the choice of graph?
Can you compare and contrast the key elements needed when constructing line plots and graphs?
How do you collect, organize, display, and interpret data to provide different kinds of information?
Can you explain how you know which interpretation of a graph is correct and the remaining interpretations are incorrect?
Prerequisite Skills Vocabulary
VDOE Vertical Alignment document K-3 VDOE Vertical Alignment document 3-6
2.17 The student will construct picture, pictograph, and bar graphs 2.20 The student will identify, create, and extend patterns
VDOE Vocabulary Word Wall Cards data pattern title categories table line plot survey rule labels poll growing bar graph repeating data points extending increments numeric pattern picture graph geometric pattern scale multiples horizontal axis function vertical axis key
LCPS MATH Unit Summary Grade 3 2016-2017
Achievement Criteria How to Assess Achievement
“The content of the mathematics standards is intended to support the following five process goals for students:
• becoming mathematical problem solvers • communicating mathematically • reasoning mathematically • making mathematical connections and • using mathematical representations to model and
interpret practical situations.” -2009 Mathematics Standards of Learning
Click here for a brief audio PowerPoint slide with more information about the Process Goals
Pre and Post Unit Assessments for each standard
can be found in PowerSchool Assessment (formerly Interactive Achievement)
Sample Math Tasks are available in VISION:
Search: LCPS-Math: K-12 Math Tasks Enrollment key: MATH
NCSM Great Tasks
(available in all LCPS Elementary Schools—click link)
Differentiation Resources
Enlarge grid paper for students with visual or motor disabilities.
Have students graph the survey results on the computer.
Have students graph the survey results on graph paper.
Have students create a human graph based on their favorite colors or their eye colors.
Have students respond to survey questions, using tactile methods, such as wooden sticks on paper cups.
Have students develop three to five questions to use in interviewing each other, and have them graph the results.
Have students put the vocabulary words into a math glossary that includes the word, a picture, and the definition.
Display graphs around the classroom, and have students keep their individual graphs in binders or folders.
Have students develop pattern sequences on the board, using plastic magnetic numbers.
Have students use calculators to skip count and find new patterns to share with classmates.
Provide each student with a personal hundred chart marked with color-coded patterns to keep in their notebooks (e.g., 2, 4, 6, 8… in red, 1, 3, 5, 7… in blue).
Intervention Ideas
(available in all LCPS Elementary Schools—click link)
ELL Model Performance Indicators (click to link)
Investigations: Mathematical Thinking in Grade 3 Investigation 3: “Data and Handfuls”, Sessions 1,2: Collecting and Representing Data Sessions 3,4: Handfuls of Cubes and Other Objects Things That Come in Groups Investigation 5: Problems with Larger Numbers Session 2: Many, Many Legs Session 3: Data Tables and Line Plots ESS lessons: 3.17 Data Mania 3.17 Statistics Through the Year 3.19 Patterns in a Staircase 3.19 Patterns on the Hundreds Chart 3.19 Exploring Multiples 3.19 The Ins and Outs of Patterns 3.19 Tunneling Through Patterns Learn Zillion: 3.19 Identify Addition and Subtraction Patterns Using a Hundreds Chart 3.19 Find Number Patterns by Using “In” and “Out” Boxes to Solve Addition and Subtraction 3.19 Find Number Patterns by Using “In” and “Out” Boxes to Solve Multiplication and Division BrainPOP Jr.: 3.17 Tally Charts and Bar Graphs 3.17 Line Graphs 3.17 Picture Graphs BrainPOP: Math Literature Connections (click link) 3.17 Graphs 3.19 Problem Solving Using Tables Additional resources (including FLIPCHARTS based on VDOE ESS lessons) may be found on the Elementary Math Resources VISION site: http://loudounvision.net/ Search: Math—Elementary Resources Enrollment key: MATH (all caps)
LCPS MATH Unit Summary Grade 3 2016-2017
Unit: 7 Quarter 2
Geometry
VDOE Standards of Learning:
3.14 The student will identify, describe, compare and contrast characteristics of plane and solid geometric figures (circle, square, rectangle, triangle, cube, rectangular prism, square pyramid, sphere, cone, and cylinder) by identifying relevant characteristics including the number of angles, vertices, and edges, and the number and shape of faces, using concrete models.
3.15 The student will identify and draw representations of points, line segments, rays, angles, and lines.
3.16 The student will identify and describe congruent and noncongruent plane figures.
VDOE Process Goals: Problem Solving, Communication, Connections, Reasoning, Representations
Learning Targets:
I can identify, describe, compare and contrast characteristics of plane and solid geometric figures.
I can identify and draw representations of points, line segments, rays, angles, and lines and name them as mathematicians do.
I can will identify and describe congruent and noncongruent plane figures and justify the identification.
Big Ideas Essential Questions
Identify and describe plane and solid geometric figures by using relevant characteristics.
Recognize the similarities and differences between plane and solid figures, and compare the figures to objects in everyday life.
Line segments and angles are components of plane polygons.
Recognize that congruent plane figures remain congruent even if they are in different spatial orientations, while noncongruent plane figures remain noncongruent even if they are in different spatial orientations.
Can you identify models and pictures of plane geometric figures (circle, square, rectangle, and triangle) and solid geometric figures (cube, rectangular prism, square pyramid, sphere, cone, and cylinder) by name?
How can you identify, describe, compare, and contrast plane geometric figures by counting the number of sides and angles?
How do you identify, describe, compare, and contrast solid geometric figures by counting the number of angles, vertices, edges, and by the number and shape of faces?
Can you identify characteristics of solid geometric figures (cylinder, cone, cube, square pyramid, and rectangular prism)?
How do you identify examples of points, line segments, rays, angles, and lines?
How do you draw representations of points, line segments, rays, angles, and lines, using a ruler or straightedge?
When identifying examples of congruent and noncongruent figures, how do you verify their congruence by laying one on top of the other using drawings or models?
Can you determine and explain why plane figures are congruent or noncongruent, using tracing procedures?
LCPS MATH Unit Summary Grade 3 2016-2017
Prerequisite Skills Vocabulary
VDOE Vertical Alignment document K-3 VDOE Vertical Alignment document 3-6
2.16 The student will identify, describe, compare, and contrast plane and solid figures. 2.15 The student will a) draw line of symmetry in a figure b) identify and create figures with one line of symmetry.
VDOE Vocabulary Word Wall Cards square point plane rectangle line figures triangle line segment circles circle ray squares right angle angle rectangles opposite endpoint triangles sphere vertex polygon cube vertices sides rectangular prism angles angle size vertices shape edges congruent faces non-congruent solid geometric figure congruency square pyramid cone cylinder plane properties
Achievement Criteria How to Assess Achievement
“The content of the mathematics standards is intended to support the following five process goals for students:
• becoming mathematical problem solvers • communicating mathematically • reasoning mathematically • making mathematical connections and • using mathematical representations to model and
interpret practical situations.” -2009 Mathematics Standards of Learning
Click here for a brief audio PowerPoint slide with more information about the Process Goals
Pre and Post Unit Assessments for each standard
can be found in PowerSchool Assessment (formerly Interactive Achievement)
Sample Math Tasks are available in VISION:
Search: LCPS-Math: K-12 Math Tasks Enrollment key: MATH
NCSM Great Tasks
(available in all LCPS Elementary Schools—click link)
Differentiation Resources
Have student pairs or groups participate in a “real-
world” solid geometric figure scavenger hunt.
Have students record their finds in a chart with
columns in which to list the examples of the solid
geometric figures that they find.
Guide students in constructing models of the solid geometric figures, using different options for materials. One idea is to use toothpicks as the edges and gumdrops as the vertices; another possibility is drinking straws and marshmallows. Students could also create a chart that would help them calculate how many toothpicks or straws and gum drops or marshmallows they would need for each figure.
Investigations: Exploring Solids and Boxes Investigation 1: Sorting and Describing Solids Investigation 2: Building Polygons and Polyhedra Investigation 3: Making Boxes Turtle Paths Investigation 1: Paths and Lengths of Paths Investigation 2: Turns in Paths
Flips, Turns, and Area
Investigation 1: Motions with Tetrominoes
LCPS MATH Unit Summary Grade 3 2016-2017
Have students use a drawing software program to create plane geometric figures. Direct students to print them, cut them out, and label them.
Once figures are cut out and labeled, have students trace them on paper. Some students find that tracing a shape is helpful for remembering it. Have students label each traced figure.
Create poster-size geometric figures, and display them in the classroom. Use various fabrics and other materials to create a variety of tactile edges and vertices.
Have students create a notebook of geometry terms. Direct them to divide each page into two sections and to draw a geometric shape (or paste a cut-out shape) in one section and label the shape in the other. Use of color to distinguish the terms may be helpful for some students.
Have students use a Venn diagram to compare the different geometric shapes according to their properties.
Provide a set of congruent/noncongruent figures on cards and two hula hoops, one for congruent figures and the other for noncongruent figures. Have students form two teams to compete at placing the figure cards into the correct hoops.
Distribute pattern blocks, and have each student use them to create a picture or model to trade with a partner. Each student must then create an image that is congruent with the traded picture or model. Allow students to trace the outlines of the pictures or models in order to create their congruent images.
Intervention Ideas (available in all LCPS Elementary Schools—click link)
ELL Model Performance Indicators
(click to link)
ESS lessons: 3.14 What Am I? 3.14 Plane Geometry Sort 3.15 Folded Geometry 3.15 Secret Sort for Geometry 3.16 Fit to be Congruent
BrainPOP Jr.: Plane Shapes Solid Shapes Points, Line Segments, Rays Congruent and Similar Shapes BrainPOP: Geometry Circles Angles Math Literature Connections (click link) Additional resources (including FLIPCHARTS based on VDOE ESS lessons) may be found on the Elementary Math Resources VISION site: http://loudounvision.net/ Search: Math—Elementary Resources Enrollment key: MATH (all caps)
LCPS MATH Unit Summary Grade 3 2016-2017
Unit: 8 Quarter 3
Fractions, Probability, & Measurement (length)
VDOE Standards of Learning:
3.3 The student will: a) name and write fractions (including mixed numbers) represented by a
model b) model fractions (including mixed numbers) and write fractions’ names c) compare fractions having like and unlike denominators using words and
symbols (>,<, or =)
3.18 The student will investigate and describe the concept of probability as chance and list possible results of a given situation.
3.9ad The student will estimate and use U.S. Customary and metric units to measure
a) length to the nearest 12 inch, inch, foot, yard, centimeter, and meter;
b) liquid volume in cups, pints, quarts, gallons, and liters; c) weight/mass in ounces, pounds, grams, and kilograms; and d) area and perimeter.
VDOE Process Goals: Problem Solving, Communication, Connections, Reasoning, Representations
Learning Targets:
I can label and create multiple pictures / models of a given fraction. * Parameters: 1. Proper Fractions, Improper Fractions, and Mixed Numbers
2. Halves, Thirds, Fourths, Fifths, Sixths, Eighths, Tenths, and Twelfths. 3. Pictures / Models – Set, Area, Linear
I can develop and use a variety of strategies (pictures / models, benchmark numbers) to compare fractions. * Parameters: 1. Only Proper Fractions
2. Halves, Thirds, Fourths, Fifths, Sixths, Eighths, Tenths, and Twelfths. 3. Like and Unlike Denominators 4. Pictures / Models: Set, Area, Linear
I can explore the idea of probability as chance and identify possible outcomes of a situation.
I can use Customary and Metric Units to measure length, volume, weight, area, and perimeter.
Big Ideas Essential Questions
The whole must be defined. Parts of a whole can be renamed as the definition of the whole changes (ie: using pattern blocks, a trapezoid is ½ of a whole hexagon, but if the whole is defined as two hexagons, then the trapezoid is ¼ of the whole).
Fractions represent parts of wholes and students need to be flexible in how they view these numbers. Area models, set models, and linear models should all be used in addition to symbols and numerals in developing a conceptual understanding of fractions.
How do you name and write fractions (including mixed numbers) represented by a model to include halves, thirds, fourths, eighths, tenths, and twelfths?
Can you explain how you would use concrete materials and pictures to model at least halves, thirds, fourths, eighths, tenths, and twelfths?
Can you compare fractions using the terms greater than, less than, or equal to and the symbols ( >, <, and =), using models, concrete materials and pictures?
What is the definition of probability?
LCPS MATH Unit Summary Grade 3 2016-2017
There are many strategies for comparing fractions including using models (same size whole), comparing to a benchmark, comparing numerators when denominators are the same, etc.
Explain that the value of a fraction is dependent on both the number of parts in a whole (denominator) and the number of those parts being considered (numerator).
Define that a proper fraction is a fraction whose numerator is less than its denominator.
Define that an improper fraction is a fraction whose numerator is greater than or equal to the denominator, is one or greater than one, and can be expressed as a whole number or a mixed number.
A mixed number is written as a whole number and a proper fraction.
Investigate, understand, and apply basic concepts of probability. Understand that probability is the chance of an event happening and can be represented as a fraction.
Estimate and measure length (to the nearest ½ inch) using rational numbers (fractions).
Perimeter is a measure of the distance around a polygon and area is a measure of square units needed to cover a surface. Rational numbers (fractions) can be used when measuring perimeter and area.
What are all possible outcomes for a given situation? How can you represent the outcome as a fraction?
Which vocabulary word would you use to Identify the degree of likelihood of an outcome occurring? (impossible, unlikely, as likely as, equally likely, likely, and certain.)
How do you estimate and determine the U.S. Customary and metric units to measure lengths
of objects to the nearest 12 of an inch, inch, foot,
yard, centimeter, and meter?
How do you estimate and use U.S. Customary and metric units to measure area and perimeter?
How do you determine the actual measure of area or perimeter using U.S. Customary and metric units?
Prerequisite Skills Vocabulary
VDOE Vertical Alignment document K-3 VDOE Vertical Alignment document 3-6
2.3 The student will a) Identify halves, thirds, fourths, sixths, eighths, tenths b) write halves, thirds, fourths, sixths, eighths, tenths c) compare halves, thirds, fourths, sixths, eighths, tenths 2.18 The student will predict outcomes if an experiment Is repeated 2.11 The student will a) estimate and measure length to nearest centimeter and inch b) estimate and measure weight/mass c) estimate and measure liquid volume
VDOE Vocabulary Word Wall Cards
fraction outcome foot greater than event inch less than predict length equal to probability measure compare impossible yard numerator unlikely centimeter denominator equally likely meter whole number likely as likely as mixed number certain most likely least likely area square units perimeter measure part whole
LCPS MATH Unit Summary Grade 3 2016-2017
Achievement Criteria How to Assess Achievement
“The content of the mathematics standards is intended to support the following five process goals for students:
• becoming mathematical problem solvers • communicating mathematically • reasoning mathematically • making mathematical connections and • using mathematical representations to model and
interpret practical situations.” -2009 Mathematics Standards of Learning
Click here for a brief audio PowerPoint slide with more information about the Process Goals
Pre and Post Unit Assessments for each standard
can be found in PowerSchool Assessment (formerly Interactive Achievement)
Sample Math Tasks are available in VISION:
Search: LCPS-Math: K-12 Math Tasks Enrollment key: MATH
NCSM Great Tasks
(available in all LCPS Elementary Schools—click link)
Differentiation Resources
Have students use grid paper to assist them in drawing representations of fractions.
Provide blank fraction bars or fraction circles for students to use to practice modeling fractions and mixed numbers.
Use pre‐made fraction strips for students with kinesthetic difficulties.
Have students use fraction strips for adding and subtracting fractions.
Use larger counters for students with gross-motor deficits.
Use counters with indentations for students with visual deficits.
Group students in pairs, and have each student cut a piece of adding machine tape to match his/her partner’s height. Then, have each student measure his/her own tape (the one that matches his/her height) with a ruler, yardstick, or meter stick. Next, have each student calculate how many toothpicks, cubes, or popsicle sticks must be laid end-to-end to equal the length of his/her tape.
Have students make measurement estimates before giving them the measuring tools to measure the designated objects.
Investigations: Fair Shares
From Paces to Feet Investigation 1: Measuring with Paces and Steps Investigation 2: From Paces to Feet
Flips, Turns, and Area
Investigation 2: Finding Area ESS lessons: 3.3a Naming and Writing Fractions 3.3b Modeling Fractions 3.3c Comparing Fractions (Related to 3.1 a,b,c) 3.18 Is There Probability in THIRD? 3.18 Probability Boxes
3.18 Two-Color-Counter-Toss
3.9a Measuring Length 3.9d Measuring Area and Perimeter (Also use with SOL 3.10) Learn Zillion: 3.3 Recognize Fractions by Breaking Shapes Into Equal Parts 3.3 Write Fractions with a Numerator Other Than 1 3.3 Write Fractions with a Numerator and a Denominator 3.3 Write Fractions Using Shapes 3.3 Write Fractions of a Set (1) 3.3 Write Fractions of a Set (2) 3.3 Identify a Fraction as a Point on a Number Line Using 3.3 Area Models 3.3 Identify Equivalent Fractions Using Models 3.3 Identify Equivalent Fractions Using a Number Line
LCPS MATH Unit Summary Grade 3 2016-2017
Give students a list of measurements, and have them locate objects in the classroom that have those exact measurements.
Have students measure distances on maps, and use the map scale to determine the actual distances between various pairs of places.
Use larger grid paper to assist students with fine motor issues.
Use appropriate graphic organizers helpful to particular groups of learners.
Intervention Ideas (available in all LCPS Elementary Schools—click link)
ELL Model Performance Indicators
(click to link)
3.3 Identify Equivalent Fractions Using Fraction Strips 3.3 Generate Equivalent Fractions Using Fraction Models 3.3 Express Fractions Equivalent to 1 Using Fractions Strips 3.3 Understand Fractions: Create Mini Stories 3.3 Place Fractions on a Number Line 3.3 Count Fractions to Make 1 Whole 3.3 Compare Fractions with the Same Denominator by Reasoning About Their Size 3.3 Express Whole Numbers as Fractions 3.9d Find the Area of a Shape Using Square Units 3.9d Cover Area of a Shape Using Square Units 3.9d Use Grid Paper to Find the Area 3.9d Find the Perimeter 3.9d Find the Perimeter with Missing Sides BrainPOP Jr.: Basic Parts of a Whole More Fractions Equivalent Fractions Mixed Fractions Measurement: Inches and Feet Measurement: Centimeters, Meters, Kilometers Area Perimeter Basic Probability Probability Combinations BrainPOP: Fractions Customary Units Metric Units Metric Vs. Customary Basic Probability Math Literature Connections (click link) Additional resources (including FLIPCHARTS based on VDOE ESS lessons) may be found on the Elementary Math Resources VISION site: http://loudounvision.net/ Search: Math—Elementary Resources Enrollment key: MATH (all caps)
LCPS MATH Unit Summary Grade 3 2016-2017
Unit: 9 Quarter 3
Computation with Fractions
VDOE Standards of Learning:
3.7 The student will add and subtract proper fractions having like denominators of 12 or less.
VDOE Process Goals: Problem Solving, Communication, Connections, Reasoning, Representations
Learning Targets:
I can use pictures / models to add and subtract fractions. * Parameters: 1. Only Proper Fractions 2. Halves, Thirds, Fourths, Fifths, Sixths, Eighths, Tenths, and Twelfths. 3. Only Like Denominators 4. Pictures / Models: Set, Area, Linear
Big Ideas Essential Questions
The whole must be defined. Parts of a whole can be renamed as the definition of the whole changes (ie: using pattern blocks, a trapezoid is ½ of a whole hexagon, but if the whole is defined as two hexagons, then the trapezoid is ¼ of the whole).
A proper fraction is a fraction whose numerator is smaller than its denominator.
An improper fraction is a fraction whose numerator is greater than or equal to the denominator and is one or greater than one.
An improper fraction can be expressed as a whole number or a mixed number.
A mixed number is written as a whole number and a proper fraction. A mixed number is the sum of a whole number and the proper fraction.
Computation with fractions can be compared and contrasted with whole number computation.
How can you model fraction operations using…
region/area models (e.g., pie pieces, pattern blocks, geoboards, drawings);
set models (e.g., chips, counters, cubes, drawings); and
length/measurement models (e.g., nonstandard units such as rods, connecting cubes, and drawings)?
How do you add and subtract with proper fractions having like denominators of 12 or less, using concrete materials and pictorial models representing area/regions (circles, squares, and rectangles), length/measurements (fraction bars and strips), and sets (counters)?
Prerequisite Skills Vocabulary
VDOE Vertical Alignment document K-3 VDOE Vertical Alignment document 3-6
2.6 The student, when given two whole numbers whose sum is 99 or less, will find the sum.
VDOE Vocabulary Word Wall Cards
fraction whole number
proper fraction numerator
improper fraction denominator
sum difference
part whole
LCPS MATH Unit Summary Grade 3 2016-2017
Achievement Criteria How to Assess Achievement
“The content of the mathematics standards is intended to support the following five process goals for students:
• becoming mathematical problem solvers • communicating mathematically • reasoning mathematically • making mathematical connections and • using mathematical representations to model and
interpret practical situations.” -2009 Mathematics Standards of Learning
Click here for a brief audio PowerPoint slide with more information about the Process Goals
Pre and Post Unit Assessments for each standard
can be found in PowerSchool Assessment (formerly Interactive Achievement)
Sample Math Tasks are available in VISION:
Search: LCPS-Math: K-12 Math Tasks Enrollment key: MATH
NCSM Great Tasks
(available in all LCPS Elementary Schools—click link)
Differentiation Resources
Have students use fraction strips and fraction circles to solve word problems.
Have students complete Exit Cards to check for understanding.
Have students use grid paper to assist them in drawing representations of fractions.
Provide blank fraction bars or fraction circles for students to use to practice modeling fractions and mixed numbers.
Intervention Ideas (available in all LCPS Elementary Schools—click link)
ELL Model Performance Indicators (click to link)
Investigations: Fair Shares
Investigation 1: Sharing Brownies
Session 4: The Fraction Cookie Game
Sessions 5, 6: Backward Sharing
ESS lessons: 3.7 Adding and Subtracting Fractions
Learn Zillion: 3.7 Add and Subtract Fractions with Like Denominators 3.7 Solve Fraction Word Problems Using Key Words and Pictures BrainPOP: Adding and Subtracting Fractions Math Literature Connections (click link) Additional resources (including FLIPCHARTS based on VDOE ESS lessons) may be found on the Elementary Math Resources VISION site: http://loudounvision.net/ Search: Math—Elementary Resources Enrollment key: MATH (all caps)
LCPS MATH Unit Summary Grade 3 2016-2017
Unit: 10 Quarter 3
Elapsed Time & Temperature
VDOE Standards of Learning:
3.11 The student will a) tell time to the nearest minute, using analog and digital clocks; and b) determine elapsed time in one-hour increments over a 12-hour period.
3.12 The student will identify equivalent periods of time, including relationships among days, months, and years, as well as minutes and hours.
3.13 The student will read temperature to the nearest degree from a Celsius thermometer and a Fahrenheit thermometer. Real thermometers and physical models of thermometers will be used.
VDOE Process Goals: Problem Solving, Communication, Connections, Reasoning, Representations
Learning Targets:
I can tell time to the nearest minute using different clock models.
I can tell time to the nearest minute and how many hours have passed (using a clock) when given a scenario involving the passing of time
I can read and write temperatures to the nearest degree using Celsius and Fahrenheit thermometers and pictorial models.
Big Ideas Essential Questions
Skip counting and computation strategies can be used to calculate elapsed time.
Identifying equivalent periods of time can be integrated into classroom routines and practical problems in other units.
Patterns can be observed when reading temperature from a thermometer (often increments of 10’s or 2’s).
Can you compare and contrast analog and digital clocks?
Can you explain and justify how to determine time on an analog clock?
Can you explain and justify how to determine elapsed time?
How is a calendar organized to measure time?
Can you describe the relationships that exist among periods of time within a calendar year?
When and why do we have a leap year?
How can you use patterns to help read temperature on a thermometer?
Prerequisite Skills Vocabulary
VDOE Vertical Alignment document K-3 VDOE Vertical Alignment document 3-6
2.12 tell and write time to nearest 5 min 2.13 a) determine past/future days of the week; b) ID days/dates on calendar 2.14 read temperature on thermometer in C or F to nearest 10 degrees
VDOE Vocabulary Word Wall Cards
analog clock one-half hour digital clock calendar hours months of the year minutes days of the week seconds quarter hour hour hand minute hand a.m. p.m. temperature thermometer degrees scale/increments Fahrenheit Celsius
LCPS MATH Unit Summary Grade 3 2016-2017
Achievement Criteria How to Assess Achievement
“The content of the mathematics standards is intended to support the following five process goals for students:
• becoming mathematical problem solvers • communicating mathematically • reasoning mathematically • making mathematical connections and • using mathematical representations to model and
interpret practical situations.” -2009 Mathematics Standards of Learning
Click here for a brief audio PowerPoint slide with more information about the Process Goals
Pre and Post Unit Assessments for each standard
can be found in PowerSchool Assessment (formerly Interactive Achievement)
Sample Math Tasks are available in VISION:
Search: LCPS-Math: K-12 Math Tasks Enrollment key: MATH
NCSM Great Tasks
(available in all LCPS Elementary Schools—click link)
Differentiation Resources
Show students times on analog and digital clocks, and have them respond verbally or use a response board to tell the times.
Have students use manipulatives, such as plastic clocks, to set different times to become skillful at using the minute and hour hands.
Have students cut out pictures of clocks and watches from magazines and flyers, glue them in their notebooks, and write the displayed times next to them.
Model elapsed time in a variety of ways including on a number line or elapsed time ruler.
Provide a felt calendar and numbers with Velcro backs. Have students construct a calendar for a given month. Ask students to point to a particular day that has happened or will happen and relate it to a class event on that day.
Have students collect weather information for the local area from newspapers, television news, and/or the Internet. Have students practice depicting the listed temperatures on physical models of thermometers.
Have students use two different colors to indicate temperatures in Celsius and temperatures in Fahrenheit.
Have students work together in groups of two or three to create, exchange, and solve five word problems dealing with the temperature changes that they have observed during the unit.
Intervention Ideas (available in all LCPS Elementary Schools—click link)
ELL Model Performance Indicators (click to link)
Investigations: 3.11 Mathematical Thinking at Grade 3 Ten Minute Math, pages 87-90 Combining and Comparing
Investigation 5: Calendar Comparisons Session 1: How Much Longer? Sessions 2, 3: School Days ESS lessons: 3.11—It’s About Time 3.11—Where Did the Time Go? 3.11—Hoppin’ on the Elapsed Time Line 3.12—Calendar Math 3.13—Was the Groundhog Correct? Learn Zillion: 3.11 Reading the Exact Time on a Clock to the Minute 3.11 Reading the Exact Time on a Clock 3.11 Drawing Exact Time on a Clock 3.11 Elapsed Time to the Nearest Minute Brain Pop: 3.11 Time to the Minute 3.11 Elapsed Time 3.12 Calendar and Dates 3.13 Temperature Math Literature Connections (click link) Additional resources (including FLIPCHARTS based on VDOE ESS lessons) may be found on the Elementary Math Resources VISION site: http://loudounvision.net/ Search: Math—Elementary Resources Enrollment key: MATH (all caps)
LCPS MATH Unit Summary Grade 3 2016-2017
Unit: 11 Quarter 4
Measuring My World
VDOE Standards of Learning:
3.9 The student will estimate and use U.S. Customary and metric units to measure
a) length to the nearest 12 inch, inch, foot, yard, centimeter, and meter;
b) liquid volume in cups, pints, quarts, gallons, and liters; c) weight/mass in ounces, pounds, grams, and kilograms; and d) area and perimeter.
3.10 The student will a) measure the distance around a polygon in order to determine
perimeter; and b) count the number of square units needed to cover a given surface in
order to determine area.
VDOE Process Goals: Problem Solving, Communication, Connections, Reasoning, Representations
Learning Targets:
I can use customary and metric units to measure length, volume, weight, area, and perimeter.
I can measure the outside of a shape (perimeter) and count the number of square units on the inside of a shape (area).
Big Ideas Essential Questions
Estimate measures of length, liquid volume, weight/mass, area and perimeter.
Determine the actual measure of length, liquid volume, weight/mass, area and perimeter.
Perimeter is a measure of the distance around a polygon.
Area is a measure of square units needed to cover a surface.
While conversions within systems are not necessarily essential in 3rd grade, skip counting and patterns can be integrated into measurement through the use of a double number line:
How do you estimate and use U.S. Customary and metric units to measure lengths of objects
to the nearest 12 of an inch, inch, foot, yard,
centimeter, and meter; liquid volume to the nearest cup, pint, quart, gallon, and liter; weight/mass of objects to the nearest ounce, pound, gram, and kilogram?
How do you determine the actual measure of length using U.S. Customary and metric units to
measure objects to the nearest 12 of an inch,
foot, yard, centimeter, and meter; liquid volume units to measure to the nearest cup, pint, quart, gallon, and liter; weight/mass of objects to the nearest ounce, pound, gram, and kilogram?
How do you estimate and use U.S. Customary and metric units to measure area and perimeter.
How do you determine the actual measure of area or perimeter using U.S. Customary and metric units.
LCPS MATH Unit Summary Grade 3 2016-2017
Prerequisite Skills Vocabulary
VDOE Vertical Alignment document K-3 VDOE Vertical Alignment document 3-6
2.11 The student will a) estimate and measure length to nearest centimeter and inch b) estimate and measure weight/mass c) estimate and measure liquid volume
VDOE Vocabulary Word Wall Cards foot cup inch pint length quart measure gallon yard liter centimeter distance meter perimeter grams area kilograms square units mass ruler ounces polygon pounds weight balance scale mass estimate liquid volume
Achievement Criteria How to Assess Achievement
“The content of the mathematics standards is intended to support the following five process goals for students:
• becoming mathematical problem solvers • communicating mathematically • reasoning mathematically • making mathematical connections and • using mathematical representations to model and
interpret practical situations.” -2009 Mathematics Standards of Learning
Click here for a brief audio PowerPoint slide with more information about the Process Goals
Pre and Post Unit Assessments for each standard
can be found in PowerSchool Assessment (formerly Interactive Achievement)
Sample Math Tasks are available in VISION:
Search: LCPS-Math: K-12 Math Tasks Enrollment key: MATH
NCSM Great Tasks
(available in all LCPS Elementary Schools—click link)
Differentiation Resources
Group students in pairs, and have each student cut a piece of adding machine tape to match his/her partner’s height. Then, have each student measure his/her own tape (the one that matches his/her height) with a ruler, yardstick, or meter stick. Next, have each student calculate how many toothpicks, cubes, or popsicle sticks must be laid end-to-end to equal the length of his/her tape.
Have students make measurement estimates before giving them the measuring tools to measure the designated objects.
Provide students with a generic, non-detailed drawing of a person to measure to the nearest one-half inch, and record the measurements on the recording sheet.
Give students a list of measurements, and have them locate objects in the classroom that have those exact measurements.
Investigations: From Paces to Feet Investigation 3: Measuring Project: Do Our Chairs Fit Us? Investigation 4: Measuring Balobbyland
Combining and Comparing Investigation 2: How Much Heavier or Lighter? Session 1: Weighing Fruits and Vegetables Session 2: Comparing the Weights ESS lessons: 3.9a Measuring Length 3.9b Measuring Liquid Volume 3.9c Measuring Weight/Mass 3.9d Measuring Area and Perimeter (Also use with SOL 3.10) 3.10a Determining Perimeter
3.10b Measuring Surface Area
LCPS MATH Unit Summary Grade 3 2016-2017
Have students measure distances on maps, and use the map scale to determine the actual distances between various pairs of places.
Use larger grid paper to assist students with fine motor issues.
Have high-ability students draw shapes that correspond to given areas or perimeters.
Discuss how area and perimeter are used in sports
Use appropriate graphic organizers helpful to particular groups of learners.
Use grid paper instead of construction paper for polygon cutouts.
Have students connect the linking cubes instead of just placing them on the polygon to make it easier to keep the cubes inside the shape.
Have students look through magazines, newspapers, and books to find examples of surfaces measured using square units.
Provide students with cloth measuring tapes to use for wrapping instead of string.
Provide students with string cut to the exact length of the perimeter of each polygon.
Provide students with a variety of rulers to use.
Display two or three large United States maps of different scales. Group students into small groups of three or four, and assign each group a state. (Note: The more regularly shaped states will work best.) Have each group use string to measure the perimeter of the assigned state on each map. Then, have students in each group compare their various perimeter measurements of the same state, discussing why they are so different. Use their findings to lead into a class discussion of map scale—how it plays a vital role in map design and why it is important to pay close attention to the scale of a map.
Intervention Ideas (available in all LCPS Elementary Schools—click link)
ELL Model Performance Indicators
(click to link)
Learn Zillion: 3.9b Understanding Volume & How Volume is Measured 3.9b Estimate Volume in Liters 3.9b Measure Volume in Liters 3.9c Understand Mass & How Mass is Measured 3.9c Estimate Mass in Grams 3.9c Measure Mass in Grams 3.9c Estimate Mass in Kilograms 3.9c Measure Mass in Kilograms 3.9d, 3.10 Find the Area of a Shape Using Square Units 3.9d, 3.10 Cover Area of a Shape Using Square Units 3.9d, 3.10 Use Grid Paper to Find the Area 3.9d, 3.10 Find Area Using Multiplication 3.9d, 3.10 Find the Perimeter 3.9d, 3.10 Find the Perimeter with Missing Sides BrainPOP Jr.: Measurement: Inches and Feet Measurement: Centimeters, Meters, Kilometers Measurement: Ounces, Pounds, Tons Measurement: Grams, Kilograms Measurement: Cups, Pints, Quarts, Gallons Area Perimeter BrainPOP: Customary Units Metric Units Metric Vs. Customary Math Literature Connections (click link) Additional resources (including FLIPCHARTS based on VDOE ESS lessons) may be found on the Elementary Math Resources VISION site: http://loudounvision.net/ Search: Math—Elementary Resources Enrollment key: MATH (all caps)
The First 20 Days Classroom Routines: Establishing a Mathematics Classroom Community
Overview: The mini lessons included in this guide are intended to be used in conjunction with your first unit of study. The daily 10-15 minute lessons will help
you set routines, develop references for students, establish protocols, and create norms for an engaging math classroom community. The lessons may be
modified or extended based on students’ need or grade level. The routines, protocols, and experiences should be revisited throughout the school year in order
to maintain a productive math community.
Goals:
Build a classroom community of learners
Support students’ understanding of math content by establishing guidelines related to the VA process goals (problem solving, communication,
reasoning, connections, and representation).
Develop routines that will help students become reflective problem solvers and engage in a rigorous study of mathematics.
Background: This guide is based on a document developed by Austin Independent School District. Their document was modeled after the First 20 Days of Independent Reading by Fountas & Pinnell. Many of the suggested routines will also connect to other effective protocols used in Being a Writer and Responsive Classroom. This guide was adapted from a resource created by Arlington Public Schools.
Mini Lesson Key Ideas Essential Understandings
Anchor Charts/Supports Resources Teacher Notes
Day 1 Management: Classroom Procedures/ Community Guidelines
Establish routines, procedures, and student expectations for daily math lessons.
Students develop criteria for a “Being a Mathematician” chart that will be posted in the classroom. Students understand that the information posted in the classroom will be a valuable reference for them.
Develop a “Being a Mathematician” anchor chart to which students can refer. The chart should have less than 6 criteria to be effective and manageable. Example behaviors:
• Remain on task • Participate/stay engaged • Listen actively • Discuss math ideas • Treat materials with respect • Always try your best
*Brainstorm the list with the students
Chart paper, Markers Have a discussion about routines and procedures with the students. This is a good time to have students talk about expectations for engaging in classroom discussions and completing their work.
Day 2 Management: Mathematical Tools VA Process Goals: Problem Solving & Representation
Mathematicians can utilize math tools to help them solve problems.
Tools are a valuable resource for mathematicians. Students are aware of the tools that are available in the classroom.
Brainstorm a list of mathematical tools and discuss how they can be used and stored. Add additional information to the “Being a Mathematician” chart about placing materials in their proper storage containers and location after use. Examples: Base ten blocks Cubes Number cubes Hundreds chart Two-colored counters
Emphasize how and why materials are to be used during math instruction.
Mini Lesson Key Ideas Essential Understandings
Anchor Charts/Supports Resources Teacher Notes
Day 3 Math Talk/ Classroom Discourse VA Process Goal: Communication
Mathematicians communicate orally about their work. Norms for classroom discussions need to be established in order to engage in respectful discourse and have equitable participation.
In order to communicate and learn from each other, mathematicians must listen to, as well as speak, with their classmates. We will function as a respectful classroom community in order to learn.
Create an anchor chart for “Norms for a Math Discussion” or “Rights and Obligations During Discussions” Example norms include: Speak respectfully Take turns (equitable participation) Give others time to think Eyes on the speaker
Norms may be similar to those you establish in other content areas. These established routines should be revisited all year long.
Day 4 Math Talk/ Classroom Discourse VA Process Goal: Communication
Mathematicians communicate orally about their work. Different talk moves can be used while facilitating classroom discussions. Students learn content through the process goal of communication.
Math can be more rigorous when you communicate with others. There are sentence starters that can be used to help one engage in discussions.
Post and discuss Talk Moves to encourage students to share their thinking. Identify 1 or 2 moves to begin the year with (based on your first units of study).
- Talk bubbles or Talk move sticks
Introduce talk moves
- Turn and Talk (also called partner talk, or think-pair-share)
- Say More: You ask an individual student to expand on what he or she said
- Revoicing (also called verify and clarify)
- Repeat - Agree/Disagree and why?
Encourage students to speak in complete thoughts when communicating orally. The utilization and introduction of talk moves is a continuous process. This day is one way to introduce moves, but it should be ongoing.
Mini Lesson Key Ideas Essential Understandings
Anchor Charts/Supports Resources Teacher Notes
Day 5 Collaboration (Game) VA Process Goal: Communication
Mathematicians can work collaboratively while playing a game in order to learn important math concepts.
Students understand that they can work with others to explore math content. Cooperation is a key component of working with a partner.
Establish rules for working with a partner while playing a math game. Try the “Say it to Play it” guideline: When playing a game in partners, the students must state their move and/or provide an explanation for why they are playing that move (Ex: In the game Compare, a student may say “9 is greater than 5, so I win the cards”).
Post rules and directions for engaging in a game with a partner. Consider utilizing a fact fluency game for this mini lesson.
Rules and clear directions will help make group work successful. After the mini lesson, have students practice a game during the math lesson for the day.
Day 6 Collaborative/ Independent Work (Rotations) VA Process Goal: Communication
Mathematicians can explore/ engage in a variety of experiences within a math period. Work may be collaborative or independent.
In order to have a variety of activities during a math block, it is important to be mindful of procedures, noise level, expectations, etc.
Review procedures for moving around the classroom to different centers Consider utilizing visual time reminders Use cues for sound control/reminders
Post clear directions at independent centers. Provide a materials checklist.
Mini Lesson Key Ideas Essential Understandings
Anchor Charts/Supports Resources Teacher Notes
Day 7 Real Life Connections to Math VA Process Goal: Connections
Mathematicians make connections between math ideas and the world around them.
Math connects to other content areas/disciplines (i.e. Science). Students relate math to the world around them.
Brainstorm a list of math concepts that relate to the real world. Consider using the following discussion prompts: Where in the world do you see numbers? When do you use math in your everyday life?
Chart paper Calendar / Daily Schedule
Consider connecting this discussion to everyday events in their life.
Day 8 Representing Thinking VA Process Goals: Representation, Communication
Mathematicians can represent ideas in multiple ways. Mathematicians use words to explain their thinking. Mathematicians can explain their thinking verbally or in writing in order to process information.
Students will become more familiar with ways they can represent math ideas. Students can show their math thinking in written words.
In order to fully communicate their understanding, mathematicians may provide written explanations of their reasoning.
Brainstorm ways that students can represent their thinking. Ex: Pictures/drawing Words Numbers Symbols Manipulative models
Utilize sentence frames: “This is a ______________. It is a ______ because it ______________. “ This example shows a picture, numbers, and a written explanation.
Encourage students to show math concepts in a variety of ways. Encourage students to write about their understanding or show their thinking using words, pictures, numbers, etc.
Mini Lesson Key Ideas Essential Understandings
Anchor Charts/Supports Resources Teacher Notes
Day 9 Recording & Reflecting in Math
VA Process Goal: Communication
Mathematicians keep a record of their daily experiences (i.e. math game).
Students will understand how to utilize a recording sheet or guide as they play a game or solve a problem. Students will record and reflect upon their work to communicate their understanding in writing.
Example of Game Recording Sheet:
Introduce a Recording Sheet as a student tool.
Day 10 Academic Language of Math VA Process Goal: Communication
Specialized language is used in math. Mathematical language can be modeled and explicitly taught.
Students will develop an understanding of specific math terminology. Conceptual understanding is developed as students use math terminology.
Post examples of key vocabulary terms with visual examples.
Math Word Wall, Word Banks, VDOE Vocabulary Cards http://www.doe.virginia.gov/instruction/mathematics/resources/vocab_cards/index.shtml The vocabulary terms introduced are then posted for class reference.
New vocabulary should be explicitly introduced and utilized within daily lessons. This is a continuous routine/ element for all units of study.
Mini Lesson Key Ideas Essential Understandings
Anchor Charts/Supports Resources Teacher Notes
Day 11 Vocabulary Development VA Process Goals: Representation, Communication, Connections
Mathematicians use a variety of strategies to build vocabulary.
Students will utilize a tool to reinforce their math vocabulary.
Select model to implement with students (i.e. Frayer).
Student math journal VDOE Math Vocabulary Cards Frayer Model
Students can utilize math journals to keep a record of math vocabulary. Their journals can also serve as a valuable resource in addition to the Word Wall or class references (see Day 10).
Day 12 Math Strategies VA Process Goals: Problem Solving, Representation, Connections
A variety of strategies can be used to solve problems and explore mathematical concepts.
Students develop a repertoire of strategies. Students see connections between different strategies used to solve problems.
Build or add to a strategy wall showing models of strategies for various skills or concepts.
Anchor charts can be developed for a wide variety of strategies depending on the grade level. Examples are shown to the left.
Mini Lesson Key Ideas Essential Understandings
Anchor Charts/Supports Resources Teacher Notes
Day 13 Connections VA Process Goals: Connections, Communication
Mathematicians make and recognize connections among mathematical ideas.
Students understand that they can make connections among math ideas. Math can be related to the world outside the classroom.
Discussion questions: How is that answer like the one you modeled yesterday? Where have you seen that before?
Consider having students glue question/ comment starters in the back of their math journal. They can refer to it during class discussions.
Day 14 Justification VA Process Goals: Reasoning, Representation
Mathematicians verify their thinking by showing it multiple ways.
Students will develop a deeper understanding of content when asked to justify their thinking.
Create an anchor chart that depicts ways that students can justify their thinking.
Justify means: explain, defend,
describe, prove, give reasons, show
you understand, validate…
Using verbal explanation first can help facilitate written justification.
Mini Lesson Key Ideas Essential Understandings
Anchor Charts/Supports Resources Teacher Notes
Day 15 Problem Solving Strategies VA Process Goals: Problem Solving, Communication
Mathematicians choose from a variety of strategies to solve problems.
Students have a resource of strategies to help them solve problems . Sample strategies: -find a pattern - estimate and check -make an organized list -draw a diagram -write an equation -work backward -solve a simpler problem -read a table/chart
Introduce problem solving strategies (a variety of strategies can be used). Explain that the different strategies can be used to help students with problem solving. Choose 1 strategy to explain/highlight for the mini lesson. You will continue to model/introduce/use the strategies throughout the year.
Students can create their own problem solving strategy icons or bookmarks as well as refer to a class anchor chart of strategies.
During classroom instruction, teachers can engage students in discourse about their problem solving strategy.
Day 16 Problem Solving Protocol VA Process Goals: Problem Solving, Communication
There are processes that can be used to help solve problems.
Students will be introduced to a problem solving protocol. Students will become familiar with the protocol steps.
Develop and post a problem solving protocol.
Post the protocol in the classroom for student reference.
Consider trying a problem as a class to model how the protocol is used. The emphasis should be on the steps, so it may be easiest to select content that is readily accessible to all learners.
Step 1: Read and quietly think on your own – release your pencils. Step 2: Talk about the problem. What is your plan to solve? Pick your strategy. Step 3: Share your strategy. Step 4: Solve the problem and communicate your thinking.
Mini Lesson Key Ideas Essential Understandings
Anchor Charts/Supports Resources Teacher Notes
Day 17 Rubric Familiarization VA Process Goals: Reasoning, Connections
There are tools mathematicians use to monitor and assess their work or behavior.
Students understand how to use a rubric to assess themselves/ their work.
Create a class rubric that is not math related. The topic should be something relevant to an everyday student activity in the classroom or school. Examples include: Lunchroom behavior Morning routine Dismissal Cubbie/desk organization
Day 18 Reflection/ Self-Monitoring VA Process Goal: Reasoning
Mathematicians modify their work as needed.
Students reflect upon and revise their work to demonstrate their full understanding.
Introduce a criteria chart and rubric for self- monitoring of work.
Sample Rubric:
Rubric & Problem Solving Protocol Create an anchor chart with “How to Self-Correct or Modify Your Work”
Help students develop a clear understanding of the criteria and how upcoming math tasks will be scored. Emphasize how this is similar to the revisions they do during the writing process.
Mini Lesson Key Ideas Essential Understandings
Anchor Charts/Supports Resources Teacher Notes
Day 19 Collaboration (Task) VA Process Goal: Communication
Mathematicians can work collaboratively on a problem solving task to learn important math concepts.
Students understand that they can work with others to solve problems and learn new information.
Review roles that pairs or small groups should follow/hold when working together on a task. Examples: Materials manager Recorder Reporter Time keeper
Develop an anchor chart with roles/procedures for group work on a task/problem. Self-assess/reflect upon collaborative work experiences. Students can use the problem solving protocol together (See Day 16).
Save time at the end of the lesson to debrief the experience. What went well? What could be improved next time they are working in a group?
Day 20
Process Goals
VA Process Goals: Problem Solving, Reasoning, Communication, Connections, & Representation
“The content of the mathematics standards is intended to support the following five process goals for students: *becoming mathematical problem solvers *communicating mathematically *reasoning mathematically *making mathematical connections and *using mathematical representations to model and interpret practical situations.”
-2009 Mathematics Standards of Learning
Student-friendly process goals poster (can be a poster for the classroom and/or a small version can be taped to desks or in math journals) Process Goals bookmark (click on picture to the left to access the file for the poster and bookmark)
Students should be engaged in process goals throughout every mathematical task and lesson throughout the year.
Mathematics Standards of Learning Curriculum Framework 2009: Grade 3
VDOE Technical Assistance Document
to be used in conjunction with the VDOE Curriculum Framework (click title above to link to document)
Virginia Mathematics Standards of Learning
Curriculum Framework 2009 Introduction
The 2009 Mathematics Standards of Learning Curriculum Framework is a companion document to the 2009 Mathematics Standards of Learning and amplifies the Mathematics Standards of Learning by defining the content knowledge, skills, and understandings that are measured by the Standards of Learning assessments. The Curriculum Framework provides additional guidance to school divisions and their teachers as they develop an instructional program appropriate for their students. It assists teachers in their lesson planning by identifying essential understandings, defining essential content knowledge, and describing the intellectual skills students need to use. This supplemental framework delineates in greater specificity the content that all teachers should teach and all students should learn. Each topic in the Mathematics Standards of Learning Curriculum Framework is developed around the Standards of Learning. The format of the Curriculum Framework facilitates teacher planning by identifying the key concepts, knowledge and skills that should be the focus of instruction for each standard. The Curriculum Framework is divided into two columns: Essential Understandings and Essential Knowledge and Skills. The purpose of each column is explained below. Essential Understandings This section delineates the key concepts, ideas and mathematical relationships that all students should grasp to demonstrate an understanding of the Standards of Learning. Essential Knowledge and Skills Each standard is expanded in the Essential Knowledge and Skills column. What each student should know and be able to do in each standard is outlined. This is not meant to be an exhaustive list nor a list that limits what is taught in the classroom. It is meant to be the key knowledge and skills that define the standard. The Curriculum Framework serves as a guide for Standards of Learning assessment development. Assessment items may not and should not be a verbatim reflection of the information presented in the Curriculum Framework. Students are expected to continue to apply knowledge and skills from Standards of Learning presented in previous grades as they build mathematical expertise.
Mathematics Standards of Learning Curriculum Framework 2009: Grade 3
3.1
The student will
a) read and write six-digit numerals and identify the place value and value of each digit;
b) round whole numbers, 9,999 or less, to the nearest ten, hundred, and thousand; and
c) compare two whole numbers between 0 and 9,999, using symbols (>, <, or = ) and words (greater than, less than, or equal to).
UNDERSTANDING THE STANDARD (Background Information for Instructor Use Only)
ESSENTIAL UNDERSTANDINGS ESSENTIAL KNOWLEDGE AND SKILLS
The structure of the Base-10 number system is
based upon a simple pattern of tens, where each
place is ten times the value of the place to its right.
This is known as a ten-to-one place value
relationship.
The structure of the Base-10 blocks is based on the
ten-to-one place value relationship (e.g., 10 units
make a long, 10 longs make a flat, 10 flats make a
cube).
Place value refers to the value of each digit and
depends upon the position of the digit in the
number. In the number 7,864, the eight is in the
hundreds place, and the value of the 8 is eight
hundred.
Flexibility in thinking about numbers — or
“decomposition” of numbers (e.g., 12,345 is 123
hundreds, 4 tens, and 5 ones) — is critical and
supports understandings essential to multiplication
and division.
Whole numbers may be written in a variety of
formats:
All students should
Understand that knowledge of place value is
essential when comparing numbers.
Understand the relationships in the place value
system, where each place is ten times the value of
the place to its right.
Understand that rounding gives an estimate to use
when exact numbers are not needed for the
situation.
Understand the relative magnitude of numbers by
comparing numbers.
The student will use problem solving, mathematical
communication, mathematical reasoning,
connections, and representations to
Investigate and identify the place and value for
each digit in a six-digit numeral, using Base-10
manipulatives (e.g., Base-10 blocks).
Use the patterns in the place value system to read
and write numbers.
Read six-digit numerals orally.
Write six-digit numerals that are stated verbally or
written in words.
Round a given whole number, 9,999 or less, to the
nearest ten, hundred, and thousand.
Solve problems, using rounding of numbers, 9,999
or less, to the nearest ten, hundred, and thousand.
Determine which of two whole numbers between 0
and 9,999 is greater.
Determine which of two whole numbers between 0
and 9,999 is less.
Compare two whole numbers between 0 and 9,999,
using the symbols >, <, or =.
Use the terms greater than, less than, and equal to
when comparing two whole numbers.
Mathematics Standards of Learning Curriculum Framework 2009: Grade 3
– Standard: 123,456;
– Written: one hundred twenty-three thousand,
four hundred fifty-six; and
– Expanded: (1 100,000) + (2 10,000) + (3
1,000) + (4 100) + (5 10) + (6 1).
Numbers are arranged into groups of three places
called periods (ones, thousands, millions, and so
on). Places within the periods repeat (hundreds,
tens, ones). Commas are used to separate the
periods. Knowing the place value and period of a
number helps students find the value of a digit in
any number as well as read and write numbers.
To read a whole number through the hundred
thousands place,
– read the digits to the first comma;
– say the name of the period (e.g., “thousands”);
then
– read the last three digits, but do not say the
name of the ones period.
Reading and writing large numbers should be
related to numbers that have meanings (e.g.,
numbers found in the students’ environment).
Concrete materials, such as Base-10 blocks may be
used to represent whole numbers through
thousands. Larger numbers may be represented on
place value charts.
Rounding is one of the estimation strategies that is
often used to assess the reasonableness of a
solution or to give an estimate of an amount.
Students should explore reasons for estimation,
using practical experiences, and use rounding to
solve practical situations.
Mathematics Standards of Learning Curriculum Framework 2009: Grade 3
3.1
The student will
a) read and write six-digit numerals and identify the place value and value of each digit;
b) round whole numbers, 9,999 or less, to the nearest ten, hundred, and thousand; and
c) compare two whole numbers between 0 and 9,999, using symbols (>, <, or = ) and words (greater than, less than, or equal to).
UNDERSTANDING THE STANDARD (Background Information for Instructor Use Only)
ESSENTIAL UNDERSTANDINGS ESSENTIAL KNOWLEDGE AND SKILLS
The concept of rounding may be introduced
through the use of a number line. When given a
number to round, locate it on the number line.
Next, determine the multiple of ten, hundred, or
thousand it is between. Then identify to which it is
closer.
A procedure for rounding numbers to the nearest
ten, hundred, or thousand is as follows:
– Look one place to the right of the digit to
which you wish to round.
– If the digit is less than 5, leave the digit in the
rounding place as it is, and change the digits
to the right of the rounding place to zero.
– If the digit is 5 or greater, add 1 to the digit in
the rounding place, and change the digits to
the right of the rounding place to zero.
A procedure for comparing two numbers by
examining may include the following:
– Line up the numbers by place value by lining
up the ones.
– Beginning at the left, find the first place value
where the digits are different.
– Compare the digits in this place value to
determine which number is greater (or
which is less).
– Use the appropriate symbol > or < or the words
greater than or less than to compare the
numbers in the order in which they are
presented.
– If both numbers are the same, use the symbol =
or the words equal to.
Mathematics Standards of Learning Curriculum Framework 2009: Grade 3
3.2
The student will recognize and use the inverse relationships between addition/subtraction and multiplication/division to
complete basic fact sentences. The student will use these relationships to solve problems.
UNDERSTANDING THE STANDARD (Background Information for Instructor Use Only)
ESSENTIAL UNDERSTANDINGS ESSENTIAL KNOWLEDGE AND SKILLS
Addition and subtraction are inverse operations, as
are multiplication and division.
In building thinking strategies for subtraction, an
emphasis is placed on connecting the subtraction
fact to the related addition fact. The same is true for
division, where the division fact is tied to the
related multiplication fact. Building fact sentences
helps strengthen this relationship.
Addition and subtraction should be taught
concurrently in order to develop understanding of
the inverse relationship.
Multiplication and division should be taught
concurrently in order to develop understanding of
the inverse relationship.
All students should
Understand how addition and subtraction are
related.
Understand how multiplication and division are
related.
The student will use problem solving, mathematical
communication, mathematical reasoning,
connections, and representations to
Use the inverse relationships between
addition/subtraction and multiplication/division to
solve related basic fact sentences. For example,
5 + 3 = 8 and 8 – 3 = __;
4 3 = 12 and 12 ÷ 4 = __.
Write three related basic fact sentences when given
one basic fact sentence for addition/subtraction and
for multiplication/division. For example, given
3 2 = 6, solve the related facts __ 3 = 6,
6 ÷ 3 = __, and 6 ÷ __ = 3.
Mathematics Standards of Learning Curriculum Framework 2009: Grade 3
3.3
The student will
a) name and write fractions (including mixed numbers) represented by a model;
b) model fractions (including mixed numbers) and write the fractions’ names; and
c) compare fractions having like and unlike denominators, using words and symbols (>, <, or =).
UNDERSTANDING THE STANDARD (Background Information for Instructor Use Only)
ESSENTIAL UNDERSTANDINGS ESSENTIAL KNOWLEDGE AND SKILLS
A fraction is a way of representing part of a whole
(as in a region/area model or a length/measurement
model) or part of a group (as in a set model).
Fractions are used to name a part of one thing or a
part of a collection of things. Models can include
pattern blocks, fraction bars, rulers, number line,
etc.
In each area/region and length/measurement model,
the parts must be equal-sized (congruent). Wholes
are divided or partitioned into equal-sized parts. In
the set model, each member of the set is an equal
part of the set. The members of the set do not have
to be equal in size.
The denominator tells how many equal parts are in
the whole or set. The numerator tells how many of
those parts are being considered.
Provide opportunities to make connections among
fraction representations by connecting concrete or
pictorial representations with oral language and
symbolic representations.
Informal, integrated experiences with fractions at
this level will help students develop a foundation
for deeper learning at later grades. Understanding
the language of fractions (e.g., thirds means “three
equal parts of a whole,” 1
3 represents one of three
equal-size parts when a pizza is shared among three
students, or three-fourths means “three of four
equal parts of a whole”) furthers this development.
All students should
Understand that the whole must be defined.
Understand that the denominator tells the number
of equal parts that represent a whole.
Understand that the numerator is a counting
number that tells how many equal size parts are
being considered.
Understand that the value of a fraction is dependent
on both the number of parts in a whole
(denominator) and the number of those parts being
considered (numerator).
Understand that a proper fraction is a fraction
whose numerator is smaller than its denominator.
Understand that an improper fraction is a fraction
whose numerator is greater than or equal to the
denominator and is one or greater than one.
Understand that an improper fraction can be
expressed as a whole number or a mixed number.
Understand that a mixed number is written as a
whole number and a proper fraction.
The student will use problem solving, mathematical
communication, mathematical reasoning,
connections, and representations to
Name and write fractions (including mixed
numbers) represented by a model to include halves,
thirds, fourths, eighths, tenths, and twelfths.
Use concrete materials and pictures to model at
least halves, thirds, fourths, eighths, tenths, and
twelfths.
Compare fractions using the terms greater than,
less than, or equal to and the symbols ( <, >, and
=). Comparisons are made between fractions with
both like and unlike denominators, using models,
concrete materials and pictures.
Mathematics Standards of Learning Curriculum Framework 2009: Grade 3
3.3
The student will
a) name and write fractions (including mixed numbers) represented by a model;
b) model fractions (including mixed numbers) and write the fractions’ names; and
c) compare fractions having like and unlike denominators, using words and symbols (>, <, or =).
UNDERSTANDING THE STANDARD (Background Information for Instructor Use Only)
ESSENTIAL UNDERSTANDINGS ESSENTIAL KNOWLEDGE AND SKILLS
Comparing unit fractions (a fraction in which the
numerator is one) builds a mental image of
fractions and the understanding that as the number
of pieces of a whole increases, the size of one
single piece decreases (e.g., 1
5 of a bar is smaller
than 1
4 of a bar).
Comparing fractions to a benchmark on a number
line (e.g., close to 0, less than 1
2 , exactly
1
2 , greater
than 1
2 , or close to 1) facilitates the comparison of
fractions when using concrete materials or pictorial
models.
Mathematics Standards of Learning Curriculum Framework 2009: Grade 3
3.4
The student will estimate solutions to and solve single-step and multistep problems involving the sum or difference of two whole
numbers, each 9,999 or less, with or without regrouping.
UNDERSTANDING THE STANDARD (Background Information for Instructor Use Only)
ESSENTIAL UNDERSTANDINGS ESSENTIAL KNOWLEDGE AND SKILLS
Addition is the combining of quantities; it uses the
following terms:
addend 423
addend + 246
sum 669
Subtraction is the inverse of addition; it yields the
difference between two numbers and uses the
following terms:
minuend 7,698
subtrahend – 5,341
difference 2,357
An algorithm is a step-by-step method for
computing.
An example of an approach to solving problems is
Polya’s four-step plan:
– Understand: Retell the problem; read it twice;
take notes; study the charts or diagrams;
look up words and symbols that are new.
– Plan: Decide what operation(s) and sequence
of steps to use to solve the problem.
– Solve: Follow the plan and work accurately. If
the first attempt does not work, try another
plan.
– Look back: Does the answer make sense?
Knowing whether to find an exact answer or to
make an estimate is learned through practical
experiences in recognizing which is appropriate.
When an exact answer is required, opportunities to
explore whether the answer can be determined
mentally or must involve paper and pencil or
All students should
Understand that estimation skills are valuable,
time-saving tools particularly in practical situations
when exact answers are not required or needed.
Understand that estimation skills are also valuable
in determining the reasonableness of the sum or
difference when solving for the exact answer is
needed.
Develop and use strategies to estimate whole
number sums and differences to determine the
reasonableness of an exact answer.
Develop flexible methods of adding whole
numbers by combining numbers in a variety of
ways, most depending on place values.
The student will use problem solving, mathematical
communication, mathematical reasoning,
connections, and representations to
Determine whether an estimate or an exact answer
is an appropriate solution for practical addition and
subtraction problems situations involving single-
step and multistep problems.
Determine whether to add or subtract in practical
problem situations.
Estimate the sum or difference of two whole
numbers, each 9,999 or less when an exact answer
is not required.
Add or subtract two whole numbers, each 9,999 or
less.
Solve practical problems involving the sum of two
whole numbers, each 9,999 or less, with or without
regrouping, using calculators, paper and pencil, or
mental computation in practical problem situations.
Solve practical problems involving the difference
of two whole numbers, each 9,999 or less, with or
without regrouping, using calculators, paper and
pencil, or mental computation in practical problem
situations.
Solve single-step and multistep problems involving
the sum or difference of two whole numbers, each
9,999 or less, with or without regrouping.
Mathematics Standards of Learning Curriculum Framework 2009: Grade 3
3.4
The student will estimate solutions to and solve single-step and multistep problems involving the sum or difference of two whole
numbers, each 9,999 or less, with or without regrouping.
UNDERSTANDING THE STANDARD (Background Information for Instructor Use Only)
ESSENTIAL UNDERSTANDINGS ESSENTIAL KNOWLEDGE AND SKILLS
calculators help students select the correct
approach.
Determining whether an estimate is appropriate and
using a variety of strategies to estimate requires
experiences with problem situations involving
estimation.
There are a variety of mental mathematics
strategies for each basic operation, and
opportunities to practice these strategies give
students the tools to use them at appropriate times.
For example, with addition, mental mathematics
strategies include
– Adding 9: add 10 and subtract 1; and
– Making 10: for column addition, look for
numbers that group together to make 10.
Using Base-10 materials to model and stimulate
discussion about a variety of problem situations
helps students understand regrouping and enables
them to move from the concrete to the abstract.
Regrouping is used in addition and subtraction
algorithms.
Conceptual understanding begins with concrete
experiences. Next, the children must make
connections that serve as a bridge to the symbolic.
One strategy used to make connections is
representations, such as drawings, diagrams, tally
marks, graphs, or written comments.
Mathematics Standards of Learning Curriculum Framework 2009: Grade 3
3.5
The student will recall multiplication facts through the twelves table, and the corresponding division facts.
UNDERSTANDING THE STANDARD (Background Information for Instructor Use Only)
ESSENTIAL UNDERSTANDINGS ESSENTIAL KNOWLEDGE AND SKILLS
The development of computational fluency relies
on quick access to number facts.
A certain amount of practice is necessary to
develop fluency with computational strategies;
however, the practice must be motivating and
systematic if students are to develop fluency in
computation, whether mental, with manipulative
materials, or with paper and pencil.
Strategies to learn the multiplication facts through
the twelves table include an understanding of
multiples/skip counting, properties of zero and one
as factors, pattern of nines, commutative property,
and related facts.
In order to develop and use strategies to learn the
multiplication facts through the twelves table,
students should use concrete materials, hundred
chart, and mental mathematics.
To extend the understanding of multiplication,
three models may be used:
– The equal-sets or equal-groups model lends
itself to sorting a variety of concrete objects
into equal groups and reinforces repeated
addition or skip counting.
– The array model, consisting of rows and
columns (e.g., 3 rows of 4 columns for a 3-
by-4 array) helps build the commutative
property.
– The length model (e.g., a number line) also
reinforces repeated addition or skip
counting.
All students should
Develop fluency with number combinations for
multiplication and division.
Understand that multiplication is repeated addition.
Understand that division is the inverse of
multiplication.
Understand that patterns and relationships exist in
the facts.
Understand that number relationships can be used
to learn and retain the facts.
The student will use problem solving, mathematical
communication, mathematical reasoning,
connections, and representations to
Recall and state the multiplication and division
facts through the twelves table.
Recall and write the multiplication and division
facts through the twelves table.
Mathematics Standards of Learning Curriculum Framework 2009: Grade 3
3.6
The student will represent multiplication and division, using area, set, and number line models, and create and solve problems
that involve multiplication of two whole numbers, one factor 99 or less and the second factor 5 or less.
UNDERSTANDING THE STANDARD (Background Information for Instructor Use Only)
ESSENTIAL UNDERSTANDINGS ESSENTIAL KNOWLEDGE AND SKILLS
The multiplication and division facts through the
twelves tables should be modeled.
Multiplication is a shortcut for repeated addition.
The terms associated with multiplication are listed
below:
factor 54
factor 3
product 162
Creating real-life problems and solving them
facilitates the connection between mathematics and
everyday experiences (e.g., area problems).
The use of Base-10 blocks and repeated addition
can serve as a model. For example, 4 12 is read
as four sets consisting of one rod and two units.
The sum is renamed as four rods and eight units or
48. This can be thought of as
12 + 12 + 12 + 12 = (SET)
The use of Base-10 blocks and the array model can
be used to solve the same problem. A rectangle
array that is one rod and two units long by four
units wide is formed. The area of this array is
represented by 4 rods and 8 units.
The number line model can be used to solve a
multiplication problem such as 3 4. This is
represented on the number line by three jumps of
four.
The number line model can be used to solve a
division problem such as 6 ÷ 3 and is represented
on the number line by noting how many jumps of
three go from 6 to 0.
All students should
Understand the meanings of multiplication and
division.
Understand the models used to represent
multiplying and dividing whole numbers.
The student will use problem solving, mathematical
communication, mathematical reasoning,
connections, and representations to
Model multiplication, using area, set, and number
line models.
Model division, using area, set, and number line
models.
Solve multiplication problems, using the
multiplication algorithm, where one factor is 99 or
less and the second factor is 5 or less.
Create and solve word problems involving
multiplication, where one factor is 99 or less and
the second factor is 5 or less.
Mathematics Standards of Learning Curriculum Framework 2009: Grade 3
3.6
The student will represent multiplication and division, using area, set, and number line models, and create and solve problems
that involve multiplication of two whole numbers, one factor 99 or less and the second factor 5 or less.
UNDERSTANDING THE STANDARD (Background Information for Instructor Use Only)
ESSENTIAL UNDERSTANDINGS ESSENTIAL KNOWLEDGE AND SKILLS
The number of jumps (two) of a given length (three) is the answer to the question.
An algorithm is a step-by-step method for computing.
0 1 2 3 4 5 6
Mathematics Standards of Learning Curriculum Framework 2009: Grade 3
3.7
The student will add and subtract proper fractions having like denominators of 12 or less.
UNDERSTANDING THE STANDARD (Background Information for Instructor Use Only)
ESSENTIAL UNDERSTANDINGS ESSENTIAL KNOWLEDGE AND SKILLS
A proper fraction is a fraction whose numerator is
less than the denominator. A proper fraction is a
fraction that is always less than one.
An improper fraction is a fraction whose numerator
is greater than or equal to the denominator. An
improper fraction is a fraction that is equal to or
greater than one.
An improper fraction can be expressed as a mixed
number. A mixed number is written as a whole
number and a proper fraction.
The strategies of addition and subtraction applied
to fractions are the same as the strategies applied to
whole numbers.
Reasonable answers to problems involving addition
and subtraction of fractions can be established by
using benchmarks such as 0, 1
2 , and 1. For
example, 3
5 and
4
5 are each greater than
1
2 , so their
sum is greater than 1.
Concrete materials and pictorial models
representing area/regions (circles, squares, and
rectangles), length/measurements (fraction bars and
strips), and sets (counters) can be used to add and
subtract fractions having like denominators of 12 or
less.
All students should
Understand that a proper fraction is a fraction
whose numerator is smaller than its denominator.
Understand that an improper fraction is a fraction
whose numerator is greater than or equal to the
denominator and is one or greater than one.
Understand that an improper fraction can be
expressed as a whole number or a mixed number.
Understand that a mixed number is written as a
whole number and a proper fraction. A mixed
number is the sum of a whole number and the
proper fraction.
Understand that computation with fractions uses the
same strategies as whole number computation.
The student will use problem solving, mathematical
communication, mathematical reasoning,
connections, and representations to
Demonstrate a fractional part of a whole, using
– region/area models (e.g., pie pieces, pattern
blocks, geoboards, drawings);
– set models (e.g., chips, counters, cubes,
drawings); and
– length/measurement models (e.g., nonstandard
units such as rods, connecting cubes, and
drawings).
Name and write fractions and mixed numbers
represented by drawings or concrete materials.
Represent a given fraction or mixed number, using
concrete materials, pictures, and symbols. For
example, write the symbol for one-fourth and
represent it with concrete materials and/or pictures.
Add and subtract with proper fractions having like
denominators of 12 or less, using concrete
materials and pictorial models representing
area/regions (circles, squares, and rectangles),
length/measurements (fraction bars and strips), and
sets (counters).
Mathematics Standards of Learning Curriculum Framework 2009: Grade 3
3.8
The student will determine, by counting, the value of a collection of bills and coins whose total value is $5.00 or less, compare
the value of the bills and coins, and make change.
UNDERSTANDING THE STANDARD (Background Information for Instructor Use Only)
ESSENTIAL UNDERSTANDINGS ESSENTIAL KNOWLEDGE AND SKILLS
The value of a collection of coins and bills can be
determined by counting on, beginning with the
highest value, and/or by grouping the coins and
bills.
A variety of skills can be used to determine the
change after a purchase, including
– counting on, using coins and bills, i.e., starting
with the amount to be paid (purchase price),
counting forward to the next dollar, and then
counting forward by dollar bills to reach the
amount from which to make change; and
– mentally calculating the difference.
All students should
Understand that a collection of coins and bills has a
value that can be counted.
Understand how to make change from $5.00 or
less.
The student will use problem solving, mathematical
communication, mathematical reasoning,
connections, and representations to
Count the value of collections of coins and bills up
to $5.00.
Compare the values of two sets of coins or bills, up
to $5.00, using the terms greater than, less than,
and equal to.
Make change from $5.00 or less.
Mathematics Standards of Learning Curriculum Framework 2009: Grade 3
3.9
The student will estimate and use U.S. Customary and metric units to measure
a) length to the nearest 1
2 inch, inch, foot, yard, centimeter, and meter;
b) liquid volume in cups, pints, quarts, gallons, and liters;
c) weight/mass in ounces, pounds, grams, and kilograms; and
d) area and perimeter.
UNDERSTANDING THE STANDARD (Background Information for Instructor Use Only)
ESSENTIAL UNDERSTANDINGS ESSENTIAL KNOWLEDGE AND
SKILLS
Weight and mass are different. Mass is the amount
of matter in an object. Weight is determined by the
pull of gravity on the mass of an object. The mass of
an object remains the same regardless of its location.
The weight of an object changes dependent on the
gravitational pull at its location. In everyday life,
most people are actually interested in determining an
object’s mass, although they use the term weight
(e.g., “How much does it weigh?” versus “What is
its mass?”).
The concept of a standard measurement unit is one
of the major ideas in understanding measurement.
Familiarity with standard units is developed through
hands-on experiences of comparing, estimating,
measuring, and constructing.
Benchmarks of common objects need to be
established for each of the specified units of measure
(e.g., the mass of a mathematics book is about one
kilogram). Practical experience measuring the mass
of familiar objects helps to establish benchmarks and
facilitates the student’s ability to estimate measures.
One unit of measure may be more appropriate than
another to measure an object, depending on the size
of the object and the degree of accuracy desired.
Correct use of measurement tools is essential to
understanding the concepts of measurement.
All students should
Understand how to estimate measures of length,
liquid volume, weight/mass, area and perimeter.
Understand how to determine the actual measure of
length, liquid volume, weight/mass, area and
perimeter.
Understand that perimeter is a measure of the
distance around a polygon.
Understand that area is a measure of square units
needed to cover a surface.
The student will use problem solving,
mathematical communication, mathematical
reasoning, connections, and representations to
Estimate and use U.S. Customary and metric
units to measure lengths of objects to the nearest 1
2 of an inch, inch, foot, yard, centimeter, and
meter.
Determine the actual measure of length using
U.S. Customary and metric units to measure
objects to the nearest 1
2 of an inch, foot, yard,
centimeter, and meter.
Estimate and use U.S. Customary and metric
units to measure liquid volume to the nearest
cup, pint, quart, gallon, and liter.
Determine the actual measure of liquid volume
using U.S. Customary and metric units to
measure to the nearest cup, pint, quart, gallon,
and liter.
Estimate and use U.S. Customary and metric
units to measure the weight/mass of objects to
the nearest ounce, pound, gram, and kilogram.
Mathematics Standards of Learning Curriculum Framework 2009: Grade 3
3.9
The student will estimate and use U.S. Customary and metric units to measure
a) length to the nearest 1
2 inch, inch, foot, yard, centimeter, and meter;
b) liquid volume in cups, pints, quarts, gallons, and liters;
c) weight/mass in ounces, pounds, grams, and kilograms; and
d) area and perimeter.
UNDERSTANDING THE STANDARD (Background Information for Instructor Use Only)
ESSENTIAL UNDERSTANDINGS ESSENTIAL KNOWLEDGE AND
SKILLS
Perimeter is the distance around any two-
dimensional figure and is found by adding the
measures of the sides.
Area is a two-dimensional measure and is therefore
measured in square units.
Area is the number of square units needed to cover a
figure, or more precisely, it is the measure in square
units of the interior region of a two-dimensional
figure.
Determine the actual measure of weight/mass
using U.S. Customary and metric units to
measure the weight/mass of objects to the
nearest ounce, pound, gram, and kilogram.
Estimate and use U.S. Customary and metric
units to measure area and perimeter.
Determine the actual measure of area or
perimeter using U.S. Customary and metric
units.
Mathematics Standards of Learning Curriculum Framework 2009: Grade 3
3.10
The student will
a) measure the distance around a polygon in order to determine perimeter; and
b) count the number of square units needed to cover a given surface in order to determine area.
UNDERSTANDING THE STANDARD (Background Information for Instructor Use Only)
ESSENTIAL UNDERSTANDINGS ESSENTIAL KNOWLEDGE AND SKILLS
A polygon is a closed plane figure composed of at
least three line segments that do not cross. None of
the sides are curved.
Perimeter is a measure of the distance around a
polygon and is found by adding the measures of the
sides.
Area is the number of iterations of a two-
dimensional unit needed to cover a surface. The
two-dimensional unit is usually a square, but it
could also be another shape such as a rectangle or
an equilateral triangle.
Opportunities to explore the concepts of perimeter
and area should involve hands-on experiences (e.g.,
placing tiles (units) around a polygon and counting
the number of tiles to determine its perimeter and
filling or covering a polygon with cubes (square
units) and counting the cubes to determine its area).
All students should
Understand the meaning of a polygon as a closed
figure with at least three sides. None of the sides
are curved and there are no intersecting lines.
Understand that perimeter is a measure of the
distance around a polygon.
Understand how to determine the perimeter by
counting the number of units around a polygon.
Understand that area is a measure of square units
needed to cover a surface.
Understand how to determine the area by counting
the number of square units.
The student will use problem solving, mathematical
communication, mathematical reasoning,
connections, and representations to
Measure each side of a variety of polygons and add
the measures of the sides to determine the
perimeter of each polygon.
Determine the area of a given surface by estimating
and then counting the number of square units
needed to cover the surface.
Mathematics Standards of Learning Curriculum Framework 2009: Grade 3
3.11
The student will
a) tell time to the nearest minute, using analog and digital clocks; and
b) determine elapsed time in one-hour increments over a 12-hour period.
UNDERSTANDING THE STANDARD (Background Information for Instructor Use Only)
ESSENTIAL UNDERSTANDINGS ESSENTIAL KNOWLEDGE AND SKILLS
While digital clocks make reading time easy, it is
necessary to ensure that students understand that
there are sixty minutes in an hour.
Use of a demonstration clock with gears ensures
that the positions of the hour hand and the minute
hand are precise when time is read.
Students need to understand that time has passed or
will pass.
Elapsed time is the amount of time that has passed
between two given times.
Elapsed time should be modeled and demonstrated
using geared analog clocks and timelines.
It is necessary to ensure that students understand
that there are sixty minutes in an hour when using
analog and digital clocks.
Elapsed time can be found by counting on from the
beginning time to the finishing time.
– Count the number of whole hours between the
beginning time and the finishing time.
For example, to find the elapsed time between
7 a.m. and 10 a.m., students can count on to
find the difference between the times (7 and
10), so the total elapsed time is 3 hours.
All students should
Apply appropriate techniques to determine time to
the nearest minute, using analog and digital clocks.
Understand how to determine elapsed time in one-
hour increments over a 12-hour period.
The student will use problem solving, mathematical
communication, mathematical reasoning,
connections, and representations to
Tell time to the nearest minute, using analog and
digital clocks.
Match the times shown on analog and digital
clocks to written times and to each other.
When given the beginning time and ending time,
determine the elapsed time in one-hour increments
within a 12-hour period (times do not cross
between a.m. and p.m.).
Solve practical problems in relation to time that has
elapsed.
Mathematics Standards of Learning Curriculum Framework 2009: Grade 3
3.12
The student will identify equivalent periods of time, including relationships among days, months, and years, as well as minutes
and hours.
UNDERSTANDING THE STANDARD (Background Information for Instructor Use Only)
ESSENTIAL UNDERSTANDINGS ESSENTIAL KNOWLEDGE AND SKILLS
The knowledge that a year has 365 and 1
4 days will
help students understand the necessity of adding a
full day every fourth year, called a leap year.
The use of a calendar facilitates the understanding
of time relationships between days and months,
days and weeks, days and years, and months and
years. Recognize that students need to know the
relationships, such as if there are 24 hours in one
day, how many hours are in three days? If the date
is January 6, what date would it be in two weeks?
How many weeks are in March, April, and May?
The use of an analog clock facilitates the
understanding of time relationships between
minutes and hours and hours and days.
All students should
Understand the relationship that exists among
periods of time, using calendars, and clocks.
The student will use problem solving, mathematical
communication, mathematical reasoning,
connections, and representations to
Identify equivalent relationships observed in a
calendar, including the number of days in a given
month, the number of days in a week, the number
of days in a year, and the number of months in a
year.
Identify the number of minutes in an hour and the
number of hours in a day.
Mathematics Standards of Learning Curriculum Framework 2009: Grade 3
3.13
The student will read temperature to the nearest degree from a Celsius thermometer and a Fahrenheit thermometer. Real
thermometers and physical models of thermometers will be used.
UNDERSTANDING THE STANDARD (Background Information for Instructor Use Only)
ESSENTIAL UNDERSTANDINGS ESSENTIAL KNOWLEDGE AND SKILLS
Estimating and measuring temperatures in the
environment in Fahrenheit and Celsius require the
use of real thermometers.
A physical model can be used to represent the
temperature determined by a real thermometer.
The symbols for degrees in Celsius (C) and
degrees in Fahrenheit (F) should be used to write
temperatures.
Celsius and Fahrenheit temperatures should be
related to everyday occurrences by measuring the
temperature of the classroom, the outside, liquids,
body temperature, and other things found in the
environment.
All students should
Understand how to measure temperature in Celsius
and Fahrenheit with a thermometer.
The student will use problem solving, mathematical
communication, mathematical reasoning,
connections, and representations to
Read temperature to the nearest degree from real
Celsius and Fahrenheit thermometers and from
physical models (including pictorial
representations) of such thermometers.
Mathematics Standards of Learning Curriculum Framework 2009: Grade 3
3.14
The student will identify, describe, compare, and contrast characteristics of plane and solid geometric figures (circle, square,
rectangle, triangle, cube, rectangular prism, square pyramid, sphere, cone, and cylinder) by identifying relevant characteristics,
including the number of angles, vertices, and edges, and the number and shape of faces, using concrete models.
UNDERSTANDING THE STANDARD (Background Information for Instructor Use Only)
ESSENTIAL UNDERSTANDINGS ESSENTIAL KNOWLEDGE AND SKILLS
The van Hiele theory of geometric understanding
describes how students learn geometry and provides a
framework for structuring student experiences that
should lead to conceptual growth and understanding.
– Level 0: Pre-recognition. Geometric figures are
not recognized. For example, students cannot
differentiate between three-sided and four-
sided polygons.
– Level 1: Visualization. Geometric figures are
recognized as entities, without any awareness
of parts of figures or relationships between
components of a figure. Students should
recognize and name figures and distinguish a
given figure from others that look somewhat
the same (e.g., “I know it’s a rectangle
because it looks like a door, and I know that
the door is a rectangle.”).
– Level 2: Analysis. Properties are perceived, but
are isolated and unrelated. Students should
recognize and name properties of geometric
figures (e.g., “I know it’s a rectangle because
it’s closed, it has four sides and four right
angles, and opposite sides are parallel.”).
A plane geometric figure is any two-dimensional
closed figure. Circles and polygons are examples of
plane geometric figures.
All students should
Understand how to identify and describe plane
and solid geometric figures by using relevant
characteristics.
Understand the similarities and differences
between plane and solid figures.
The student will use problem solving, mathematical
communication, mathematical reasoning,
connections, and representations to
Identify models and pictures of plane geometric
figures (circle, square, rectangle, and triangle) and
solid geometric figures (cube, rectangular prism,
square pyramid, sphere, cone, and cylinder) by
name.
Identify and describe plane geometric figures by
counting the number of sides and angles.
Identify and describe solid geometric figures by
counting the number of angles, vertices, edges, and
by the number and shape of faces.
Compare and contrast characteristics of plane and
solid geometric figures (e.g., circle/sphere,
square/cube, triangle/square pyramid, and
rectangle/rectangular prism), by counting the
number of sides, angles, vertices, edges, and the
number and shape of faces.
Compare and contrast characteristics of solid
geometric figures (i.e., cube, rectangular prism,
square pyramid, sphere, cylinder, and cone) to
similar objects in everyday life (e.g., a party hat is
like a cone).
Identify characteristics of solid geometric figures
(cylinder, cone, cube, square pyramid, and
rectangular prism).
Mathematics Standards of Learning Curriculum Framework 2009: Grade 3
3.14
The student will identify, describe, compare, and contrast characteristics of plane and solid geometric figures (circle, square,
rectangle, triangle, cube, rectangular prism, square pyramid, sphere, cone, and cylinder) by identifying relevant characteristics,
including the number of angles, vertices, and edges, and the number and shape of faces, using concrete models.
UNDERSTANDING THE STANDARD (Background Information for Instructor Use Only)
ESSENTIAL UNDERSTANDINGS ESSENTIAL KNOWLEDGE AND SKILLS
Three-dimensional figures are called solid figures or
simply solids. Solids enclose a region of space. The
interior of both plane and solid figures are not part of
the figure. Solids are classified by the types of
surfaces they have. These surfaces may be flat,
curved, or both.
The study of geometric figures must be active, using
visual images and concrete materials.
Access to a variety of concrete tools such as graph
paper, pattern blocks, geoboards, and geometric
solids is greatly enhanced by computer software tools
that support exploration.
Opportunity must be provided for building and using
geometric vocabulary to describe plane and solid
figures.
A cube is a solid figure with six congruent square
faces and with every edge the same length. A cube
has 8 vertices and 12 edges.
A cylinder is a solid figure formed by two congruent
parallel circles joined by a curved surface.
A cone is a solid, pointed figure that has a flat, round
face (usually a circle) that is joined to a vertex by a
curved surface.
A rectangular prism is a solid figure in which all six
faces are rectangles with three pair of parallel
congruent opposite faces.
Mathematics Standards of Learning Curriculum Framework 2009: Grade 3
3.14
The student will identify, describe, compare, and contrast characteristics of plane and solid geometric figures (circle, square,
rectangle, triangle, cube, rectangular prism, square pyramid, sphere, cone, and cylinder) by identifying relevant characteristics,
including the number of angles, vertices, and edges, and the number and shape of faces, using concrete models.
UNDERSTANDING THE STANDARD (Background Information for Instructor Use Only)
ESSENTIAL UNDERSTANDINGS ESSENTIAL KNOWLEDGE AND SKILLS
A sphere is a solid figure with all of its points the
same distance from its center.
A square pyramid is a solid figure with one square
face and four triangular faces that share a common
vertex.
A face is a polygon that serves as one side of a solid
figure (e.g., a square is a face of a cube).
An angle is formed by two rays with a common
endpoint. This endpoint is called the vertex. Angles
are found wherever lines intersect. An angle can be
named in three different ways by using
– three letters to name, in this order, a point on one
ray, the vertex, and a point on the other ray;
– one letter at the vertex; or
– a number written inside the rays of the angle.
An edge is the line segment where two faces of a
solid figure intersect.
A vertex is the point at which two lines, line
segments, or rays meet to form an angle. It is also the
point on a three dimensional figure where three or
more faces intersect.
Students should be reminded that a solid geometric
object is hollow rather than solid. The “solid”
indicates a three-dimensional figure.
Mathematics Standards of Learning Curriculum Framework 2009: Grade 3
3.15
The student will identify and draw representations of points, line segments, rays, angles, and lines.
UNDERSTANDING THE STANDARD (Background Information for Instructor Use Only)
ESSENTIAL UNDERSTANDINGS ESSENTIAL KNOWLEDGE AND SKILLS
A point is an exact location in space. It has no
length or width. Usually, a point is named with a
capital letter.
A line is a collection of points going on and on in
both directions. It has no endpoints. When a line is
drawn, at least two points on it can be marked and
given capital letter names. The line can also be
named with a single, lower-case letter. Arrows
must be drawn to show that the line goes on in both
directions infinitely.
A line segment is part of a line. It has two
endpoints and includes all the points between those
endpoints. The endpoints are used to name a line
segment.
A ray is part of a line. It has one endpoint and
continues on and on in one direction.
An angle is formed by two rays having a common
endpoint. This endpoint is called the vertex. Angles
are found wherever lines and line segments
intersect. An angle can be named in three different
ways by using
– three letters to name, in this order, a point on
one ray, the vertex, and a point on the other
ray;
– one letter at the vertex; or
– a number written inside the rays of the angle.
Angle rulers may be particularly useful in
developing the concept of an angle.
All students should
Understand that line segments and angles are
fundamental components of plane polygons.
Understand that a line segment is a part of a
line, has two end points, and contains all the
points between those two endpoints.
Understand that points make up a line.
Understand that a line continues indefinitely in two
opposite directions.
Understand that a ray is part of a line, has one
endpoint, and continues indefinitely in only one
direction.
Understand that an angle is formed by two rays
having a common endpoint.
The student will use problem solving, mathematical
communication, mathematical reasoning,
connections, and representations to
Identify examples of points, line segments, rays,
angles, and lines.
Draw representations of points, line segments, rays,
angles, and lines, using a ruler or straightedge.
Mathematics Standards of Learning Curriculum Framework 2009: Grade 3
3.16
The student will identify and describe congruent and noncongruent plane figures.
UNDERSTANDING THE STANDARD (Background Information for Instructor Use Only)
ESSENTIAL UNDERSTANDINGS ESSENTIAL KNOWLEDGE AND SKILLS
Congruent plane figures are figures having exactly
the same size and shape. Noncongruent plane
figures are figures that are not exactly the same size
and shape. Opportunities for exploring figures that
are congruent and/or noncongruent can best be
accomplished by using physical models.
Have students identify figures that are congruent or
noncongruent by using direct comparisons and/or
tracing procedures.
All students should
Understand that congruent plane figures match
exactly.
Understand that noncongruent plane figures do not
match exactly.
Understand that congruent plane figures remain
congruent even if they are in different spatial
orientations.
Understand that noncongruent plane figures remain
noncongruent even if they are in different spatial
orientations.
The student will use problem solving, mathematical
communication, mathematical reasoning,
connections, and representations to
Identify examples of congruent and noncongruent
figures. Verify their congruence by laying one on
top of the other using drawings or models.
Determine and explain why plane figures are
congruent or noncongruent, using tracing
procedures.
Mathematics Standards of Learning Curriculum Framework 2009: Grade 3
3.17
The student will
a) collect and organize data, using observations, measurements, surveys, or experiments;
b) construct a line plot, a picture graph, or a bar graph to represent the data; and
c) read and interpret the data represented in line plots, bar graphs, and picture graphs and write a sentence analyzing the
data.
UNDERSTANDING THE STANDARD (Background Information for Instructor Use Only)
ESSENTIAL UNDERSTANDINGS ESSENTIAL KNOWLEDGE AND SKILLS
Investigations involving data should occur
frequently and relate to students’ experiences,
interests, and environment.
Formulating questions for investigations is student-
generated at this level. For example: What is the
cafeteria lunch preferred by students in the class
when four lunch menus are offered?
The purpose of a graph is to represent data gathered
to answer a question.
Bar graphs are used to compare counts of different
categories (categorical data). Using grid paper
ensures more accurate graphs.
– A bar graph uses parallel, horizontal or vertical
bars to represent counts for categories. One
bar is used for each category, with the
length of the bar representing the count for
that category.
– There is space before, between, and after the
bars.
– The axis displaying the scale representing the
count for the categories should extend one
increment above the greatest recorded piece
of data. Third grade students should collect
data that are recorded in increments of
All students should
Understand how data can be collected and
organized.
Understand that data can be displayed in different
types of graphs depending on the data.
Understand how to construct a line plot, picture
graph, or bar graph.
Understand that data sets can be interpreted and
analyzed to draw conclusions.
The student will use problem solving, mathematical
communication, mathematical reasoning,
connections, and representations to
Formulate questions to investigate.
Design data investigations to answer formulated
questions, limiting the number of categories for
data collection to four.
Collect data, using surveys, polls, questionnaires,
scientific experiments, and observations.
Organize data and construct a bar graph on grid
paper representing 16 or fewer data points for no
more than four categories.
Construct a line plot with no more than 30 data
points.
Read, interpret and analyze information from line
plots by writing at least one statement.
Label each axis on a bar graph and give the bar
graph a title. Limit increments on the numerical
axis to whole numbers representing multiples of 1,
2, 5, or 10.
Read the information presented on a simple bar or
picture graph (e.g., the title, the categories, the
description of the two axes).
Mathematics Standards of Learning Curriculum Framework 2009: Grade 3
3.17
The student will
a) collect and organize data, using observations, measurements, surveys, or experiments;
b) construct a line plot, a picture graph, or a bar graph to represent the data; and
c) read and interpret the data represented in line plots, bar graphs, and picture graphs and write a sentence analyzing the
data.
UNDERSTANDING THE STANDARD (Background Information for Instructor Use Only)
ESSENTIAL UNDERSTANDINGS ESSENTIAL KNOWLEDGE AND SKILLS
whole numbers, usually multiples of 1, 2, 5, or 10.
– Each axis should be labeled, and the graph
should be given a title.
– Statements representing an analysis and
interpretation of the characteristics of the data
in the graph (e.g., similarities and differences,
least and greatest, the categories, and total
number of responses) should be written.
A line plot shows the frequency of data on a
number line. Line plots are used to show the spread
of the data and quickly identify the range, mode,
and any outliers.
Number of Books Read
Each x represents one student
When data are displayed in an organized manner,
the results of the investigations can be described
and the posed question answered.
Recognition of appropriate and inappropriate
statements begins at this level with graph
interpretations.
Analyze and interpret information from picture and
bar graphs, with up to 30 data points and up to 8
categories, by writing at least one sentence.
Describe the categories of data and the data as a
whole (e.g., data were collected on four ways to
cook or prepare eggs — scrambled, fried, hard
boiled, and egg salad — eaten by students).
Identify parts of the data that have special
characteristics, including categories with the
greatest, the least, or the same (e.g., most students
prefer scrambled eggs).
Select a correct interpretation of a graph from a set
of interpretations of the graph, where one is correct
and the remaining are incorrect. For example, a bar
graph containing data on four ways to cook or
prepare eggs — eaten by students show that more
students prefer scrambled eggs. A correct answer
response, if given, would be that more students
prefer scrambled eggs than any other way to cook
or prepare eggs.
Mathematics Standards of Learning Curriculum Framework 2009: Grade 3
3.18
The student will investigate and describe the concept of probability as chance and list possible results of a given situation.
UNDERSTANDING THE STANDARD (Background Information for Instructor Use Only)
ESSENTIAL UNDERSTANDINGS ESSENTIAL KNOWLEDGE AND SKILLS
A spirit of investigation and experimentation
should permeate probability instruction, where
students are actively engaged in explorations and
have opportunities to use manipulatives.
Investigation of experimental probability is
continued at this level through informal activities
using two-colored counters, spinners, and random
number generators (number cubes).
Probability is the chance of an event occurring.
The probability of an event occurring is the ratio of
desired outcomes to the total number of possible
outcomes. If all the outcomes of an event are
equally likely to occur, the probability of the event
= number of favorable outcomes
total number of possible outcomes .
The probability of an event occurring is represented
by a ratio between 0 and 1. An event is
“impossible” if it has a probability of 0 (e.g., the
probability that the month of April will have 31
days). An event is “certain” if it has a probability of
1 (e.g., the probability that the sun will rise
tomorrow morning).
When a probability experiment has very few trials,
the results can be misleading. The more times an
experiment is done, the closer the experimental
probability comes to the theoretical probability
(e.g., a coin lands heads up half of the time).
Students should have opportunities to describe in
informal terms (i.e., impossible, unlikely, as likely
as, equally likely, likely, and certain) the degree of
likelihood of an event occurring. Activities should
include real-life examples.
All students should
Investigate, understand, and apply basic concepts
of probability.
Understand that probability is the chance of an
event happening.
The student will use problem solving, mathematical
communication, mathematical reasoning,
connections, and representations to
Define probability as the chance that an event will
happen.
List all possible outcomes for a given situation
(e.g., heads and tails are the two possible outcomes
of flipping a coin).
Identify the degree of likelihood of an outcome
occurring using terms such as impossible,
unlikely, as likely as, equally likely, likely, and certain.
Mathematics Standards of Learning Curriculum Framework 2009: Grade 3
3.18
The student will investigate and describe the concept of probability as chance and list possible results of a given situation.
UNDERSTANDING THE STANDARD (Background Information for Instructor Use Only)
ESSENTIAL UNDERSTANDINGS ESSENTIAL KNOWLEDGE AND SKILLS
For any event, such as flipping a coin, the equally
likely things that can happen are called outcomes.
For example, there are two equally likely outcomes
when flipping a coin: the coin can land heads up, or
the coin can land tails up.
A sample space represents all possible outcomes of
an experiment. The sample space may be organized
in a list, table, or chart.
Mathematics Standards of Learning Curriculum Framework 2009: Grade 3
3.19
The student will recognize and describe a variety of patterns formed using numbers, tables, and pictures, and extend the
patterns, using the same or different forms.
UNDERSTANDING THE STANDARD (Background Information for Instructor Use Only)
ESSENTIAL UNDERSTANDINGS ESSENTIAL KNOWLEDGE AND SKILLS
Exploring patterns requires active physical and
mental involvement.
The use of materials to extend patterns permits
experimentation or trial-and-error approaches that
are almost impossible without them.
Reproduction of a given pattern in a different
representation, using symbols and objects, lays the
foundation for writing numbers symbolically or
algebraically.
The simplest types of patterns are repeating
patterns. In each case, students need to identify the
basic unit of the pattern and repeat it. Opportunities
to create, recognize, describe, and extend repeating
patterns are essential to the primary school
experience.
Growing patterns are more difficult for students to
understand than repeating patterns because not only
must they determine what comes next, they must
also begin the process of generalization. Students
need experiences with growing patterns in both
arithmetic and geometric formats.
Create an arithmetic number pattern. Sample
numeric patterns include
– 6, 9, 12, 15, 18, (growing pattern);
– 1, 2, 4, 7, 11, 16, (growing pattern);
– 20, 18, 16, 14,…(growing pattern); and
– 1, 3, 5, 1, 3, 5, 1, 3, 5 (repeating pattern).
All students should
Understand that numeric and geometric patterns
can be expressed in words or symbols.
Understand the structure of a pattern and how it
grows or changes.
Understand that mathematical relationships exist in
patterns.
Understand that patterns can be translated from one
representation to another.
The student will use problem solving, mathematical
communication, mathematical reasoning,
connections, and representations to
Recognize repeating and growing numeric and
geometric patterns (e.g., skip counting, addition
tables, and multiplication tables).
Describe repeating and growing numeric and
geometric patterns formed using numbers, tables,
and/or pictures, using the same or different forms.
Extend repeating and growing patterns of numbers
or figures using concrete objects, numbers, tables,
and/or pictures.
Mathematics Standards of Learning Curriculum Framework 2009: Grade 3
3.19
The student will recognize and describe a variety of patterns formed using numbers, tables, and pictures, and extend the
patterns, using the same or different forms.
UNDERSTANDING THE STANDARD (Background Information for Instructor Use Only)
ESSENTIAL UNDERSTANDINGS ESSENTIAL KNOWLEDGE AND SKILLS
In geometric patterns, students must often
recognize transformations of a figure, particularly
rotation or reflection. Rotation is the result of
turning a figure around a point or a vertex, and
reflection is the result of flipping a figure over a
line.
Sample geometric patterns include
– O Δ O O Δ Δ O O O Δ Δ Δ ; and
– □□★★□★□□★★□★.
A table of values can be analyzed to determine the
pattern that has been used, and that pattern can then
be used to find the next value.
Mathematics Standards of Learning Curriculum Framework 2009: Grade 3
3.20
The student will
a) investigate the identity and the commutative properties for addition and multiplication; and
b) identify examples of the identity and commutative properties for addition and multiplication.
UNDERSTANDING THE STANDARD (Background Information for Instructor Use Only)
ESSENTIAL UNDERSTANDINGS ESSENTIAL KNOWLEDGE AND SKILLS
Investigating arithmetic operations with whole
numbers helps students learn about several
different properties of arithmetic relationships.
These relationships remain true regardless of the
numbers.
The commutative property for addition states that
changing the order of the addends does not affect
the sum (e.g., 4 + 3 = 3 + 4). Similarly, the
commutative property for multiplication states that
changing the order of the factors does not affect the
product (e.g., 2 3 = 3 2).
The identity property for addition states that if zero
is added to a given number, the sum is the same as
the given number. The identity property of
multiplication states that if a given number is
multiplied by one, the product is the same as the
given number.
A number sentence is an equation with numbers
(e.g., 6 + 3 = 9; or 6 + 3 = 4 + 5).
All students should
Understand that mathematical relationships can be
expressed using number sentences.
Understand the identity property for addition.
Understand the identity property for multiplication.
Understand the commutative property of addition.
Understand the commutative property of
multiplication.
Understand that quantities on both sides of an
equals sign must be equal.
Understand that quantities on both sides of the not
equal sign are not equal.
The student will use problem solving, mathematical
communication, mathematical reasoning,
connections, and representations to
Investigate the identity property for addition and
determine that when the number zero is added to
another number or another number is added to the
number zero, that number remains unchanged.
Examples of the identity property for addition are
0 + 2 = 2; 5 + 0 = 5.
Investigate the identity property for multiplication
and determine that when the number one is
multiplied by another number or another number is
multiplied by the number one, that number remains
unchanged. Examples of the identity property for
multiplication are 1 x 3 = 3; 6 x 1 = 6.
Recognize that the commutative property for
addition is an order property. Changing the order
of the addends does not change the sum (5 + 4 = 9
and 4 + 5 = 9).
Recognize that the commutative property for
multiplication is an order property. Changing the
order of the factors does not change the product (2
3 = 3 2).
Write number sentences to represent equivalent
mathematical relationships (e.g., 4 x 3 = 14 - 2).
Identify examples of the identity and commutative
properties for addition and multiplication.
Loudoun County Public Schools Mathematics Office – Department of Curriculum and Instruction Grade 3
Learning Progressions The following pages are the Learning Progressions for the curriculum. More information about the Learning Progressions can be found on VISION. The Grading and Assessment, Module 3: Learning Progressions is about what Learning Progressions are, how they were developed, and how they are used to support instruction and build student learning.
Loudoun County Public Schools Mathematics Office – Department of Curriculum and Instruction Grade 3
LP 3.1a SOL 3.1: The student will:
a) read and write six-digit numerals and identify the place value and value of each digit; Learning Target: I can read, write, and model six-digit numerals and identify the place value positions, value of each digit, and the relationship of each place value position to the next.
Learning Progression The student will use problem solving, mathematical communication,
mathematical reasoning, connections, and representations at each level of the learning progression.
Advanced Proficient
I can take the relationship of the places in the place value system (the value of each place is ten times the value of the place to its right) and extend this relationship to places more than one place to the right or left and give a correct proof of this relationship.
Proficient
I can read, write, and model six-digit numerals and identify the place value positions, value of each digit, and the relationship of each place value position to the next.
Intermediate
I can read, write, or model six-digit numerals.
Beginner
I can understand that different digits in a multi-digit number have different values depending on their place value position.
Loudoun County Public Schools Mathematics Office – Department of Curriculum and Instruction Grade 3
LP 3.1b SOL 3.1: The student will:
b) round whole numbers, 9,999 or less, to the nearest ten, hundred, and thousand; and Learning Target: I can round whole numbers, 9,999 or less, to the nearest ten, hundred, and thousand and represent my thinking using pictures, numbers, and words.
Learning Progression The student will use problem solving, mathematical communication,
mathematical reasoning, connections, and representations at each level of the learning progression.
Advanced Proficient
I can compare and contrast the accuracy of rounding compared to other forms of estimations (compatible number, front-end estimation, etc.).
Proficient
I can round whole numbers, 9,999 or less, to the nearest ten, hundred, and thousand and represent my thinking using pictures, numbers, and words.
Intermediate
I can determine whether a number is closer to one landmark number or another using a model (for example: on a number line, visualizing that 571 is closer to 600 than 500).
Beginner
I understand that if I don’t need an exact answer, I can round numbers as one way to estimate.
Loudoun County Public Schools Mathematics Office – Department of Curriculum and Instruction Grade 3
LP 3.1c SOL 3.1: The student will: c) compare two whole numbers between 0 and 9,999, using symbols (>, <, or = ) and words (greater than, less than, or equal to). Learning Target: I can compare two whole numbers between 0 and 9,999, using symbols (>, <, or = ) and words (greater than, less than, or equal to).
Learning Progression The student will use problem solving, mathematical communication,
mathematical reasoning, connections, and representations at each level of the learning progression.
Advanced Proficient
I can determine two numbers and how they compare when given clues (for example: What two 4 digit numbers could I be thinking of when one number is 300 less than the other and the digits in the hundreds place are both even?).
Proficient
I can compare two whole numbers between 0 and 9,999, using symbols (>, <, or = ) and words (greater than, less
than, or equal to).
Intermediate
I understand that, when comparing numbers, the largest place value of each number should be evaluated first, followed by each consecutive place value (for example: when comparing 569 and 837, the digits in the hundreds place should be evaluated first).
Beginner
I understand the magnitude of numbers (500 is more than 50).
Loudoun County Public Schools Mathematics Office – Department of Curriculum and Instruction Grade 3
LP 3.2 SOL 3.2: The student will recognize and use the inverse relationships between addition/subtraction and multiplication/division to complete basic
fact sentences. The student will use these relationships to solve problems. Learning Target: I can use inverse relationships between addition/subtraction and multiplication/division to complete basic fact sentences and solve problems.
Learning Progression The student will use problem solving, mathematical communication,
mathematical reasoning, connections, and representations at each level of the learning progression.
Advanced Proficient
I can create problems involving inverse fact relationships and analyze a model of why the facts are related.
Proficient
I can use inverse relationships between addition/subtraction and multiplication/division to complete basic fact
sentences and solve problems.
Intermediate
I can find a subtraction fact when given a related addition fact/find a division fact when given a multiplication fact.
Beginner
I know that addition facts are related to subtraction facts and that multiplication facts are related to division facts.
Loudoun County Public Schools Mathematics Office – Department of Curriculum and Instruction Grade 3
LP 3.3ab SOL 3.3: The student will:
d) name and write fractions (including mixed numbers) represented by a model e) model fractions (including mixed numbers) and write fractions’ names
Learning Target: I can label and create multiple pictures / models of a given fraction. * Parameters: 1. Proper Fractions, Improper Fractions, and Mixed Numbers 2. Halves, Thirds, Fourths, Fifths, Sixths, Eighths, Tenths, and Twelfths. 2. Pictures / Models – Set, Area, Linear
Learning Progression The student will use problem solving, mathematical communication,
mathematical reasoning, connections, and representations at each level of the learning progression.
Advanced Proficient
Using pictures / models and words, I can create and explain a real life example of how fractions are used.
Proficient
I can create and label multiple pictures / models of a given fraction.
Intermediate
I can identify the part (numerator) and whole (denominator) in a picture / model.
Loudoun County Public Schools Mathematics Office – Department of Curriculum and Instruction Grade 3
Beginner
I understand that the value of a fraction can be greater than 1 and can explain what improper fractions (3/2) and mixed numbers (1 ½) mean.
LP 3.3c SOL 3.3: The student will c) compare fractions having like and unlike denominators using words and symbols (>,<, or =) Learning Target: I can develop and use a variety of strategies (pictures / models, benchmark numbers) to compare fractions.
* Parameters: 1. Only Proper Fractions
2. Halves, Thirds, Fourths, Fifths, Sixths, Eighths, Tenths, and Twelfths. 3. Like and Unlike Denominators 2. Pictures / Models: Set, Area, Linear
Learning Progression The student will use problem solving, mathematical communication,
mathematical reasoning, connections, and representations at each level of the learning progression.
Advanced Proficient
Using pictures / models and words, I can create and explain a real life example of fractional pieces being compared and the strategy used to determine which is greater.
Proficient
I can develop and use a variety of strategies (pictures / models, benchmark numbers) to compare fractions.
Loudoun County Public Schools Mathematics Office – Department of Curriculum and Instruction Grade 3
Intermediate
I can describe the value of a fraction compared to a benchmark number (close to 0, less than 1/2, exactly 1/2, greater than 1/2, close to 1).
Beginner
I understand that when working with unit fractions, the larger the denominator (number of pieces that make up the whole), the smaller the pieces and therefore the smaller the value of the fraction. I understand that I only need to compare the numerators of fractions that have like denominators.
LP 3.4 SOL 3.4: The student will estimate solutions to and solve single-step and multistep problems involving the sum or difference of two whole
numbers, each 9,999 or less, with or without regrouping. Learning Target: I can estimate answers and solve problems involving one or more steps in which I will need to add and/or subtract numbers that
are 9,999 or less.
Learning Progression The student will use problem solving, mathematical communication,
mathematical reasoning, connections, and representations at each level of the learning progression.
Advanced Proficient
I can create multi-step contexts and solve for a solution, using and comparing/contrasting multiple strategies.
Proficient
I can estimate answers and solve problems involving one or more steps in which I will need to add and/or
subtract numbers that are
9,999 or less.
Loudoun County Public Schools Mathematics Office – Department of Curriculum and Instruction Grade 3
Intermediate
I can estimate and solve problems involving one step in which I will need to add and/or subtract numbers that are 9,999 or less.
Beginner
I can understand that some contexts represent addition (combining) and others represent subtraction (separating).
LP 3.5 SOL 3.5: The student will recall multiplication facts through the twelves table, and the corresponding division facts. Learning Target: I can understand models and patterns of multiplication in order to recall multiplication facts and relate them to division facts.
Learning Progression The student will use problem solving, mathematical communication,
mathematical reasoning, connections, and representations at each level of the learning progression.
Advanced Proficient
I can generalize patterns I observe from models of multiplication and compare them to patterns and models of division.
Proficient
I can understand models and patterns of multiplication in order to recall multiplication facts and relate them to division facts.
Loudoun County Public Schools Mathematics Office – Department of Curriculum and Instruction Grade 3
Intermediate
I can create models (arrays, number lines, equal group pictures, etc.) to represent repeated addition and repeated subtraction.
Beginner
I understand the inverse relationship between addition and subtraction and use that relationship to help recall those number facts.
LP 3.6 SOL 3.6: The student will represent multiplication and division, using area, set, and number line models, and create and solve problems that
involve multiplication of two whole numbers, one factor 99 or less and the second factor 5 or less. Learning Target: I can create and use models (area, set, and number lines) of multiplication to create and solve multiplication problems (one factor
99 or less and the second factor 5 or less).
Learning Progression The student will use problem solving, mathematical communication,
mathematical reasoning, connections, and representations at each level of the learning progression.
Advanced Proficient
I can compare and contrast models of multiplication and justify the use of a particular model as it relates to solving practical, real-life problems.
Loudoun County Public Schools Mathematics Office – Department of Curriculum and Instruction Grade 3
Proficient
I can create and use models (area, set, and number lines) of multiplication to create and solve multiplication
problems (one factor 99 or less and the second factor 5 or less).
Intermediate
I can create area, set, and number line models for multiplication.
Beginner
I can identify area, set, and number line models and use them to model addition and subtraction problems.
LP 3.7 SOL 3.7: The student will add and subtract proper fractions having like denominators of 12 or less. Learning Target: I can use pictures / models to add and subtract fractions. * Parameters: 1. Only Proper Fractions 2. Halves, Thirds, Fourths, Fifths, Sixths, Eighths, Tenths, and Twelfths. 3. Only Like Denominators 4. Pictures / Models: Set, Area, Linear
Learning Progression The student will use problem solving, mathematical communication,
mathematical reasoning, connections, and representations at each level of the learning progression.
Loudoun County Public Schools Mathematics Office – Department of Curriculum and Instruction Grade 3
Advanced Proficient
Using pictures / models and words, I can create and explain a real life situation involving adding and subtracting fractions and correctly explain how I would solve the problem.
Proficient
I can use pictures / models to add and subtract fractions.
Intermediate
I understand that when adding and subtracting fractions with like denominators, I can use the same whole number computation strategies with the numerators.
Beginner
I understand that fractions with the like denominators have the same size pieces that make up the whole.
LP 3.8 SOL 3.8: The student will determine, by counting, the value of a collection of bills and coins whose total value is $5.00 or less, compare the value of
the bills and coins, and make change. Learning Target: I can count the value of a collection of coins ($5.00 or less), compare the value of bills and coins, and use multiple strategies to make change.
Learning Progression
The student will use problem solving, mathematical communication,
Loudoun County Public Schools Mathematics Office – Department of Curriculum and Instruction Grade 3
mathematical reasoning, connections, and representations at each level of the learning progression.
Advanced Proficient
I can apply strategies for making change to real-life situations and explain the most efficient strategy depending on the practical problem.
Proficient
I can count the value of a collection of coins ($5.00 or less), compare the value of bills and coins, and use multiple
strategies to make change.
Intermediate
I can count the value of a collection of coins and count up when an additional set of coins is given.
Beginner
I can recognize coins and bills and compare their values.
LP 3.9 SOL 3.9: The student will estimate and use US Customary and metric units to measure
a) length to the nearest ½ inch, inch. Foot, yard, centimeter, and meter; b) liquid volume in cups, pints, quarts, gallons, and liters; c) weight/mass in ounces, pounds, grams and kilograms; and d) area and perimeter.
Learning Target: The student can measure in US Customary and metric units and apply length measurements to find areas and perimeters.
Loudoun County Public Schools Mathematics Office – Department of Curriculum and Instruction Grade 3
Learning Progression The student will use problem solving, mathematical communication,
mathematical reasoning, connections, and representations at each level of the learning progression.
Advanced Proficient
I can compare and contrast area and perimeter.
Proficient I can measure in US Customary and metric units and apply length measurements to find areas and perimeters.
Intermediate I can measure length, mass, and liquid volume in US Customary and metric (standard) units and determine benchmarks for some measurements.
Beginning I can estimate length (centimeter and inch); weight/mass (pounds, ounces, kilograms, grams); and liquid volume (cups, pints, quarts, gallons, and liters). (Grade 2)
LP 3.10 SOL 3.10: The student will
a) measure the distance around a polygon in order to determine perimeter; and b) count the number of square units needed to cover a given surface in order to determine area.
Loudoun County Public Schools Mathematics Office – Department of Curriculum and Instruction Grade 3
Learning Target: I can find the perimeter of a polygon by adding the lengths of the line segments forming the polygon and the area of the region inside the polygon (polygonal region) by covering the polygon with square units.
Learning Progression The student will use problem solving, mathematical communication,
mathematical reasoning, connections, and representations at each level of the learning progression.
Advanced Proficient
I can investigate strategies and solve problems involving both perimeter and area (ie: create a representation for a polygon with a perimeter of 20 and an area of 25).
Proficient
I can find the perimeter of a polygon by adding the lengths of the line segments forming the polygon and the area of the region inside the polygon (polygonal region) by covering the polygon with square units.
Intermediate I can explore perimeter and area of polygons using several representations.
Beginning I can describe/define polygon and know that a polygon does not include the area inside the polygon, only the line segments forming the polygon.
LP 3.11a SOL 3.11: The student will:
a) tell time to the nearest minute, using analog and digital clocks
Loudoun County Public Schools Mathematics Office – Department of Curriculum and Instruction Grade 3
Learning Target: I can tell time to the nearest minute using different clock models.
Learning Progression The student will use problem solving, mathematical communication,
mathematical reasoning, connections, and representations at each level of the learning progression.
Advanced Proficient
I can create a model for an analog and digital clock when given a time.
Proficient
I can tell time to the nearest minute using different clock models.
Intermediate
I can use skip counting by 5’s and 1’s to tell time by using one or more clock models.
Beginner
I can match a written time to a time shown on a clock, to the nearest minute.
LP 3.11b SOL 3.11: The student will:
b) determine elapsed time in one-hour increments over a 12-hour period.
Loudoun County Public Schools Mathematics Office – Department of Curriculum and Instruction Grade 3
Learning Target: I can tell time to the nearest minute and how many hours have passed (using a clock) when given a scenario involving the passing of time.
Learning Progression The student will use problem solving, mathematical communication,
mathematical reasoning, connections, and representations at each level of the learning progression.
Advanced Proficient
I can create my own situation involving the passing of time and can describe a situation when it would be important to know the time to the nearest minute.
Proficient
I can tell time to the nearest minute and how many hours have passed (using a clock or elapsed time ruler) when given a scenario involving the passing of time.
Intermediate I can determine how many hours have passed by using a clock.
Beginning I can tell time to the nearest 5 minutes using analog and digital clocks and I understand that there are 60 minutes in an hour.
LP 3.13 SOL 3.13: The student will read temperature to the nearest degree from a Celsius thermometer and a Fahrenheit thermometer. Real
thermometers and physical models of thermometers will be used.
Loudoun County Public Schools Mathematics Office – Department of Curriculum and Instruction Grade 3
Learning Target: I can read and write temperatures to the nearest degree using Celsius and Fahrenheit thermometers and pictorial models.
Learning Progression The student will use problem solving, mathematical communication,
mathematical reasoning, connections, and representations at each level of the learning progression.
Advanced Proficient
I can create a model of a thermometer to fit an everyday situation involving temperature.
Proficient
I can read and write temperatures to the nearest degree using Celsius and Fahrenheit thermometers and pictorial
models.
Intermediate
I can use a thermometer or pictorial model to estimate temperatures in Celsius and Fahrenheit.
Beginner
I understand that thermometers are used to measure temperature and that there are two units of temperature measurement (Celsius and Fahrenheit).
LP 3.14
Loudoun County Public Schools Mathematics Office – Department of Curriculum and Instruction Grade 3
SOL 3.14: The student will identify, describe, compare and contrast characteristics of plane and solid geometric figures (circle, square, rectangle, triangle, cube, rectangular prism, square pyramid, sphere, cone, and cylinder) by identifying relevant characteristics including the number of angles, vertices, and edges, and the number and shape of faces, using concrete models. Learning Target: I can identify, describe, compare and contrast characteristics of plane and solid geometric figures.
Learning Progression The student will use problem solving, mathematical communication,
mathematical reasoning, connections, and representations at each level of the learning progression.
Advanced Proficient
I can justify characteristics of solid figures based on characteristics of plane figures.
Proficient I can identify, describe, compare and contrast characteristics of plane and solid geometric figures.
Intermediate I can identify, compare and contrast characteristics of solid geometric figures.
Beginning I can identify, compare and contrast characteristics of plane geometric figures.
Loudoun County Public Schools Mathematics Office – Department of Curriculum and Instruction Grade 3
LP 3.15 SOL 3.15: The student will identify and draw representations of points, line segments, rays, angles, and lines. Learning Target: I can identify and draw representations of points, line segments, rays, angles, and lines and name them as mathematicians do.
Learning Progression The student will use problem solving, mathematical communication,
mathematical reasoning, connections, and representations at each level of the learning progression.
Advanced Proficient
I can compare and contrast points, line segments, rays, angles, and lines, with justifications.
Proficient
I can identify and draw representations of points, line segments, rays, angles, and lines and name them as mathematicians do.
Intermediate I can identify examples of points, line segments, rays, angles, and lines in my environment and justify my identification.
Beginning I can identify line segments, angles, and points as fundamental parts of polygons.
Loudoun County Public Schools Mathematics Office – Department of Curriculum and Instruction Grade 3
LP 3.16 SOL 3.16: The student will identify and describe congruent and non-congruent plane figures. Learning Target: I can will identify and describe congruent and non-congruent plane figures and justify the identification.
Learning Progression The student will use problem solving, mathematical communication,
mathematical reasoning, connections, and representations at each level of the learning progression.
Advanced Proficient
I can explain why figures with different spatial orientations are congruent or not congruent, using multiple strategies.
Proficient I can identify and describe congruent and noncongruent plane figures and justify my identification.
Intermediate I can use direct comparison or tracing to determine congruence.
Beginning I can describe congruence as same shape and same size.
Mathematics Learning Progressions: Grade 3
LP 3.19 SOL 3.19: The student will recognize and describe a variety of patterns formed using numbers, tables, and pictures, and extend the patterns, using the same or different forms. Learning Target: I can recognize, describe, and extend numeric and geometric patterns (repeating or growing) using concrete objects, numbers,
tables, and pictures and identify mathematical relationships that exist within patterns.
Learning Progression The student will use problem solving, mathematical communication,
mathematical reasoning, connections, and representations at each level of the learning progression.
Advanced Proficient
I can compare and contrast similar patterns using different models and generalize a pattern by extending the pattern even when it does not begin with 1.
Proficient
I can recognize, describe, and extend numeric and geometric patterns (repeating or growing) using concrete
objects, numbers, tables, and pictures and identify mathematical relationships that exist within patterns (for
example, skip counting on a hundreds chart models multiplication).
Intermediate
I can extend repeating and growing numeric and growing patterns and describe the pattern.
Beginner
I can recognize repeating and growing numeric and growing patterns.
Mathematics Learning Progressions: Grade 3
LP 3.20 SOL 3.20: The student will
a) investigate the identity and the commutative properties for addition and multiplication; and b) identify examples of the identity and commutative properties for addition and multiplication.
Learning Target: I can investigate the identity and commutative properties for addition and multiplication and identify examples of the properties.
Learning Progression The student will use problem solving, mathematical communication,
mathematical reasoning, connections, and representations at each level of the learning progression.
Advanced Proficient
I can compare and contrast properties and justify why each property holds true.
Proficient
I can investigate the identity and commutative properties for addition and multiplication and identify examples of
the properties.
Intermediate
I can recognize patterns of number properties and match an example with its correct property.
Beginner
I can recognize a number sentence and know that both sides of a number sentence are equivalent expressions when I use an equal sign.
Grade 3 Math Intervention Ideas
Unit 2 – Place Value
Hands-On Standards Book Grades 3-4 Every Day Counts Partner Games
Number and Operations Lessons 1-2 Game #1: The $1,000 Club Game #4: Try for $5,000 Game #7: Rounding Game (tens place) Game #11: Double Trouble(hundreds place) Game #17: Number Maker(thousands place) Game #19: From Here to There
Unit 3 – Computation With Whole Numbers (addition/subtraction)
Hands-On Standards Book Grades 3-4 Every Day Counts Partner Games
Number and Operations Lessons 3-4 Algebra Lesson 5
Game #2: Doubles & Doubles Plus One Game #3: Teen Take-Away Game #5: Fast Ten-Yes or No? Game #6: Empty the Bank
Unit 4 – Money
Hands-On Standards Book Grades 3-4 Every Day Counts Partner Games
Game #9: Pocket Money Game #18: Try for $5.00
Unit 5 – Computation With Whole Numbers (multiplication/division)
Hands-On Standards Book Grades 3-4 Every Day Counts Partner Games
Number and Operations Lessons 5-7, 11-12 Algebra Lesson 6
Game #8: Groups Galore Game #10: Fishy Multiplication Game #11: Double Trouble Game #12: Array Game Game #13: Product Comparing Game #14: Side By Side
Unit 6 – Patterns & Data
Hands-On Standards Book Grades 3-4 Every Day Counts Partner Games Algebra Lessons 1-2, 10 Data Analysis and Probability Lessons 2-3
Unit 7 – Geometry
Hands-On Standards Book Grades 3-4 Every Day Counts Partner Games
Geometry Lessons 1-3, 5, 8-9
Unit 8 – Fractions, Probability, & Measurement
Hands-On Standards Book Grades 3-4 Every Day Counts Partner Games
Number and Operations Lessons 15-19 Data Analysis and Probability Lessons 6-9
Game #16: Make a Pound
Unit 9 – Computation With Fractions
Hands-On Standards Book Grades 3-4 Every Day Counts Partner Games
Number and Operations Lesson 20 Game #16: Make a Pound
Unit 10 – Elapsed Time & Temperature
Hands-On Standards Book Grades 3-4 Every Day Counts Partner Games
Measurement Lesson 2
Unit 11 – Measuring My World
Hands-On Standards Book Grades 3-4 Every Day Counts Partner Games
Measurement Lessons 3-6, 8-9, 11 Game #16: Make a Pound
Resources available in all LCPS Elementary Schools
Hands-On Standards books Every Day Counts Partner Games
NCSM Great Tasks K-5 (available in all LCPS Elementary Schools)
VA SOL Alignment
Kindergarten Math
Domino Addition and Subtraction
Launch
SOL K.2 The student, given a set containing 15 or fewer concrete objects, will a) tell how many are in the set by counting the number of objects orally; b) write the numeral to tell how many are in the set; and c) select the corresponding numeral from a given set of numerals.
Activity
SOL K.1 The student, given two sets, each containing 10 or fewer concrete objects, will identify and describe one set as having more, fewer, or the same number of members as the other set, using the concept of one-to-one correspondence.
Counting Sheep
Launch
SOL K.2 The student, given a set containing 15 or fewer concrete objects, will a) tell how many are in the set by counting the number of objects orally; d) write the numeral to tell how many are in the set; and e) select the corresponding numeral from a given set of numerals.
Activity SOL K.3 The student, given an ordered set of ten objects and/or
pictures, will indicate the ordinal position of each object, first through tenth, and the ordered position of each object.
How Big is Your Foot?
Launch & Activity
SOL K.10 The student will compare two objects or events, using direct comparisons or nonstandard units of measure, according to one or more of the following attributes: length (shorter, longer), height (taller, shorter), weight (heavier, lighter), temperature (hotter, colder). Examples of nonstandard units include foot length, hand span, new pencil, paper clip, and block.
1st Grade Math
Bunny Hip Hop
Launch
SOL 1.1 The student will a) count from 0 to 100 and write the corresponding numerals;
and b) group a collection of up to 100 objects into tens and ones and
write the corresponding numeral to develop an understanding of place value.
Activity
SOL 1.2 The student will count forward by ones, twos, fives, and tens to 100 and backward by ones from 30.
When does it Happen?
Launch & Activity
SOL 1.8 The student will tell time to the half-hour, using analog and digital clocks.
Ten is our Friend!
Launch
SOL 1.5 The student will recall basic addition facts with sums to 18 or less and the corresponding subtraction facts.
Activity SOL 1.6 The student will create and solve one-step story and picture
problems using basic addition facts with sums to 18 or less and the corresponding subtraction facts.
2nd Grade Math
Creative Cards
Launch & Activity
SOL 2.16 The student will identify, describe, compare, and contrast plane and solid geometric figures (circle/sphere, square/cube, and rectangle/rectangular prism).
Piggy Banks
Launch & Activity
SOL 2.10 The student will a) count and compare a collection of pennies, nickels, dimes, and
quarters whose total value is $2.00 or less; and b) correctly use the cent symbol (¢), dollar symbol ($), and
decimal point (.).
Show What You Know!
Launch
SOL 2.2 The student will a) identify the ordinal positions first through twentieth, using an
ordered set of objects; and b) write the ordinal numbers.
Activity
SOL 2.8 The student will create and solve one- and two-step addition and subtraction problems, using data from simple tables, picture graphs, and bar graphs.
SOL 2.9 The student will recognize and describe the related facts that represent and describe the inverse relationship between addition and subtraction.
Pies for Sale
Launch SOL 2.19 The student will analyze data displayed in picture graphs,
pictographs, and bar graphs.
Activity
SOL 2.17 The student will use data from experiments to construct picture graphs, pictographs, and bar graphs.
SOL 2.19 The student will analyze data displayed in picture graphs, pictographs, and bar graphs.
3rd Grade Math
Playful Puppies
Launch
SOL 3.10 The student will a) measure the distance around a polygon in order to determine
perimeter; and b) count the number of square units needed to cover a given
surface in order to determine area.
SOL 3.20 The student will a) investigate the identity and the commutative properties for
addition and multiplication; and b) identify examples of the identity and commutative properties
for addition and multiplication.
Activity
SOL 3.5 The student will recall multiplication facts through the twelves table, and the corresponding division facts.
SOL 3.6 The student will represent multiplication and division, using area, set, and number line models, and create and solve problems that involve multiplication of two whole numbers, one factor 99 or less and the second factor 5 or less.
SOL 3.10 The student will a) measure the distance around a polygon in order to determine
perimeter; and b) count the number of square units needed to cover a given
surface in order to determine area.
SOL 3.20 The student will a) investigate the identity and the commutative properties for
addition and multiplication; and b) identify examples of the identity and commutative properties
for addition and multiplication.
Correcting the Calculator
Launch & Activity
SOL 3.1 The student will a) read and write six-digit numerals and identify the place value
and value of each digit; b) round whole numbers, 9,999 or less, to the nearest ten,
hundred, and thousand; and c) compare two whole numbers between 0 and 9,999, using
symbols (>, <, or = ) and words (greater than, less than, or equal to).
SOL 3.2 The student will recognize and use the inverse relationships between addition/subtraction and multiplication/division to complete basic fact sentences. The student will use these relationships to solve problems.
Fraction Reactions
Launch & Activity
SOL 3.3 The student will a) name and write fractions (including mixed numbers)
represented by a model; b) model fractions (including mixed numbers) and write the
fractions’ names; and c) compare fractions having like and unlike denominators, using
words and symbols (>, <, or =).
4th Grade Math
Bugs, Giraffes, Elephants, and More
Launch
SOL 4.2 The student will a) compare and order fractions and mixed numbers; b) represent equivalent fractions; and c) identify the division statement that represents a fraction.
SOL 4.7 The student will a) estimate and measure length, and describe the result in
both metric and U.S. Customary units; and b) identify equivalent measurements between units within
the U.S. Customary system (inches and feet; feet and yards; inches and yards; yards and miles) and between units within the metric system (millimeters and centimeters; centimeters and meters; and millimeters and meters).
SOL 4.14 The student will collect, organize, display, and interpret data from a variety of graphs.
Activity
SOL 4.14 The student will collect, organize, display, and interpret data from a variety of graphs.
Does it Make Sense?
Launch
SOL 4.3 The student will a) read, write, represent, and identify decimals expressed
through thousandths; b) round decimals to the nearest whole number, tenth, and
hundredth; c) compare and order decimals; and
SOL 4.4 The student will a) estimate sums, differences, products, and quotients of whole
numbers; b) add, subtract, and multiply whole numbers; c) divide whole numbers, finding quotients with and without
remainders; and d) solve single-step and multistep addition, subtraction, and
multiplication problems with whole numbers.
Activity
SOL 4.4 The student will a) estimate sums, differences, products, and quotients of whole
numbers; b) add, subtract, and multiply whole numbers; c) divide whole numbers, finding quotients with and without
remainders; and d) solve single-step and multistep addition, subtraction, and
multiplication problems with whole numbers.
The Bigger Half
Launch & Activity
SOL 4.2 The student will a) compare and order fractions and mixed numbers; b) represent equivalent fractions; and c) identify the division statement that represents a fraction.
Harry’s Hike
Launch
SOL 4.2 The student will a) compare and order fractions and mixed numbers; b) represent equivalent fractions; and c) identify the division statement that represents a fraction.
Activity
SOL 4.5 The student will a) determine common multiples and factors, including least
common multiple and greatest common factor; b) add and subtract fractions having like and unlike
denominators that are limited to 2, 3, 4, 5, 6, 8, 10, and 12, and simplify the resulting fractions, using common multiples and factors;
c) add and subtract with decimals; and d) solve single-step and multistep practical problems involving
addition and subtraction with fractions and with decimals.
5th Grade Math
Packed Parking
Launch
SOL 5.4 The student will create and solve single-step and multistep practical problems involving addition, subtraction, multiplication, and division with and without remainders of whole numbers.
Activity
SOL 5.5 The student will a) find the sum, difference, product, and quotient of two numbers
expressed as decimals through thousandths (divisors with only one nonzero digit); and
b) create and solve single-step and multistep practical problems involving decimals.
SOL 5.6 The student will solve single-step and multistep practical problems involving addition and subtraction with fractions and mixed numbers and express answers in simplest form.
Finding Fractions
Launch
SOL 5.2 The student will a) recognize and name fractions in their equivalent decimal form
and vice versa; and b) compare and order fractions and decimals in a given set from
least to greatest and greatest to least.
Activity
SOL 5.17 The student will describe the relationship found in a number pattern and express the relationship.
SOL 5.18 The student will a) investigate and describe the concept of variable; b) write an open sentence to represent a given mathematical
relationship, using a variable; c) model one-step linear equations in one variable, using addition
and subtraction; and d) create a problem situation based on a given open sentence,
using a single variable.
SOL 5.19 The student will investigate and recognize the distributive property of multiplication over addition.
Varying Volumes
Launch & Activity
SOL 5.8 The student will a) find perimeter, area, and volume in standard units of measure; b) differentiate among perimeter, area, and volume and identify
whether the application of the concept of perimeter, area, or volume is appropriate for a given situation;
c) identify equivalent measurements within the metric system; d) estimate and then measure to solve problems, using U.S.
Customary and metric units; and e) choose an appropriate unit of measure for a given situation
involving measurement using U.S. Customary and metric units.
SOL 5.13 The student, using plane figures (square, rectangle, triangle, parallelogram, rhombus, and trapezoid), will
a) develop definitions of these plane figures; and b) investigate and describe the results of combining and
subdividing plane figures.
Location, Location, Location
Launch
SOL 5.17 The student will describe the relationship found in a number pattern and express the relationship.
Activity
SOL 5.18 The student will a) investigate and describe the concept of variable; b) write an open sentence to represent a given mathematical
relationship, using a variable; c) model one-step linear equations in one variable, using addition
and subtraction; and d) create a problem situation based on a given open sentence,
using a single variable.
SOL 5.19 The student will investigate and recognize the distributive property of multiplication over addition.
Mathematics Literature Connections Organized by Curriculum Units
Grade K Math Literature Connections
Unit 2: Counting
One, Two, Skip a Few: First Number Rhymes by Roberta Arenson
98,99,100! Ready or Not, Here I come! by Marilyn Bums and Teddy Slater
Unit 3: Comparing Sets
20 Hungry Piggies: A Number Book by Trudy Harris
Ten Little Rubber Ducks by Eric Carle
Ten Little Caterpillars by Bill Martin Jr
Henry the Fourth by Stuart J. Murphy
One Monday Morning by Uri Shulevitz
The Napping House by Audrey Wood
Tally O’Malley by Stewart J. Murphy
So you want to be President? By Judith St. George
The Great Graph Contest By Loreen Leedy
Unit 4: Geometry & Sorting
Dave’s Down-to-Earth Rock Shop by Stuart J. Murphy
Unit 5: Shapes in Space
Twizzlers Shapes and Patterns by Jerry Pallotta
Unit 6: Geometry & Fractions
Give Me Half by Stuart J. Murphy
Full House by Dayle Ann Dodds
Unit 7: Measuring My World
Measuring Up by J.E. Osborne
Dumpling Soup by Jama Kim Rattigan
How Big is a Foot by Rolf Myller
Big and Little by Steven Jenkins
Time to… by Bruce McMillan
Telling Time: How to Tell Time on Digital and Analog Clocks by Jules Older
Telling Time with Big Mama Cat by D. Harper
Biggest, Strongest, Fastest by Steven Jenkins
Inch by Inch by Leo Lionni
Before and After: A Book of Nature Timescapes by Jan Thornhill
Unit 8: Skip Counting & Money
Arctic Fives Arrive by Elinor J. Pinczes
26 Letters and 99 Cents by Tana Hoban
Unit 9: Combining & Separating
More or Less by Stuart J. Murphy
Animals on Board by Stuart J. Murphy
A Quarter from the Tooth Fairy by Caren Holtzman
Grade 1 Math Literature Connections
Unit 2: Sorting, Ordering, & Patterns
Twizzlers Shapes and Patterns by Jerry Pallotta
Unit 3: Developing a Base Ten System
Moira’s Birthday by Robert Munsch
Something Good by Robert Munsch
Is It Larger? Is It Smaller? By T. Hoban
One Hundred Hungry Ants by Elinor J. Pinczes
Ten Sly Piranhas: A Counting Story in Reverse by William Wise
How Many, How Many, How Many by Rick Walton
98, 99, 100! Ready or Not, Here I Come! By Marilyn Burns and Teddy Slater
Stay in Line by Teddy Slater
Unit 4: Geometry & Fractions
Three Pigs, One Wolf, and Seven Magic Shapes by Grace Maccarone
Flat Stanley by J. Brown
The Shapes We Eat by Simone T. Ribke
Give Me Half! By Stuart J. Murphy
Gator Pie by L. Mathews
Unit 5: Time & Fractions
Give Me Half by Stuart J. Murphy
Telling Time: How to Tell Time on Digital and Analog Clock by Jules Older
Before and After: A Book of Nature Timescapes by Jan Thornhill
Unit 6: Working With Data
Probably Pistachio by Stuart J. Murphy
So You Want to be President? By Judith St. George
The Great Graph Contest by Loreen Leedy
Ready, Set, Hop! By Stuart J. Murphy
Bunches and Bunches of Bunnies by Mathews and Bassett
Unit 7: Combining & Separating
Rooster’s Off to See the World by Eric Carle
Round Trip by A. Jonas
Lemonade For Sale by Stuart J. Murphy
Unit 8: Measuring My World
How Do You Measure Weight? by Thomas K. and Heather Adamson
The Greedy Triangle by Marilyn Burns
Dumpling Soup by Jama Kim Rattigan
How Big is a Foot? by Rolf Myller
Big and Little by Steven Jenkins
Biggest, Strongest, Fastest by Steven Jenkins
Inch by Inch by Leo Lionni
More or Less by Stuart J. Murphy
Best Bug Parade by Stuart J. Murphy
Me and the Measure of Things by J. Sweeney
Unit 9: Applying Place Value
Shoes, Shoes, Shoes by A. Morris
Unit 10: Whole Number Computation
Animals on Board by Stuart J. Murphy
Elevator Magic by Stuart J. Murphy
Ten Black Dots by Donald Crew
Rooster’s Off to See the World by Eric Carle
Elevator Magic by Stuart J. Murphy
How High Can a Dinosaur Count? by V. Fisher
Unit 11: Skip Counting & Money
The Penny Pot by Stuart J. Murphy
Grade 2 Math Literature Connections
Unit 2: Extending Place Value
The Crayon Counting Book by Pam Munoz
Underwater Counting: Even Numbers by Jerry Pallotta
Unit 3: Computational Fluency
Growing Patterns: Fibonacci Numbers in Nature by S.G. and R.P. Campbell
Mission: Addition by Loreen Leedy
Each Orange Had 8 Slices: A Counting Book by Paul Giganti
Elevator Magic by Stuart J. Murphy
Unit 4: Applying Place Value to Computation/Problem Solving
Great Estimations by Bruce Goldstone
How Many Seeds in a Pumpkin? By Margaret McNamara and G. Brian Karas
How Many Feet? How Many Tails? A Book of Math Riddles by Marilyn Burns
Sam and the Lucky Money by K. Chinn
Balancing Act by Ellen Stoll Walsh
Betcha by Stuart J. Murphy
Unit 5: Probability & Data
Frog and Toad are Friends by A. Lobel
Polar Bear Math: Learning About Fractions from Klondike and Snow by Nagda and Bickel
Get Up and Go! By Stuart J. Murphy
Unit 6: Data & Problem Solving
So You Want to be President? By Judith St. George
Unit 7: Time & Temperature
Telling Time: How to Tell Time on Digital and Analog Clock by Jules Older
Before and After: A Book of Nature Timescapes by Jan Thornhill
Why Mosquitoes Buzz in People’s Ears: A West African Tale by V. Aardema
The Grouchy Lady Bug by Eric Carle
Chimp Math: Learning About Time from a Baby Chimpanzee by Nagda and Bickel
What Time Is It? A Book of Math Riddles by Sheila Keenan
Unit 8: Geometry & Fractions
Eating Fractions by Bruce McMillan
Give Me Half by Stuart J. Murphy
Full House by Dayle Ann Dodds
The Patchwork Quilt by Valerie Flournoy
Unit 9: Measuring My World
Inch by Inch by Leo Lionni
How Big is a Foot? By Rolf Myller
Dumpling Soup by Jama Kim Rattigan
Big and Little by Steven Jenkins
Biggest, Strongest, and Fastest by Steven Jenkins
More or Less by Stuart J. Murphy
Unit 10: Skip Counting & Money
Jelly Beans for Sale by Bruce McMillan
The Penny Pot by Stuart J. Murphy
The Coin Counting Book by Rosanne Lanczak Williams
Once Upon a Dime by Nancy Kelly Allen
Grade 3 Math Literature Connections
Unit 2: Place Value
Many Is How Many? By Illa Pondendorf
A Light in the Attic (“How Many, How Much” and “Overdues”) by Shel Silverstein
Counting on Frank by Rod Clement
How Much Is a Million? by David M. Schwartz
If You Made a Million by David M. Schwartz
Moira’s Birthday by Robert Munsch
Something Good by Robert Munsch
Unit 3: Computation With Whole Numbers (addition/subtraction)
Ten Black Dots by Donald Crews
Dealing with Addition Lynette Long
One Duck Stuck by Phyllis Root
One Gorilla by Atsuko Morozumi
A Three Hat Day by Laura Geringer
Unit 4: Money
Alexander, Who Used To Be Rich Last Sunday by Judith Viorst
Penny: The Forgotten Coin by Denise Brenna-Nelson
The Coin Counting Book by Rozanne Lanczak Williams
The Penny Pot by Stuart Murphy
Pigs Will Be Pigs: Fun With Math and Money by Amy Axelrod
Unit 5: Computation With Whole Numbers (multiplication/division)
Amanda Bean’s Amazing Dream by Cindy Neuschwander
A Remainder of One (*extension) by Elinor J. Pinczes
One Hundred Angry Ants by Elinor J. Pinczes
2 x 2 = Boo by Loreen Leedy
7 x 9 Trouble by Claudia Mills
Too Many Kangaroo Things to Do by Stuart Murphy
Divide and Ride by Stuart Murphy
Bananas Jacqueline Farmer
Centipede’s 100 Shoes by Tony Ross
Ten Times Better by Richard Michelson
Unit 6: Patterns & Data
Emma’s Christmas by Irene Trivias
The Doorbell Rang by Pat Hutchins
One Hundred Angry Ants by Elinor Pinczes
She Came Bringing Me That Little Baby Girl by Eloise Greenfield
Knots on a Counting Rope by Bill Martin Jr.
Berries, Nuts, and Seeds by Diane L. Burns
Lemonade for Sale by Stuart Murphy
Tiger Math: Learning to Graph from a Baby Tiger by Ann Whitehead Nagda
Grapes of Math by Greg Tang
The Quilting Bee by Gail Gibbons
Two Ways to Count to Ten: A Liberian Folktale by Ruby Dee
Unit 7: Geometry
The Important Book by Margaret Wise Brown
Three Pigs, One Wolf, and Severn Magic Shapes by Grace Maccarone
Pablo’s Tree Pat Mora
If You Were a Polygon Marcie Aboff
It Looked Like Spilt Milk by Charles G. Shaw
Mummy Math by Cindy Neuschwander
Shape Up by David Adler
A Cloak for the Dreamer by Aileen Friedman
Unit 8: Fractions, Probability, & Measurement (length) / Unit 9: Computation With Fractions
Eating Fractions by Bruce McMillan
Seven Little Hippos by Mike Thaler
Shoes, Shoes, Shoes by Ann Morris
Biggest, Strongest, Fastest Steve Jenkins
The Wolf’s Chicken Stew Keiko Kasza
A Very Improbably Story: A Math Adventure by Edward Einhorn
The Thirteen Days of Halloween Carool Greene
The Doorbell Rang Pat Hutchins
Whole-y Cow, Fractions are Fun! by Taryn Souders
Apple Fractions by Jerry Pallotta
The Hershey’s Milk Chocolate Bar Fractions BookU by Jerry Pallotta
Fraction Action by Loreen Leedy
Unit 10: Elapsed Time and Temperature
Telling Time: How to Tell Time on Digital and Analog Clocks by Jules Older
What Time is it, Mr. Crocodile? By Judy Sierra
Chimp Math by Ann Whitehead Nagda
Unit 11: Measurement
Spaghetti and Meatballs for All by Marilyn Burns
Perimeter, Area, and Volume David A. Adler
Pastry School in Paris Cindy Neuschwander
Measuring Penny (length) by Loreen Leedy
Biggest, Strongest, Fastest by Steve Jenkins
Is a Blue Whale the Biggest Thing There Is? by Robert E. Wells
Polly’s Pen Pal by Stuart L. Murphy
Spaghetti and Meatballs for All by Marilyn Burns
Room for Ripley by Stuart Murphy
Grade 4 Math Literature Connections
Unit 2: Number Sense: Whole Numbers
A Million Fish…More or Less by Patricia C. McKissack
Unit 3: Whole Number Operations & Applications (adding & subtracting)
Math Curse by Jon Scieszka and Lane Smith
The $1.00 Word Riddle Book by Marilyn Burns
Esio Trot by Roald Dahl
From Seashells to Smart Cards: Money and Currency (everyday economics) by Ernestine
Giesecke
Anno’s Magic Seeds by Mitsumasa Anno
Equal Shmequal by Virginia Kroll
Unit 4: Whole Number Operations & Applications (multiplication & division)
The King’s Chessboard by David Birch
The Man Who Counted: A Collection of Mathematical Adventures by Malba Tahan
Math Curse by Jon Scieszka and Lane Smith
Hottest, Coldest, Highest, Deepest by Steve Jenkins
In the Next Three Seconds…Predictions for the Millenium by Comp. Rowland Morgan
Ten Times Better by Richard Michelson
Two Ways to Count to Ten: A Liberian Folktale by Ruby Dee
A Remainder of One by Elinor J. Pinczes
Counting on Frank by Rod Clement
Unit 5: Data & Statistics
The Great Graph Contest by Loreen Leedy
Unit 6: Number Sense: Rational Numbers
The Man Who Counted: A Collection of Mathematical Adventures by Malba Tahan
One Riddle, One Answer by Lauren Thompson
Icebergs and Glaciers by Seymour Simon
Tiger Math: Learning to Graph from a Baby Tiger by Ann W. Nagda and Cindy Bickel
Unit 7: Rational Number Operations
Jump, Kangaroo Jump (Math Start) by Stuart Murphy and Kevin O’Malley
Pizza Counting by Christina Dobson
Piece=Part=Portion by Gifford and Thaler
Fractions=Trouble! By Claudia Mills
Unit 8: Probability & Data Using Rational Numbers
Jumanji by Chris Van Allsburg
A Very Improbable Story by Edward Einhorn and Adam Gustavson
Pigs at Odds by Amy Axelrod and Sharon Nally
Unit 9: Patterns & Measurement
G is for Googol: A Math Alphabet Book by David M. Schwartz
How Much, How Many, How Far, How Heavy, How Long, How Tall Is 1000? by Helen
Nolan
Icebergs and Glaciers by Seymour Simon
If You Hopped Like a Frog by David M. Schwartz
Is a Blue Whale the Biggest Thing There Is? By Robert E. Wells
Biggest, Strongest, Fastest by Steve Jenkins
Unit 10: Plane Geometry & Transformations
Marvelous Math by Lee Bennett Hopkins
The Warlord’s Puzzle by Virginia Walton Pilegard
Shape Up! Fun with Triangles and Other Polygons by David Adler and Nancy Tobin
Spaghetti and Meatballs for All! by Marilyn Burns and Debbie Tilley
Chickens on the Move (Math Matters!) by Pamela Pollack
Grade 5 Math Literature Connections
Unit 2
A Remainder of One by Elinor Pinczes
My Even Day by Doris Fisher
The Grapes of Math by Greg Tang
Math Appeal by Greg Tang
Among the Odds and Evens by Prescilla Turner
Spaghetti and Meatballs for All by Marilyn Burns
Unit 3
Germs Make Me Sick by Melvin Berger
Bats on Parade by Kathi Appelt
Unit 4
Alexander Who Used to Be Rich Last Sunday by Judith Viorst
Fraction Fun by David Adler
Unit 5
Measuring Penny by Loreen Leedy
Alexander Who Used to Be Rich Last Sunday by Judith Viorst
Counting On Frank by Rod Clements
How Long? How Wide? by Brian Cleary
Millions to Measure by David Schwartz
Fractions, Decimals, and Percents by David Adler
Unit 6
The Greedy Triangle by Marilyn Burns
Sir Cumference and the Dragon of Pi by Cindy Neuschwander
Unit 7
Chimp Math, Tiger Math, Polar Bear Math, and Cheetah Math (series) by Anne Nagda
A More Perfect Union by Betsy Maestro
Model Performance Indicator Information for Curriculum Guides
Embedded in the LCPS curriculum guides are sample Model Performance Indicator (MPI) tables (below).
These tables will be useful as you differentiate instruction for all of your learners, but they are especially
helpful for English Language Learners. Below are frequently asked questions about MPI.
What is a Model Performance Indicator (MPI)?
An MPI is a tool that can be used to show examples of how language is processed or produced within a
particular context, including the language with which students may engage during classroom instruction and
assessment.
Each MPI contains three main parts:
Language Function: The first part of an MPI, this shows how students are processing/producing
language at each level of language proficiency
Content Stem: This will remain consistent throughout an MPI strand and should reflect the knowledge
and skills of the state’s content standards
Support: The final part of an MPI, this highlights the differentiation that should be incorporated for
students at each language level by suggesting appropriate instructional supports for students at each
level of language proficiency
The samples provided also include an example context for language use that provides a brief descriptor of the
activity or task in which students would be engaged, while the inclusion of topic-related language helps to
support the emphasis on imbedding academic language instruction into our content-area teaching practices.
How can these sample MPIs help me?
Educators can use MPI strands in several ways:
to align students’ performance to levels of language development
as a tool for creating language objectives/targets that will help extend students’ level of language
proficiency
as a means for differentiating instruction that incorporates the language of the content area in a way that
meets the needs of students’ levels of language proficiency
An MPI strand helps illustrate the progression of language development from one proficiency level to the next
within a particular context. As these strands are examples, they represent one of many possibilities; therefore,
they can be transformed in order to be made more relevant to the individual classroom context.
Where can I get more information about WIDA, MPIs, etc.?
See My Learning Plan for several WIDA training modules
Introduction to the WIDA ELD Standards
Transforming the WIDA ELD Standards
Interpreting the WIDA ACCESS Score Report
The information above was adapted from the 2012 Amplification of the English Development Standards Kindergarten-Grade 12 resource guide and can be accessed at www.wida.us
SOL Strand and Bullet: 3.17 The student will
a) Collect and organize data, using observations, measurements, surveys, or experiments;
b) Construct a line plot, a picture graph, or a bar graph to represent the data; and
c) Read and interpret the data represented in line plots, bar graphs, and picture graphs and write a sentence analyzing the data.
Example Context for Language Use: Students will gather data from their classmates on a topic of their choice (e.g., birthdays, favorite color,
favorite sport, number of siblings) or data from a newspaper on a topic of their choice (e.g., daily temperatures, sports scores). Students will create a
bar graph, picture graph, or line plot to record their data and write a sentence analyzing the data. As a class, students will practice interpreting
student-graphed or student-plotted data.
COGNITIVE FUNCTION: Students at all levels of English language proficiency will ANALYZE data represented in line plots, picture graphs,
and bar graphs.
SP
EA
KIN
G
Level 1
Entering
Level 2
Emerging
Level 3
Developing
Level 4
Expanding
Level 5
Bridging
Lev
el 6-R
each
ing
Identify the categories of
data represented in a line
plot, picture graph, or bar
graph using an illustrated
word bank in a small
group
Describe the categories
of data represented in a
line plot, picture graph,
or bar graph using an
illustrated word/phrase
bank and oral sentence
frames with a partner
Discuss data represented
in a line plot, picture
graph, or bar graph using
oral sentence starters and
following a model with a
partner
Present data represented
in a line plot, picture
graph, or bar graph with
a partner
Present and explain
data represented in a
line plot, picture graph,
or bar graph with a
partner
RE
AD
ING
Distinguish categories of
data represented in a line
plot, picture graph, or bar
graph using an illustrated
and labeled example and
an illustrated word bank
in a small group
Compare categories of
data represented in a
line plot, picture graph,
or bar graph using an
illustrated and labeled
example in a small
group
Formulate questions about
data represented in a line
plot, picture graph, or bar
graph based on a template
in a small group
Interpret data
represented in a line plot,
picture graph, or bar
graph in a small group
Analyze data
represented in a line
plot, picture graph, or
bar graph in a small
group
WR
ITIN
G
Level 1
Entering
Level 2
Emerging
Level 3
Developing
Level 4
Expanding
Level 5
Bridging Lev
el 6-R
each
ing
Create labels for data
represented in line plots,
picture graphs, and bar
graphs using an
illustrated template and
an illustrated word bank
in a small group
Create labels for data
represented in line plots,
picture graphs, and bar
graphs using a template
with a partner
Describe data represented
in line plots, picture
graphs, and bar graphs
using written sentence
frames with a partner
Interpret data represented
in line plots, picture
graphs, and bar graphs
using a written example
and a phrase bank
Analyze data
represented in line
plots, picture graphs,
and bar graphs in a
math journal
TOPIC-RELATED LANGUAGE: Students at all levels of English language proficiency interact with grade level words and expressions such as:
data, collect, organize, observations, measurements, surveys, experiments, line plot, picture graph, bar graph, title, axis, key increments, number line,
categories, identify, describe, discuss, present, explain, create, interpret, analyze
SOL Strand and Bullet: 3.18 The student will investigate and describe the concept of probability as chance and list possible results of a give situation Example Context for Language Use: After reviewing the definition of probability (the chance of an event happening), students will explore the
meaning of vocabulary words associated with the concept of probability: certain, likely, equally likely, as likely as, unlikely, impossible. Given a
scenario presented with realia (e.g., a cookie jar has 5 chocolate chip cookies and 15 oreo cookies), students will answer questions about the
probability of reaching into the cookie jar and selecting an oreo (likely) or a chocolate chip cookie (unlikely) or an oatmeal cookie (impossible).
Students will then create their own scenarios and a set of probability questions.
COGNITIVE FUNCTION: Students at all levels of English language proficiency will ANALYZE the concept of probability and all possible
outcomes of a given situation.
SP
EA
KIN
G
Level 1
Entering
Level 2
Emerging
Level 3
Developing
Level 4
Expanding
Level 5
Bridging
Lev
el 6-R
each
ing
Discuss the concept of
probability and all
possible outcomes of a
given situation (e.g.,
different types of cookies
in a cookie jar) using
visuals, realia, and
following a model in a
small group
Discuss the concept of
probability and all
possible outcomes of a
given situation (e.g.,
different types of
cookies in a cookie jar)
using realia and oral
sentence frames in a
small group
Ask and answer questions
about the concept of
probability and all
possible outcomes of a
given situation (e.g.,
different types of cookies
in a cookie jar) using
realia in a small group
Explain the concept of
probability and all
possible outcomes of a
given situation (e.g.,
different types of cookies
in a cookie jar) with a
partner
Justify a prediction
based on the concept of
probability and all
possible outcomes of a
given situation (e.g.,
different types of
cookies in a cookie jar)
with a partner
R
EA
DIN
G
Associate experiment
results with the concept
of probability and all
possible outcomes of a
given situation based on
illustrated text and
labeled illustrations in a
small group using L1
Associate experiment
results with the concept
of probability and all
possible outcomes of a
given situation based on
illustrated text and
labeled illustrations in a
small group
Formulate questions about
the concept of probability
and all possible outcomes
of a given situation from
written scenarios using a
bilingual dictionary with a
partner
Draw conclusions about
the concept of probability
and all possible outcomes
of a given situation from
written scenarios with a
partner
Analyze the concept of
probability and all
possible outcomes of a
given situation from
written scenarios
WR
ITIN
G
Level 1
Entering
Level 2
Emerging
Level 3
Developing
Level 4
Expanding
Level 5
Bridging
Lev
el 6-R
each
ing
Describe in a math
journal the concept of
probability and all
possible outcomes of a
given situation using a
template and an
illustrated word/phrase
bank in a small group
using L1 or L2
Describe in a math
journal the concept of
probability and all
possible outcomes of a
given situation using a
writing template and a
word/phrase bank in a
small group
Write questions about the
concept of probability and
all possible outcomes of a
given situation using
question frames and a
bilingual dictionary with a
partner
Create a diagram to show
the concept of probability
and all possible outcomes
of a given situation with
a partner
Create written
scenarios to teach the
concept of probability
and all possible
outcomes of a given
situation with a partner
TOPIC-RELATED LANGUAGE: Students at all levels of English language proficiency interact with grade level words and expressions such as:
probability, investigate, possible outcome, predict, certain, likely, equally likely, as likely as, unlikely, impossible, counters, spinners, number cubes,
discuss, ask and answer questions, explain, justify, associate, formulate questions, draw conclusions, analyze, describe