Math Curriculum - dinwiddie.k12.va.us Curriculum . 2 ... read, write, identify place value in 3‐digit numeral; b) ... leave the digit in the rounding place as it is, and

1 Revised: 8/20/16

Dinwiddie County Public Schools provides each student the

opportunity to become a productive citizen, engaging the

entire community in the educational needs of our children.

3rd Grade

Math Curriculum

2 Revised: 8/20/16

Dinwiddie County Public Schools

3rd Grade Math Curriculum

The DCPS scope and sequence/pacing guide contains key topics that must be cross referenced continuously with the

VDOE enhanced scope and sequence and VDOE curriculum framework.

Once taught, target skills should be cumulatively reviewed throughout the school year; emphasis should be placed on covering skills that were most challenging according to assessment results.

Weekly math drills should start during the first nine weeks.

Manipulatives should be utilized throughout the entire school year to enhance number sense and promote mastery of

concepts and facts.

Daily thirty minute blocks should be dedicated to reviewing previously taught concepts and skills.

Use of Interactive Achievement should be incorporated into math instruction and assessment paying close attention to

technology enhanced items, terminology, and Webb’s DOK.

DOE LINKS

Mathematics SOL Curriculum Framework

Mathematical Instructional Resources

http://www.doe.virginia.gov/testing/sol/standards_docs/mathematics/index.shtml

http://www.doe.virginia.gov/instruction/mathematics/index.shtml

3 Revised: 8/20/16

Nine Weeks

Approximate

# of Days Taught

Topic Targeted SOL Curriculum Framework

1

12

Place Value: Read and write 6 digit numerals, Identify value and place value of digit

Rounding: tens, hundreds, or thousands Comparing: two whole numbers

3.1a-c

p. 2-4

1

10

Adding Whole Numbers: estimate and solve for the sum of

two whole numbers 4 digits or less Fact Families: Recognize and use the inverse relationships to complete basic fact sentences

Single and Multi-Step Word Problems

3.4 3.2

p. 5 p. 9-10

1

12

Subtracting Whole Numbers: estimate and solve to find the difference of

two whole numbers 4 digits or less with/without regrouping

Fact Families: Recognize and use the inverse relationships to complete basic fact sentences

Single and Multi-Step Word Problems

3.2 3.4

p. 5 p. 9-10

1

5

Data & Graphs: Construct, Read and Interpret Picture Graphs

Write a sentence analyzing the data

3.17 a-c

p. 30-31

1

5

Review/Test 1st Nine Weeks Benchmark

See Above

Review

4 Revised: 8/20/16

Nine Weeks

Approximate

# of Days Taught


2 5

Data & Graphs: Construct, Read and Interpret Line Plots and Bar Graphs

Write a sentence analyzing the data

3.17 a-c

p. 30-31

2

10

Multiplication Concepts (using area, set, and number line models); Facts and Fact Families through 12’s

(Recognize and use the inverse relationships to complete basic fact sentences); Single and Multi-Step Word Problems

(Note: 2 x 1 concept will be taught in 3rd

Nine Weeks)

3.2 3.5 3.6

p. 5, 11-13

2

9

Division Concepts (using area, set, and number line models); Facts & Fact Families through 12’s

(Recognize and use the inverse relationships to complete basic fact sentences); Single and Multi-Step Word Problems

3.2 3.5

p. 5, 11

2 5

Fractions: name and write fractions and mixed numbers (halves, thirds, fourths, eighths, tenths, twelfths) represented by a model;

Comparing fractions having like and unlike denominators using concrete materials and pictorial models representing area/regions, length/measurements,

number lines, and sets.

3.3 a-c p. 6-7

2 3

Adding and Subtracting Proper Fractions with like denominators of twelve or less , Using concrete materials and pictorial models representing area/regions,

length/measurements, number lines, and sets.

3.7 p. 14

2 4

Telling Time to the nearest minute, Determine elapsed time in 1 hour increment;

Solve practical problems in relation to the time that has elapsed.

3.11 a, b p. 20

2

3

Equivalent Time Periods: the relationships among days, months, and years, number of minutes in an hour and hours in a day

3.12

p. 22

5 Revised: 8/20/16

Nine Weeks

Approximate

# of Days Taught


2 2

Temperature: read to nearest degree (Celsius and Fahrenheit )

3.13 p. 22

2 3

Review/ Test 2nd Nine Weeks Benchmark

See Above Review

3 5

Multiplication 2 by 1 digit Introduction of concept (building number sense using arrays, base ten blocks, number

line, and repeated addition) and the use of algorithms.

3.6 p. 12-13

3 10

Linear Measurement: estimate and determine actual length in customary and metric units

inch, ½ inch, foot, yard, centimeter, and meter

3.9 a p. 17-18

3 4

Liquid Volume: estimate and determine actual volume in customary and metric units

cup, pint, quart, gallon, liter

3.9b p. 17-18

3 4

Weight/Mass: estimate and determine actual weight/mass in customary and metric units

ounce, pound, gram, and kilogram

3.9 c p. 17-18

3 4

Perimeter: measure each side of a polygon and add to determine the perimeter Area: count square units to find area

3.9d, 3.10 p. 17-19

3 8

Geometry: 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) Identify and draw representations of points, line segments, rays, angles, and lines

Identify and describe congruent and noncongruent plane figures

3.14, 3.15, 3.16 p. 24-28

3 8

Money: Count the value of a collection of bills and coins total value $5.00 or less Compare the value of two sets of bills and coins

3.8 p. 16

6 Revised: 8/20/16

Nine Weeks

Approximate

# of Days Taught


Make change from $5.00 or less

3

3 Review/Test 3

rd Nine Weeks Benchmark See Above Review

4 5

Probability: Define probability, list all possible outcomes(tree diagrams),

identify the degree of likelihood of an outcome occurring (unlikely, impossible, likely, equally likely)

3.18 p. 32-33

4 10

Patterns: Recognize, describe, and extend repeating and

growing numeric and geometric patterns (numbers, tables, and pictures)

3.19 p. 35-36

4 5

Algebra: Identity and Commutative Properties for Addition and Multiplication

(Identify examples) Write number sentences to represent equivalent mathematical relationships (4x3=14-2)

3.20a-b p. 37

4

5 EOY Student Growth Assessment See Above

4 Remainder

SOL Test Review

SOL

Review

7 Revised: 8/20/16

Dinwiddie County Public Schools Math Curriculum

SOL 3.1 – 1st Nine Weeks Blueprint Categories Number of Items Number of

Items 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).

Number and Number Sense Grade 3 SOL 7

Prior Knowledge

2.1 a) read, write, identify place value in 3‐digit numeral; b) round 2‐digit numbers to nearest ten; c) compare two whole numbers 0‐999 with symbols and words

Understanding the Standard

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: – 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,

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

8 Revised: 8/20/16

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.

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: (please teach number sense FIRST!)

– 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.

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.

9 Revised: 8/20/16

Additional Instructional Strategies

Play Video Developing Early Number Sense (grades K-2)

Play Video Using a Beaded Number Line (grades K-2)

Round to the nearest ten using a number line - LearnZillion

Students should use number lines, hundreds charts, and base ten blocks/hundreds grid to round before learning cute rhymes that teach rules. It is important to

develop a number sense of which two tens the number lays between in counting order and which ten it is closest to when counting up or down.

http://www.vdoe.whro.org/instruction/math_2011/developing_early_number_sense/DOE_NUMBER_SENSE_2_1.swf

http://www.vdoe.whro.org/instruction/math_2011/fractions_3/fractions_3.swf

https://www.google.com/url?sa=t&rct=j&q=&esrc=s&source=web&cd=1&cad=rja&uact=8&ved=0CB0QFjAAahUKEwj4ju_-vP7GAhVXGZIKHeA7CjM&url=https%3A%2F%2Flearnzillion.com%2Flessons%2F1786-round-to-the-nearest-ten-using-a-number-line&ei=vcy3Vbi8M9eyyATg96iYAw&usg=AFQjCNGPmYgDJKP__8t-N-kdXJ7rM0gIhw&bvm=bv.98717601,d.aWw

http://www.doe.virginia.gov/instruction/mathematics/resources/videos/index.shtml

http://www.doe.virginia.gov/instruction/mathematics/resources/videos/index.shtml

10 Revised: 8/20/16

Allow students to model the number to be rounded with base ten blocks. Then have students model the tens the number falls between when counting. Ask the

child to count the ones and decide which ten it is closest to. Make sure the student can verbalize his or her thinking.

11 Revised: 8/20/16

Additional Math Curriculum Resources

http://www.dinwiddie.k12.va.us/infosite/resources/

12 Revised: 8/20/16

Vocabulary

Lessons and TEI Items Trade Books

DOE Vocabulary Cards Handout available: Working with Vocabulary / Concept Development (Word)

Place Value - The value a digit represents depending on its place in the number

Thousands Ones/Units

Hundred Ten One Hundreds Tens Ones

Value - How much a digit is worth according to its place in a number Digit - There are 10 digits; any one of the symbols, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9 Greater Than = (>) Less Than = (<) Equal To = (=) Rounding- means reducing the digits in a number while trying to keep its value similar

Compare – seeing whether two numbers are equal, greater than, or less than each other.

Number and Number Sense Place Value Rounding Whole Numbers Comparing Whole Numbers Grand Prix Place Value Can I Get Your Digits?

Sir Cumference and All the King’s Tens by Cindy

Newschwander

One Hundred Ways to Get to 100 by Jerry Pallotta

A Fair Bear Share by Stuart J. Murphy

How Much, How Many, How Far, How Heavy, How

Long, How Tall is 1000? by Helen Nolan

A Million Fish…More or Less by Patricia C. McKissack

Can You Count to a Googol? by Robert E. Wells

A Place for Zero by Angeline Sparagna Lopresti

Earth Day--Hooray! by Stuart Murphy

How Big is a Million? by Anna Milbourne

How Much is a Million? by David Schwartz

A Million Dots by Andrew Clements

Big Numbers by Edward Packard

Picture Book Lesson Ideas

http://www.doe.virginia.gov/instruction/mathematics/resources/vocab_cards/math_vocab_cards_3.pdf

http://www.doe.virginia.gov/instruction/mathematics/resources/videos/handouts/working_with_vocabulatory.doc


http://www.doe.virginia.gov/instruction/mathematics/elementary/number_sense_module/nns_grade3.pdf

http://www.doe.virginia.gov/testing/solsearch/sol/math/3/mess_3-1a.pdf

http://www.doe.virginia.gov/testing/solsearch/sol/math/3/mess_3-1b.pdf

http://www.doe.virginia.gov/testing/solsearch/sol/math/3/mess_3-1c.pdf

http://www.nsa.gov/academia/_files/collected_learning/elementary/arithmetic/Grand_Prix_Place_Value.pdf

http://www.nsa.gov/academia/_files/collected_learning/elementary/arithmetic/Can_I_Get_Your_Digits.pdf

http://sc45.weebly.com/uploads/5/1/1/0/5110912/meeting_the_math_standards_with_favorite_picture_books.pdf

13 Revised: 8/20/16

Additional Links and Resources – 3rd Grade

Student Links

Practice Test Items

Virtual Manipulatives

Instructional Resources

ABCya

Fun 4 the Brain

Recess Room

Sheppard Software

StarrMatica

Turtle Diary

DOE Practice Items

DOE Released Test

IQ Practice Tests

Jefferson Lab

New York State Assessments *Multiple Languages Interactive Achievement

Quia

Allen Interactive Assessment

Interactivate

National Library of Virtual

Manipulatives

NCTM Illuminations

Grade Level Technology Folder

Internet 4 Classrooms

iPad™ Resources Math Study Jams Pearson Success Net

Promethean Planet

Super Teacher Worksheets

RCPS Math Resources

http://www.abcya.com/

http://www.fun4thebrain.com/index.html

http://www.roomrecess.com/

http://www.sheppardsoftware.com/math.htm

http://www.starrmatica.com/

http://www.turtlediary.com/

http://www.doe.virginia.gov/testing/sol/practice_items/index.shtml

http://www.doe.virginia.gov/testing/sol/released_tests/index.shtml

http://www.iq.poquoson.org/math.htm#two

http://education.jlab.org/solquiz/

http://www.nysedregents.org/elementary.html

http://www.interactiveachievement.com/

http://www.quia.com/

http://www.allenteachers.com/interactive/

http://www.shodor.org/interactivate/activities/byAudience/

http://nlvm.usu.edu/en/nav/vlibrary.html


http://illuminations.nctm.org/Search.aspx?view=search&type=ac&gr=Pre-K-2_3-5

http://www.internet4classrooms.com/math_elem_index.htm

http://studyjams.scholastic.com/studyjams/jams/math/index.htm

https://www.pearsonsuccessnet.com/snpapp/login/PsnLandingPage.jsp?showLandingPage=true

http://www.prometheanplanet.com/

http://www.superteacherworksheets.com/

https://1134461b98b787e104243863e2080174325bad9f.googledrive.com/host/0B2w2sv-hoeskbDdKRVNsNlNldWM/3math.htm

14 Revised: 8/20/16


SOL 3.4 – 1st Nine Weeks Blueprint Categories Grade 3 SOL Number of

Items

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.

Computation and Estimation 3.4, 3.5, 3.6, 3.7 7

Prior Knowledge

SOL 2.8 - create and solve one or two‐step addition or subtraction problems with data from tables, picture graphs, or bar graphs SOL 2.6 - estimate the sum of two whole numbers, each of which is 99 or less SOL 2.7 - estimate the difference of two whole numbers, each of which is 99 or less



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.

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.


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

15 Revised: 8/20/16

– 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 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.

Develop flexible methods of adding whole numbers by combining numbers in a variety of ways, most depending on place values.

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.

16 Revised: 8/20/16


Regrouping Video Teacher Regrouping Video Student Regrouping Video Alternative Subtraction Methods Video

Students need additional practice solving multistep problems involving the addition and/or subtraction of whole numbers, in particular when information is presented in a table. The questions here provide practice with both addition and subtraction; students continue to find problems of this nature challenging.

http://www.youtube.com/watch?v=Y7qkyMyanjU

http://www.youtube.com/watch?v=DEPA6scSTcg

http://www.youtube.com/watch?v=DEPA6scSTcg

https://www.teachingchannel.org/videos/teaching-subtraction-methods

17 Revised: 8/20/16

Student performance was weaker on single-step subtraction problems when regrouping in more than one place value position was required, as in the examples provided.

18 Revised: 8/20/16

Additional algorithms should be taught to all students and the student allowed to choose the method that works best for them. Alternative algorithms should be modeled throughout the year and encouraged by allowing students to share during Number Talk or Calendar Math. Regrouping of whole numbers should be assessed through the use of manipulatives as well as various algorithms.

19 Revised: 8/20/16

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\

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24 Revised: 8/20/16


Vocabulary


DOE Vocabulary Cards Handout available: Working

with Vocabulary / Concept Development (Word)

Sum - the answer in an addition problem

Difference - the distance between 2 numbers on a number line; the answer to a subtraction problem Regrouping – an equal exchange from one place to the next Whole Numbers - a number from the set {0, 1, 2, 3…}; Numbers greater than 0 with no decimals or fractions.

Addition and Subtraction Number and Number Sense Borrowing from Our Neighbors Add It Up In Number Ville! Adding 2-Digit Numbers with and Without Regrouping Score with Soccer Subtraction

Among the Odds and Evens by Priscilla Turner

Dinner at the Panda Palace by Nadine Bernard

Wescott

Fair Bear Share by Stuart J. Murphy

Math Fables by Greg Tang

Mission Addition by Loreen Leedy

More M & M’s Math by Roger Glass

Subtraction Action by Loreen Leedy

Two Tickets to Ride by Sweigart Brothers Picture Book Lesson Ideas





http://www.doe.virginia.gov/testing/solsearch/sol/math/3/mess_3-4.pdf


http://www.nsa.gov/academia/_files/collected_learning/elementary/arithmetic/Borrowing_from_our_Neighbors.pdf

http://www.nsa.gov/academia/_files/collected_learning/elementary/arithmetic/add_it_up.pdf

http://www.nsa.gov/academia/_files/collected_learning/elementary/arithmetic/add_it_up.pdf

http://www.nsa.gov/academia/_files/collected_learning/elementary/arithmetic/score_with_soccer_sub.pdf

http://www.amazon.com/Priscilla-Turner/e/B001KHTQJI/ref=dp_byline_cont_book_1


25 Revised: 8/20/16


Student Links

Practice Test Items



ABCya

Fun 4 the Brain

Recess Room

Sheppard Software

StarrMatica

Turtle Diary

DOE Practice Items

DOE Released Test

IQ Practice Tests

Jefferson Lab


Quia


Interactivate


Manipulatives

NCTM Illuminations




Promethean Planet


Worksheet Fun

RCPS Math Resources
























http://www.worksheetfun.com/


26 Revised: 8/20/16


SOL 3.2 – 1st Nine Weeks Blueprint Categories Grade 3 SOL Number of Items

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.

Number and Number Sense 3.1a-c, 3.2, 3.3a-c 7

Prior Knowledge

2.5 - Recall basic addition facts and the corresponding subtraction facts



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.


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.

27 Revised: 8/20/16


Additional Math Curriculum Resources Student performance was significantly stronger on questions that required students to identify one related fact sentence when compared to questions that required students to identify all of the related fact sentences in a set. (add, subtract, multiply, divide)


28 Revised: 8/20/16


Student Links

Practice Test Items



ABCya

Fun 4 the Brain

Recess Room

Sheppard Software

StarrMatica

Turtle Diary

DOE Practice Items

DOE Released Test

IQ Practice Tests

Jefferson Lab

New York State Assessments *Multiple Languages


Interactivate


Manipulatives

NCTM Illuminations




Promethean Planet

Vocabulary


DOE Vocabulary Cards Handout available: Working with

Vocabulary / Concept Development (Word)

Fact Families- Inverse Relationships Inverse Relationships-Operations that are opposite of each other; addition and subtraction are inverse operations; multiplication and division are inverse operations

Number and Number Sense Inverse Relationships


























29 Revised: 8/20/16

Interactive Achievement

Quia


Worksheet Fun

RCPS Math Resources






30 Revised: 8/20/16


SOL 3.17 – 1st Nine Weeks – Picture Graphs 2nd Nine Weeks – Line Plots and Bar Graphs

Blueprint Categories Grade 3 SOL Number of Items

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.

Probability, Statistics, Patterns, Functions and Algebra

3.17a-c, 3.18, 3.19, 3.20a-b 6

Prior Knowledge

2.17 - construct picture graphs, pictographs, and bar graphs 2.19 - analyze data displayed in picture graphs, pictographs, and bar graphs



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 whole numbers, usually multiples of 1, 2, 5, or 10.

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.

31 Revised: 8/20/16

– 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.

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).

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.

32 Revised: 8/20/16


Students would benefit from additional practice with questions that require interpretation and analysis of line plots. Student performance is much stronger when questions do not require analysis. Take a moment to read the example. For the example shown on the screen a lower level question could be, “How many neighbors own exactly 1 pet?” Questions such as the ones shown require students to consider what each X represents. For example, students should understand that the two X’s located above the zero on the number line represent the fact that two of Simon’s neighbors own zero pets; the two X’s located above the one on the number line represent the fact that two of Simon’s neighbors each own one pet; the one X located above the two on the number line represents the fact that one of Simon’s neighbors owns two pets; and finally, the one X located above the three on the number line represents the fact that one of Simon’s neighbors owns three pets. The answers to the questions are provided on the screen. A common mistake that students might make in answering the second question would be to simply count all of the X’s, which is the number of neighbors polled. In the equation shown for the solution to the second question, each of the addends is represented by an X on the line plot.

33 Revised: 8/20/16

Students continue to need practice analyzing information presented in pictographs. This item is also an example of how teachers can provide experience with questions that may have more than one correct answer.

34 Revised: 8/20/16

Students need additional practice interpreting bar graphs, particularly with determining which of several statements about the graph is true. The answer to this example and most common error are shown on the screen.



35 Revised: 8/20/16

Vocabulary




Data: pieces of information collected to answer a question

Graph: represents data gathered to answer a question Bar Graph: used to compare amounts of different categories

Horizontal: going side-to-side; like the horizon Vertical: in an up-and-down position; upright Category: a general group Axis: a reference line drawn on a graph; labeled with x and y Scale: a progression of steps

Statistics Through The Year Data Mania Mardi Gras Mania Our Carnival Adventure Vroom! Vroom! Start Your Engines!!!

Probability and Statistics K-5

Lemonade for Sale by Stuart J. Murphy

The Great Graph Contest by Loreen Leedy

Who’s Got Spots? by Linda W. Aber

Family Reunion by Bonnie Bader







http://www.nsa.gov/academia/_files/collected_learning/elementary/data_analysis/mardi_gras_mania.pdf

http://www.nsa.gov/academia/_files/collected_learning/elementary/data_analysis/carnival_adventure.pdf

http://www.nsa.gov/academia/_files/collected_learning/elementary/data_analysis/start_your_engines.pdf

http://www.doe.virginia.gov/testing/sol/standards_docs/mathematics/2001/resources/elementary/probability_module/mprobstatentire.pdf


36 Revised: 8/20/16


Student Links Practice Test Items Virtual Manipulatives


ABCya

Fun 4 the Brain

Recess Room

Sheppard Software

DOE Practice Items

DOE Released Test

IQ Practice Tests

Jefferson Lab

New York State Assessments


Interactivate


Manipulatives

NCTM Illuminations



iPad™ Resources Math Study Jams

Increment: an amount by which something increases or grows Extend: to increase the length or duration of Line Plot: a type of graph used to display data; in a line plot each piece of data is represented

Frequency: how often something happens during a period of time

















37 Revised: 8/20/16

StarrMatica

Turtle Diary

*Multiple Languages Interactive Achievement

Quia

Pearson Success Net

Promethean Planet


Worksheet Fun

RCPS Math Resources










38 Revised: 8/20/16


SOL 3.2 – 2nd Nine Weeks Blueprint Categories Grade 3 SOL Number of Items

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.


Prior Knowledge

2.5 - Recall basic addition facts and the corresponding subtraction facts



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.


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.

39 Revised: 8/20/16


Additional Math Curriculum Resources Student performance was significantly stronger on questions that required students to identify one related fact sentence when compared to questions that required students to identify all of the related fact sentences in a set. (add, subtract, multiply, divide)


40 Revised: 8/20/16


Student Links

Practice Test Items



ABCya

Fun 4 the Brain

Recess Room

Sheppard Software

StarrMatica

Turtle Diary

DOE Practice Items

DOE Released Test

IQ Practice Tests

Jefferson Lab



Interactivate


Manipulatives

NCTM Illuminations




Promethean Planet

Vocabulary




Fact Families- Inverse Relationships Inverse Relationships-Operations that are opposite of each other; addition and subtraction are inverse operations; multiplication and division are inverse operations

Number and Number Sense Inverse Relationships Bugs Can Multiply, So Can I


























http://www.nsa.gov/academia/_files/collected_learning/elementary/arithmetic/bugs_can_multiply.pdf

41 Revised: 8/20/16


Quia


Worksheet Fun

RCPS Math Resources






42 Revised: 8/20/16


SOL 3.5 - 2nd Nine Weeks Blueprint Categories Grade 3 SOL Number of Items

The student will recall multiplication facts through the twelves table, and the corresponding division facts.

Computation and Estimation

3.4, 3.5, 3.6, 3.7 7

Blueprint Categories

2.4 - The student will count forward by twos, fives, and tens to 100, starting at various multiples of 2, 5, or 10…



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

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.


Recall and state the multiplication and division facts through the twelves table.

Recall and write the multiplication and division facts through the twelves table.

43 Revised: 8/20/16

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.



Vocabulary




Multiplication – repeated addition Factors – the numbers that are multiplied to get the product Product – the answer to a multiplication problem Division – repeated subtraction

Multiplication and Division Inverse Relationships How Does Your Garden Grow? Multiplication Strategies-A Day at the Zoo. Multiplication Matters Bugs Can Multiply, So Can I

Amanda Bean’s Amazing Dream by Cindy

Neuschwander

The Best of Times by Greg Tang

The Doorbell Rang by Pat Hutchins

The Great Divide: A Mathematical Marathon by

Dayle Ann Dodds and Tracy Mitchell







http://www.nsa.gov/academia/_files/collected_learning/elementary/arithmetic/How_Does_Your_Garden_Grow.pdf

http://www.nsa.gov/academia/_files/collected_learning/elementary/arithmetic/multiplication_strategies_day_at_zoo.pdf

http://www.nsa.gov/academia/_files/collected_learning/elementary/fractions/multiplication_matters.pdf

http://www.nsa.gov/academia/_files/collected_learning/elementary/arithmetic/bugs_can_multiply.pdf

44 Revised: 8/20/16

Quotient- the answer to a division problem

Skip Counting - counting by the same amount each time Array- a way of displaying objects in rows and columns

The Hershey’s Milk Chocolate Multiplication Book

by Jerry Pallota and Rob Bolster

How Many Feet in the Bed? by Diane Johnston

Hamm and Kate Salley Palmer

Just Add Fun! by Joanne Rocklin and Martin

Lemelman

The King’s Commissioners by Aileen Friedman and

Susan Guevara

One Grain of Rice by Demi

Lemon & Ice & Everything Nice by Catherine

Weiskopf, Marilyn Burns, and Cristina Ong

Multiplying Menace-The Revenge of

Rumpelstiltskin by Pam Calvert

One Hundred Hungry Ants by Elinor J. Pinczes and

Bonnie MacKain

A Remainder of One by Elinor J. Pinczes

What Comes in 2’s, 3’s, & 4’s by Suzanne Aker and

Bernie Karlin

Stay in Line by Teddy Slater, Gioia Fiammenghi and

Marilyn Burns

2 X 2 =Boo! by Loreen Leedy



45 Revised: 8/20/16


Student Links

Practice Test Items



ABCya

Fun 4 the Brain

Recess Room

Sheppard Software

StarrMatica

Turtle Diary

DOE Practice Items

DOE Released Test

IQ Practice Tests

Jefferson Lab


Quia


Interactivate


Manipulatives

NCTM Illuminations




Promethean Planet


Worksheet Fun

RCPS Math Resources


























46 Revised: 8/20/16


SOL 3.6 – 2nd Nine Weeks Blueprint Categories Grade 3 SOL Number of Items

The student will represent multiplication and division, using area, set, and number line models (2nd NW), and create and solve problems that involve multiplication of two whole numbers, one factor 99 or less and the second factor 5 or less (3rd NW).


Prior Knowledge

SOL 3.2, 3.5 – multiplication concepts including inverse relationships SOL 2.5 - The student will recall addition facts with sums to 20 or less and the corresponding subtraction facts.



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)

All students should

Understand the meanings of multiplication and division.

Understand the models used to represent multiplying and dividing whole numbers.


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.

47 Revised: 8/20/16

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.

The number of jumps (two) of a given length (three) is the answer to the question.


Create and solve word problems involving multiplication, where one factor is 99 or less and the second factor is 5 or less.

0 1 2 3 4 5 6

48 Revised: 8/20/16


For SOL 3.6, students need additional practice solving multiplication problems presented in the context of a word problem. The story problems provided on this screen involve situations that are multiplicative, although students might use a less efficient method to arrive at a correct solution.

49 Revised: 8/20/16

Students would benefit from additional practice solving multiplication problems presented in a horizontal format like the first two examples provided. Teachers are encouraged to continue providing students with practice solving multiplication story problems, as in example 3.



50 Revised: 8/20/16




ABCya

Fun 4 the Brain

Room Recess

DOE Practice Items

DOE Released Test

IQ Practice Tests


Interactivate


Manipulatives




Vocabulary



Area –the number of square units needed to cover a surface Set - a collection of distinct items or elements Multiplication- Finding the product of two numbers Division- Finding the quotient of two numbers Number line- A line of numbers in order Factor- The numbers in multiplication problems.

Multiplication and Division Representations Debuting Single Digit by Double Digit Multiplication

















https://www.nsa.gov/academia/_files/collected_learning/elementary/arithmetic/Single__by_Double_Digit_Multiplication.pdf

51 Revised: 8/20/16

Sheppard Software

StarrMatica

Turtle Diary

Jefferson Lab


Quia

NCTM Illuminations

Pearson Success Net

Promethean Planet


Worksheet Fun

RCPS Math Resources














52 Revised: 8/20/16


SOL 3.3 – 2nd Nine Weeks Blueprint Categories Grade 3 SOL Number of

Items 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 +=).


Prior Knowledge

SOL 2.3 - The student will d. identify the parts of a set and/or region that represent fractions for halves, thirds, fourths, sixths, eighths, and tenths; e. write the fractions; and f. compare the unit fractions for halves, thirds, fourths, sixths, eighths, and tenths.



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.

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


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

53 Revised: 8/20/16

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.

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.

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.

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.


Models for Teaching Fractions Video

http://www.vdoe.whro.org/instruction/math_2011/models_for_teaching_fractions/DOE_MODELS_FOR_TEACHING_1.swf

54 Revised: 8/20/16

Students’ errors on items of this nature suggest that students have difficulty determining what to count (Do I count the hatch marks or the spaces between them?) and/or where to start and end the counting (Do I count the marks at zero and at B ?). Using the example provided, a common error is to name this fraction as 4/8 rather than 3/8.

Students need additional practice comparing fractions with unlike denominators. Students use models when comparing fractions in grade 3, as in the example shown here. The answer to the example is shown on the screen. As a follow-up question, the teacher could ask students to use each of the answer options that is not selected and write an inequality statement that compares that fraction to the fraction shaded in Model 1. For example, for the answer choice that has 7/10 shaded, students could write 7/10> 6/9 or 6/9<7/10. Additionally, since both 7/10 and 6/9 have 3 unshaded portions, students might also use the reasoning that 3/10<3/9 or 3/9>3/10 to defend the decision that this answer option does not have a value equal to the fraction shaded in Model 1. As another extension to this example, the teacher might ask students to represent another fraction that has the same value as Model 1, but to use a different type of model such as a measurement or number line model, a set of objects, or a rectangular region.

55 Revised: 8/20/16

Students continue to have difficulty when symbolic notation is used in comparisons. Teachers are encouraged to explore whether students are having difficulty determining which modeled fraction is greater, whether the symbolic notation (the less than or greater than symbol) is the confusing issue, or whether students are struggling with both of these issues.

56 Revised: 8/20/16


Vocabulary




Fraction - part of a group or part of a whole

Naming and Writing Fractions Modeling Fractions Comparing Fractions Number and Number Sense Pizzarama

Eating Fractions by Bruce McMillan

Fraction Action by Loreen Leedy

Give Me Half! by Stuart J. Murphy

The Hershey’s Milk Chocolate Fractions Book by

Jerry Pallotta and Robert C. Bolster

Full House: An Invitation to Fractions by Dayle Ann









http://www.nsa.gov/academia/_files/collected_learning/elementary/arithmetic/pizzarama.pdf

57 Revised: 8/20/16


Student Links

Practice Test Items



ABCya

Fun 4 the Brain

Recess Room

Sheppard Software

DOE Practice Items

DOE Released Test

IQ Practice Tests

Jefferson Lab

New York State Assessments


Interactivate


Manipulatives

NCTM Illuminations




Mixed Numbers - a quantity expressed as a number and a proper fraction Model - Something that is made to be like another thing Numerator - The top number in a fraction. Shows how many parts we have. Denominator - The bottom number in a fraction. Shows how many equal parts the item is divided into Equivalent – equal Improper fraction- a fraction in which the numerator is greater than the denominator

Marathon Markers (Comparing and Ordering Fractions) What Fraction Am I? Inching Into Fractions Pizza Party

Dodds


















http://www.nsa.gov/academia/_files/collected_learning/elementary/fractions/Marathon_Markers.pdf

http://www.nsa.gov/academia/_files/collected_learning/elementary/fractions/Marathon_Markers.pdf

http://www.nsa.gov/academia/_files/collected_learning/elementary/fractions/What_Fraction_am_I.pdf

http://www.nsa.gov/academia/_files/collected_learning/elementary/fractions/inching_into_fractions.pdf

http://www.nsa.gov/academia/_files/collected_learning/elementary/fractions/pizza_party.pdf


58 Revised: 8/20/16

StarrMatica

Turtle Diary

*Multiple Languages Interactive Achievement

Quia

Pearson Success Net

Promethean Planet


Worksheet Fun

RCPS Math Resources










59 Revised: 8/20/16



Items

The student will add and subtract proper fractions having like denominators or 12 or less.


Prior Knowledge

SOL 2.3 - The student will a. identify the parts of a set and/or region that represent fractions for halves, thirds, fourths, sixths, eighths, and tenths; b. write the fractions; and c. compare the unit fractions for halves, thirds, fourths, sixths, eighths, and tenths. SOL 2.5 - The student will recall addition facts with sums to 20 or less and the corresponding subtraction facts.



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

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


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

60 Revised: 8/20/16

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.

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.

– 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).


For SOL 3.7, students need additional practice subtracting fractions with like denominators. Models should be provided. In addition to having a strategy to subtract fractions that are modeled, students must understand the vocabulary associated with both addition and subtraction. Experiences with both multiple-choice and free response or fill-in-the-blank situations are strongly encouraged.

61 Revised: 8/20/16

See models below.



62 Revised: 8/20/16


Student Links

Practice Test Items



ABCya

Fun 4 the Brain

DOE Practice Items

DOE Released Test


Interactivate




iPad™ Resources

Vocabulary


DOE Vocabulary Cards Working with Vocabulary /

Concept Development (Word)

Fraction – any part of a group Proper Fraction – a fraction less than one whole. The bottom number is bigger than the top number. Denominator – bottom number of a fraction Numerator – the top number of a fraction

Adding and Subtracting Fractions Fraction Action

Eating Fractions by Bruce McMillan

Fraction Action by Loreen Leedy

Give Me Half! by Stuart J. Murphy

The Hershey’s Milk Chocolate Me Counting Time

from Seconds to Centuries by Joan Sweeney and

Annette Cable

Fractions Book by Jerry Pallotta and Robert C.

Bolster














http://www.nsa.gov/academia/_files/collected_learning/elementary/fractions/Fraction_Action08.pdf


63 Revised: 8/20/16

Room Recess

Sheppard Software

StarrMatica

Turtle Diary

IQ Practice Tests

Jefferson Lab


Quia

Manipulatives

NCTM Illuminations

Math Study Jams Pearson Success Net

Promethean Planet


Worksheet Fun

RCPS Math Resources


















64 Revised: 8/20/16


SOL 3.11 – 2nd Six Weeks Blueprint Categories Grade 3 SOL Number of

Items

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.

Measurement and Geography

3.8, 3.9a-d, 3.10a-b, 3.11a-b, 3.12, 3.13, 3.14,

3.15, 3.16

8

Prior Knowledge

SOL 2.12 - The student will tell and write time to the nearest five minutes, using analog and digital clocks.



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.

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.


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.).

65 Revised: 8/20/16

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.

Solve practical problems in relation to time that has elapsed.


For SOL 3.11, students need additional practice determining which clock shows a given time. Students would benefit from additional practice reading the time shown on an analog clock. In addition to determining what time is shown on a single given clock, students should be able to determine which of several clocks shows a given time.

66 Revised: 8/20/16

Student performance data also indicate a need for additional practice determining elapsed time. In the example provided, students must correctly read the analog clock to determine the starting time and then apply the elapsed time provided within the description to determine the ending time.

67 Revised: 8/20/16


Vocabulary


It's About Time Where Did The Time Go? Hoppin on the Elapsed Timeline A Day in Elapsed Time

Pigs on a Blanket by Amy Axelrod and Sharon

McGinley-Nally




http://www.doe.virginia.gov/testing/solsearch/sol/math/3/mess_3-11b_1.pdf

http://www.doe.virginia.gov/testing/solsearch/sol/math/3/mess_3-11b_2.pdf

http://www.nsa.gov/academia/_files/collected_learning/elementary/measurements/A_Day_in_Elapsed_Time.pdf


68 Revised: 8/20/16


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69 Revised: 8/20/16



Items

The student will identify equivalent periods of time, including relationships among days, months, and years, as well as minutes and hours.

Measurement and Geography 3.8, 3.9a-d, 3.10a-b, 3.11a-b, 3.12, 3.13,

3.14, 3.15, 3.16 8

Prior Knowledge

SOL 2.12 - The student will tell and write time to the nearest five minutes, using analog and digital clocks. SOL 2.13 - The student will a. determine past and future days of the week; and b. identify specific days and dates on a given calendar.



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.


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.

70 Revised: 8/20/16

Additional Instructional Activities


Vocabulary




Leap year: A year containing one extra day.

Calendar: a tool for measuring time in days, weeks, months, and years; yesterday, tomorrow, next week, last week

Day: A unit of time equal to 24 hours.

Week: A unit of time equal to 7 days.

Month: A unit of time that is approximately 30 days.

Year: A unit of time equal to 365 days or 12 months.

Date: A particular day that something happens.

Analog clock: A clock with a minute hand and an hour hand.

Calendar Math

Me Counting Time from Seconds to Centuries by

Joan Sweeney and Annette Cable








71 Revised: 8/20/16


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72 Revised: 8/20/16



Items

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.

Measurement and Geography

3.8, 3.9a-d, 3.10a-b, 3.11a-b, 3.12, 3.13,

3.14, 3.15, 3.16 8

Prior Knowledge

SOL 2.14 - The student will read the temperature on a Celsius and/or Fahrenheit thermometer to the nearest 10 degrees.



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.


Read temperature to the nearest degree from real Celsius and Fahrenheit thermometers and from physical models (including pictorial representations) of such thermometers.

73 Revised: 8/20/16



Vocabulary




Temperature: Measuring how hot or cold something is. Can be measured in degrees Fahrenheit or degrees Celsius.

Was the Groundhog Correct?






74 Revised: 8/20/16


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Thermometer: an instrument used to measure temperature in degrees; temperature.

Fahrenheit(F): The temperature measurement used in the U.S. customary system. Celsius(C): The temperature of measurement used in the metric system. Degree()- The symbol that comes before the unit of temperature.











75 Revised: 8/20/16

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76 Revised: 8/20/16


SOL 3.6 –3rd Nine Weeks Blueprint Categories Grade 3 SOL Number of Items

The student will represent multiplication and division, using area, set, and number line models (2nd NW), and create and solve problems that involve multiplication of two whole numbers, one factor 99 or less and the second factor 5 or less (3rd NW).


Prior Knowledge

SOL 3.2, 3.5 – multiplication concepts including inverse relationships SOL 2.5 - The student will recall addition facts with sums to 20 or less and the corresponding subtraction facts.



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

All students should

Understand the meanings of multiplication and division.

Understand the models used to represent multiplying and dividing whole numbers.


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

77 Revised: 8/20/16

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.

The number of jumps (two) of a given length (three) is the answer to the question.


multiplication, where one factor is 99 or less and the second factor is 5 or less.

0 1 2 3 4 5 6

78 Revised: 8/20/16


For SOL 3.6, students need additional practice solving multiplication problems presented in the context of a word problem. The story problems provided on this screen involve situations that are multiplicative, although students might use a less efficient method to arrive at a correct solution.

79 Revised: 8/20/16

Students would benefit from additional practice solving multiplication problems presented in a horizontal format like the first two examples provided. Teachers are encouraged to continue providing students with practice solving multiplication story problems, as in example 3.



80 Revised: 8/20/16




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Vocabulary



Area –the number of square units needed to cover a surface Set - a collection of distinct items or elements Multiplication- Finding the product of two numbers Division- Finding the quotient of two numbers Number line- A line of numbers in order Factor- The numbers in multiplication problems.

Multiplication and Division Representations Debuting Single Digit by Double Digit Multiplication

















https://www.nsa.gov/academia/_files/collected_learning/elementary/arithmetic/Single__by_Double_Digit_Multiplication.pdf

81 Revised: 8/20/16

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82 Revised: 8/20/16


SOL 3.9a – 3rd Nine Weeks Blueprint Categories Grade 3 SOL Number of

Items

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;

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

Prior Knowledge

2.11 - The student will estimate and measure a. length to the nearest centimeter and inch;



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.

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.


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.

83 Revised: 8/20/16


Student performance for this content (3.9a w/perimeter) is inconsistent, particularly when questions require students to estimate the length of an object in U.S. Customary units or when students must measure to find the perimeter of a figure. In items like this example provided, students most frequently selected the measurement with the incorrect U.S. Customary unit- in this case, 1 foot. This error seems to indicate a lack of understanding of the relationship that exists between feet and yards.


Vocabulary



Measuring Length

Measuring Penny by Loreen Leedy

Length-Length (Math Counts) by Henry Arthur Pluck






84 Revised: 8/20/16


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Centimeter – a metric unit for measuring length Meter – a metric unit for measuring length – 100 centimeters (approx one arm span) are in a meter Ruler – a customary unit of measurement for length = 12 inches Inch – a standard unit for measuring length Foot – a standard unit for measuring length – 12 inches are in a foot Yard – a standard unit for measuring length - 3 feet are in a yard and 36 inches are in a yard.

Rose

Length-Twelve Snails to One Lizard: A Tale of

Mischief and Measurement by Susan Hightower

Length-How Big is a Foot? By Rolf Myller

Length-How Long or How Wide? By Brian P. Cleary

How Tall, How Short, How Far Away by David Adler

Inchworm and a Half by Elinor Pinczes Picture Book Lesson Ideas























85 Revised: 8/20/16

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86 Revised: 8/20/16


SOL 3.9 b – 3rd Nine Weeks Blueprint Categories Grade 3 SOL Number of

Items


b). liquid volume in cups, pints, quarts, gallons, and liters;


3.14, 3.15, 3.16 8

Prior Knowledge

SOL 2.11 - The student will estimate and measure c. liquid volume in cups, pints, quarts, gallons, and liters.






All students should




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.

87 Revised: 8/20/16



Vocabulary



Vocabulary / Concept Development (Word) Cup – a customary unit of measure for liquids – 8 fluid ounces

Gallon – a customary unit of measure for liquids – 16 cups

Liter – a metric unit for measuring capacity (approx a quart)

Pint – a customary unit of measurement for capacity-= 2 cups

Quart – a customary unit of measurement for capacity = 4 cups

Volume – amount of space occupied by a 3D object

Measuring Liquid Volume Go for the Gallon


Capacity-Room for Ripley by Stuart J Murphy

Capacity-Pastry School in Paris: An Adventure in

Capacity by Cindy Neuschwander

Capacity-Lulu’s Lemonade by Barbara deRubertis

Capacity-Pigs in the Pantry by Amy Axelrod

Counting On Frank by Rod Clement

Millions to Measure by David M. Schwartz







http://www.nsa.gov/academia/_files/collected_learning/elementary/fractions/go_for_the_gallon.pdf


88 Revised: 8/20/16


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89 Revised: 8/20/16


SOL 3.9 c – 3rd Nine Weeks Blueprint Categories Grade 3 SOL Number of

Items


c). weight/mass in ounces, pounds, grams, and kilograms; and


3.14, 3.15, 3.16 8

Prior Knowledge

SOL 2.11 - The student will estimate and measure b. weight/mass of objects in pounds/ounces and kilograms/grams, using a scale; and



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?”).


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.

All students should




Estimate and use U.S. Customary and metric units to measure the weight/mass of objects to the nearest ounce, pound, gram, and kilogram.

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.

90 Revised: 8/20/16





Vocabulary



Vocabulary / Concept Development (Word) Gram – a metric unit for measuring mass Kilogram – a metric unit for measuring mass Weight – the measurement of the heaviness of an object Mass – the measure of how much matter is in an

Measuring Weight/Mass


Weight - On the Scale, a Weighty Tale by Brian P.

Cleary

Counting on Frank by Rod Clement

Millions to Measure by David M. Schwartz








91 Revised: 8/20/16


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object. Ounce – a standard unit for measuring weight Pound – a standard unit for measuring weight. There are 16 ounces in a pound.


























92 Revised: 8/20/16


SOL 3.9 d – 3rd Nine Weeks Blueprint Categories Grade 3 SOL Number of

Items


d.) area and perimeter.


3.14, 3.15, 3.16 8

Prior Knowledge

SOL 2.11A - The student will estimate and measure length to the nearest centimeter and inch.






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.

All students should



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.


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.

93 Revised: 8/20/16



Vocabulary



Area – the size a surface takes up measured in square units

Perimeter – distance around the outside of a shape

Measuring Area and Perimeter Geometry for Elementary School Teachers K-5 (Word)

Spaghetti and Meatballs for All! by Marilyn Burns

and Debbie Tilley

Racing Around by Stuart J Murphy






http://www.doe.virginia.gov/testing/solsearch/sol/math/3/mess_3-9d.pdf

http://www.doe.virginia.gov/testing/sol/standards_docs/mathematics/2001/resources/elementary/geometry_module/elem_entire_document.doc


94 Revised: 8/20/16


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95 Revised: 8/20/16


SOL 3.10 – 3rd Nine Weeks Blueprint Categories Grade 3 SOL Number of

Items

The student will b.) measure the distance around a polygon in order to determine

perimeter; and c.) count the number of square units needed to cover a given surface in

order to determine area.

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

Prior Knowledge

SOL 2.11A - The student will estimate and measure length to the nearest centimeter and inch.



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.


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.

96 Revised: 8/20/16


Question 1 in the Grades 3-8 Tools Practice available on the Virginia Department of Education website provides practice using the ruler tools.

For SOL 3.10, students need additional practice determining the perimeter of a figure on a grid. When students are given a figure on a grid and asked to find the perimeter, a common error is to respond with the area of the figure. When a question asks for the perimeter and area of the figure, similar to the example shown on the screen, a common error is to interchange these answers. Student performance on items that ask only for the area of a figure on a grid remains high.

https://vastatic.testnav.com/vatrngqc/testnav-7.5.22.36/epatLogin.jsp?testnavTestId=3070&testnavFormId=Practice%20Test

97 Revised: 8/20/16

The most common error students make is to select the response that indicates they have not included the length of one or more sides in the perimeter. In this example, students who leave out any two of the shorter sides would select option A.


Question 2 in the Grades

3-8 Tools Practice

accessible on the

Virginia Department of

Education website is like

the questions that

students found most

difficult, which required

them to measure one

figure to determine its

perimeter.




98 Revised: 8/20/16

Vocabulary



Polygon: a closed plane figure composed of line segments that do not cross.

Perimeter: a measure of the distance around a polygon and is found by adding the measures of the sides.

Area: the number of square units needed to cover a surface.

Measuring Area and Perimeter Cover It Up...With Area Geometry for Elementary School Teachers K-5 (Word)

Spaghetti and Meatballs for All! by Marilyn Burns

and Debbie Tilley

Racing Around by Stuart J Murphy





http://www.doe.virginia.gov/testing/solsearch/sol/math/3/mess_3-9d.pdf

http://www.nsa.gov/academia/_files/collected_learning/elementary/geometry/cover_it_up.pdf



99 Revised: 8/20/16


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100 Revised: 8/20/16



Items

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.


3.14, 3.15, 3.16 8

Prior Knowledge

SOL 2.16 - The student will identify, describe, compare, and contrast plane and solid geometric figures (circle/sphere, square/cube, and rectangle/rectangular prism).



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

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.


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.

101 Revised: 8/20/16

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.

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. A solid geometric object can be hollow rather than solid. The word “solid” indicates a three-dimensional figure.

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 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.

A rectangular prism is a solid figure in which all six faces are rectangles with three pair of parallel congruent opposite faces. A cube is a special rectangular prism with six congruent square faces and with every edge the same length.

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 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. The curved surface of a cone or cylinder is not considered a face. Since circles are not polygons, the circular bases are not considered faces either. Cylinders and cones do not have edges.

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).

102 Revised: 8/20/16




103 Revised: 8/20/16

Vocabulary



Plane figure: a two-dimensional figure

Geometric solids: three-dimensional figures such as cone, pyramid, prism, cylinder

Circle: a closed curve with all points in one plane and the same distance (radius) from a fixed point, the center; the center is not part of the circle

Square: a rectangle with all sides congruent

Rectangle: a quadrilateral with 4 right angles (all three shapes below are rectangles)

Cube: solid figure with six congruent, square faces; all edges are the same length; a cube has 8 vertices, 12 edges and 6 faces

Rectangular prism: a solid in which all 6 faces are rectangles

Plane Geometry Sort What Am I? Triangles Shapes and Solids Scavenger Hunt Geometry for Elementary School Teachers K-5 (Word)

A Cloak for a Dreamer by Aileen Friedman and Kim Howard The Greedy Triangle by Marilyn Burns Sigmund Square Finds His Family by Jennifer Taylor-Cox (see math facilitator for story on flash drive) Mummy Math: An Adventure in Geometry by Cindy Neuschwander Picture Book Lesson Ideas




http://www.doe.virginia.gov/testing/solsearch/sol/math/3/mess_3-14_1.pdf


http://www.nsa.gov/academia/_files/collected_learning/elementary/geometry/triangles.pdf

http://www.nsa.gov/academia/_files/collected_learning/elementary/geometry/scavenger_hunt.pdf



104 Revised: 8/20/16

Square pyramid: a solid with a square base with 4 sloping triangular faces that share a vertex

Sphere: a three-dimensional object with all of its points the same distance from its center

Cone: solid figure with a usually circular base joined to a vertex by a curved surface

Cylinder: solid figure with two congruent, parallel, usually circular bases joined by a curved surface

105 Revised: 8/20/16

Angles: the intersection of two lines

Vertices: the point of intersection of 2 adjacent line segments that comprise a polygon

Edges: in a solid figure, a line segment where two faces of the solid meet

Faces: a polygon that serves as a side of a solid

Concrete model: manipulative

106 Revised: 8/20/16


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107 Revised: 8/20/16


SOL 3.15 – 3rd Grade Blueprint Categories Grade 3 SOL Number of

Items

The student will identify and draw representations of points, line segments, rays, angles, and lines.


3.14, 3.15, 3.16 8

Prior Knowledge



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.


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.

108 Revised: 8/20/16

Vocabulary


DOE Vocabulary Cards

Handout available: Working with Vocabulary / Concept

Development (Word)

Point: exact location in space; no length or width; usually named with a capital letter Line: a collection of points of points going on and on in both directions; has no endpoints; an arrow must be drawn so the line goes on forever Endpoints: a point marking the end of a line point Line segment: a part of a line; has 2 endpoints and includes all the points in between Ray: a part of a line; has one endpoint and continues on and on in one direction Angle: formed by two rays having a common endpoint; found where ever lines and line segments intersect Vertex: the common endpoint shared by two rays in an angle Intersect: a meeting point

Secret Sort for Geometry Folded Geometry Geometry for Elementary School Teachers K-5 (Word)

Lines that Wiggle by Candace Whitman When a Line Bends…A Shape Begins by Rhonda Gowler Greene and James Kaczman The Dot and the Line: A Romance in Lower Mathematics by Norton Juster Picture Book Lesson Ideas








109 Revised: 8/20/16


Student Links

Practice Test Items



ABCya

Fun 4 the Brain

Room Recess

Sheppard Software

StarrMatica

Turtle Diary

DOE Practice Items

DOE Released Test

IQ Practice Tests

Jefferson Lab



Quia


Interactivate


Manipulatives

NCTM Illuminations




Promethean Planet


RCPS Math Resources

























110 Revised: 8/20/16


SOL 3.16 – 3rd Nine Weeks Blueprint Categories Grade 3 SOL Number of Items

The student will identify and describe congruent and noncongruent plane figures.

Measurement and Geography 3.8, 3.9a-d, 3.10a-b, 3.11a-b, 3.12, 3.13,

3.14, 3.15, 3.16 8

Prior Knowledge



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.


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.

111 Revised: 8/20/16



Vocabulary


DOE Vocabulary Cards Handout available: Working with Vocabulary / Concept

Development (Word)

Congruent Plane Figures: figures having the exact same size and shape Noncongruent Plane Figures: figures that are not exactly the same size and shape

Fit To Be Congruent Geometry for Elementary School Teachers K-5 (Word)







112 Revised: 8/20/16


Student Links

Practice Test Items



ABCya

Fun 4 the Brain

Room Recess

Sheppard Software

StarrMatica

Turtle Diary

DOE Practice Items

DOE Released Test

IQ Practice Tests

Jefferson Lab


Quia


Interactivate


Manipulatives

NCTM Illuminations




Promethean Planet


Worksheet Fun

RCPS Math Resources


























113 Revised: 8/20/16



Items

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.


3.14, 3.15, 3.16 8

Prior Knowledge

SOL 2.10 a) count and compare collection of coins w/ value of $2.00 or less; b) use cent, dollar symbol, and decimal point



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.


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.

114 Revised: 8/20/16


The most common error on an item like this is selecting option A (second animation). Students selecting option A may be combining the three dollars in this set of money with the two dollars in the context of the story to arrive at five dollars; or, students selecting option A may recognize that the 27 cents added to the 73 cents will make a dollar but then fail to add that dollar to the total, which would make $6 instead of $5.



115 Revised: 8/20/16

Vocabulary


DOE Vocabulary Cards Handout available: Working with Vocabulary / Concept Development (Word) Make change – the difference between cost and amount paid

Money Counts Money Makes the Fair-Go-Round Applying Knowledge of Money Coin Carnival Count Pennies, Save a Dollar

Alexander, Who Used to be Rich Last Saturday by Judith Viorst The Coin Counting Book by Rozanne Lanczak Williams If You Made a Million by David Schwartz Lemon & Ice & Everything Nice by Marilyn Burns and Cristina Ong Pigs will be Pigs by Amy Axelrod Picture Book Lesson Ideas




http://www.doe.virginia.gov/testing/solsearch/sol/math/3/mess_3-8.doc

http://www.nsa.gov/academia/_files/collected_learning/elementary/arithmetic/Money_Makes_the_Fair-Go-Round.pdf

http://www.nsa.gov/academia/_files/collected_learning/elementary/arithmetic/applying_knowledge.pdf

http://www.nsa.gov/academia/_files/collected_learning/elementary/arithmetic/arith_coin_carnival.pdf

http://www.nsa.gov/academia/_files/collected_learning/elementary/arithmetic/count_pennies.pdf


116 Revised: 8/20/16


Student Links

Practice Test Items



ABCya

Fun 4 the Brain

Room Recess

Sheppard Software

StarrMatica

Turtle Diary

DOE Practice Items

DOE Released Test

IQ Practice Tests

Jefferson Lab


Quia


Interactivate


Manipulatives

NCTM Illuminations




Promethean Planet


Worksheet Fun

RCPS Math Resources


























117 Revised: 8/20/16


SOL 3.18 – 4th Nine Weeks Blueprint Categories Grade 3 SOL Number of Items

The student will investigate and describe the concept of probability as chance and list possible results of a given situation.


3.17a-c, 3.18, 3.19, 3.20a-b

6

Prior Knowledge

SOL 2.18 - The student will use data from experiments to predict outcomes when the experiment is repeated.



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).

All students should

Investigate, understand, and apply basic concepts of probability.

Understand that probability is the chance of an event happening.


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.

118 Revised: 8/20/16

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.

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.


119 Revised: 8/20/16

Students need additional practice describing the probability of a situation as the chance that an event will happen. Students should be able to apply their understanding of chance to create a situation that fits given criteria. In the example provided, students must understand that if it is certain that Julia will select a red candy, then all the candy in the box must be red. The answer to this example is shown on the screen. The next two screens provide extension questions for this same situation.

120 Revised: 8/20/16

In the first extension question, students must understand that for this situation to be impossible, none of the six candies can be brown. Any combination of six candies that does not include any brown candies would be a correct response to this question.

In this extension to the situation, students must create a set that has equal amounts of blue candies and red candies. In the correct response shown on the screen, there are 3 red and 3 blue candies.



121 Revised: 8/20/16

Vocabulary



Probability: the chance of an even occurring Outcome: result of an experiment Impossible: an event is impossible if it has a probability of 0 Unlikely: not likely to occur As likely as: equally likely Equally likely: outcomes that have the same probability Likely: seeming like certainty Certain: an event is certain to occur if it has a probability of 1

Two Color Counter Toss Probability Boxes Is There Probability in Third?

Probability and Statistics K-5







http://www.doe.virginia.gov/testing/sol/standards_docs/mathematics/2001/resources/elementary/probability_module/mprobstatentire.pdf

122 Revised: 8/20/16


Student Links

Practice Test Items



ABCya

Fun 4 the Brain

Room Recess

Sheppard Software

StarrMatica

Turtle Diary

DOE Practice Items

DOE Released Test

IQ Practice Tests

Jefferson Lab


Quia


Interactivate


Manipulatives

NCTM Illuminations




Promethean Planet


Worksheet Fun

RCPS Math Resources


























123 Revised: 8/20/16


SOL 3.19 – 4th Nine Weeks Blueprint Categories Grade 3 SOL Number of

Items

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.


3.17a-c, 3.18, 3.19, 3.20a-b

6

Prior Knowledge

SOL 2.20 - The student will identify, create, and extend a wide variety of patterns



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);

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.


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.

124 Revised: 8/20/16

– 20, 18, 16, 14,…(growing pattern); and – 1, 3, 5, 1, 3, 5, 1, 3, 5 (repeating pattern).

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.


Patterns involving numbers are more challenging to students than those using pictures or those presented in tables.

125 Revised: 8/20/16


Vocabulary



Pattern: numbers or objects that follow a repeating or growing rule

Patterns on a Hundreds Chart Patterns in a Staircase Exploring Multiples Tunneling Through Patterns The Ins and Outs of Patterns Patterns in Nature A Parade of Patterns










http://www.nsa.gov/academia/_files/collected_learning/elementary/patterns/Patterns_in_Nature.pdf

http://www.nsa.gov/academia/_files/collected_learning/elementary/patterns/A_Parade_of_Patterns.pdf

126 Revised: 8/20/16

Symbol: a pattern or image used instead of words Growing Pattern: a pattern that increases or decreases by a predictable amount

·6, 9, 12, 15, 18, (growing pattern);

·1, 2, 4, 7, 11, 16, (growing pattern); ·20, 18, 16, 14,…(growing pattern);

Repeating Pattern: a pattern that continues with the same symbols/numbers over and over again

1, 3, 5, 1, 3, 5, 1, 3, 5 (repeating pattern)

Transformation: moving a shape so that it is in a different position, but still has the same size, area, angles, and line lengths.

Rotation: the result of turning a point around a point or vertex Reflection: the result of flipping a figure over a line

Repeated Pattern, Growing Patterns, and Functions Patterns, Functions and Algebra K-5 (PDF)

http://www.nsa.gov/academia/_files/collected_learning/elementary/patterns/Repeated_Patterns.pdf

http://www.doe.virginia.gov/testing/sol/standards_docs/mathematics/2001/resources/elementary/patterns_funct_algebra_module/PFAEntire.pdf

127 Revised: 8/20/16


Student Links

Practice Test Items



ABCya

Fun 4 the Brain

Room Recess

Sheppard Software

StarrMatica

Turtle Diary

DOE Practice Items

DOE Released Test

IQ Practice Tests

Jefferson Lab


Quia


Interactivate


Manipulatives

NCTM Illuminations




Promethean Planet


Worksheet Fun

RCPS Math Resources


























128 Revised: 8/20/16


SOL 3.20 – 4th Nine Weeks Blueprint Categories Grade 3 SOL Number of

Items

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.


3.17a-c, 3.18, 3.19, 3.20a-b

6

Prior Knowledge

SOL 2.22 - The student will demonstrate an understanding of equality by recognizing that the symbol “=” in an equation indicates equivalent quantities and the symbol “≠” indicates that quantities are not equivalent.



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

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.

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

129 Revised: 8/20/16

+ 3 = 9; or 6 + 3 = 4 + 5).

Understand that quantities on both sides of the not equal sign are not equal.

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.


Commutative Properties

http://www.vdoe.whro.org/instruction/math_2011/grade_3_commutative_property/DOE_PROPERTY_2.swf

130 Revised: 8/20/16

131 Revised: 8/20/16


Vocabulary



Identity for addition = 0, no matter what you add to 0 you always get the same number back. Identity for Multiplication = 1, no matter what you multiply by 1 you always get the same answer. Commutative Property for Addition =

My Identity is in my Pocket ARRAY for the Commutative Property of Multiplication! Property Commute Outdoor Algebra Patterns, Functions and Algebra K-5 (PDF)





http://www.doe.virginia.gov/testing/solsearch/sol/math/3/mess_3-20ab_1.pdf




http://www.nsa.gov/academia/_files/collected_learning/elementary/patterns/Outside_Algebra.pdf

http://www.doe.virginia.gov/testing/sol/standards_docs/mathematics/2001/resources/elementary/patterns_funct_algebra_module/PFAEntire.pdf

132 Revised: 8/20/16


Student Links

Practice Test Items



ABCya

Fun 4 the Brain

Room Recess

Sheppard Software

StarrMatica

Turtle Diary

DOE Practice Items

DOE Released Test

IQ Practice Tests

Jefferson Lab


Quia


Interactivate


Manipulatives

NCTM Illuminations




Promethean Planet


Worksheet Fun

a + b = b +a; Example: 5+3 = 3+5 Commutative Property for Multiplication = a X b = b X a; Example: 7 X 4 = 4 X 7

























133 Revised: 8/20/16


SOL Review– 4th Nine Weeks Blueprint Categories Grade 3 SOL Number of

Items Teachers should use data from county and released SOL assessments to plan

remediation and practice of all Standards of Learning.

SOL Blueprint (PDF)

All

Prior Knowledge


See County Shared (Z) Drive for additional resources. (Elementary/Grade 3/Math/SOL Review)

IMPORTANT!! The following 3rd grade online practice is required for all students! All students must be exposed to practice items. This is NOT the same as the

practice conducted with the Guidance Counselor using the sign-in sheets with username and password. Teachers should use the script found in the Guide to

guide students through the practice. This practice will take several math blocks to complete if covered sufficiently. These practice items are good for reteaching

as well as exposing students to the tools available for testing.

Grade 3 Practice Items

Practice Items – Audio

Guide

View a narrated demonstration with examples of various technology-enhanced item types that appear on the new Mathematics SOL tests. These new SOL tests

may consist of approximately 15 percent technology-enhanced items. To download this narrated demonstration as a MOV file, right-click here. MOV video files

require the free Apple QuickTime player plug-in.

Mathematics Tools Practice: The online Mathematics Tools Practice allows students to practice using the online tools (such as the ruler, protractor or compass)

available within TestNav, the online testing software used in Virginia. All tools that are available for any grades 3-8 test are provided within the Grades 3-8 Tools

http://www.doe.virginia.gov/testing/sol/blueprints/mathematics_blueprints/2009/blueprint_math3%20.pdf

https://vastatic.testnav.com/vaqc/epatLogin.jsp?testnavTestId=epat5125&testnavFormId=EP3M

https://vastatic.testnav.com/vaqc/epatLogin.jsp?testnavTestId=epat5125&testnavFormId=AEP3M

http://www.doe.virginia.gov/testing/sol/practice_items/mathematics/guides/gr_3_math.pdf

http://vaassessments.com/teidemo

http://www.vdoe.whro.org/testing/sol/practice_items/math/math.mov

http://www.doe.virginia.gov/tips/download_instructions.shtml#quicktime

134 Revised: 8/20/16

Practice. Likewise, all tools that are available for any EOC test are provided within the End-of-Course Tools Practice. This means that the tools included within each

application do not necessarily indicate the tools that will be available for a particular test. To reference the tools available for a particular online mathematics test,

see Online Tools Available on the Mathematics SOL Tests (PDF) Grades 3-8 Tools Practice

Released Spring Test 2015: Online PDF

Answer Sheet

For Released Tests prior to Spring 2012, see: Archived Released Tests

Released SOL tests and test items can be found on Interactive Achievement. Students should be exposed to these (especially TEI items) throughout the year.

More Resources

1. SMART Exchange lessons

2. Harvey Almarode's SMARTBoard Math Files

3. Several Math Interactive & SMARTBoard Resources by Math SOLS

4. Great Math Interactive website

5. BBC Math Interactive website

6. Harcout Math Book website

7. Joe Hill's Math PortaPortal Interactive Math Websites

8. TEI Practice Items

9. Internet4Classrooms 3rd Grade Math

10. Add & Subtract SOL Senteo (SMART Response) Review

11. Are you Smarter than a 3rd grader SOL Math Review PowerPoint

http://www.doe.virginia.gov/testing/sol/practice_items/mathematics/online_mathematics_tools.pdf

https://vastatic.testnav.com/vatrngqc/epatLogin.jsp?testnavTestId=3070&testnavFormId=Practice%20Test

https://vastatic.testnav.com/vaqc/epatLogin.jsp?testnavTestId=EP3R&testnavFormId=R0114

http://www.doe.virginia.gov/testing/sol/released_tests/2015/gr_3_reading_released_spring_2015.pdf

http://www.doe.virginia.gov/testing/sol/released_tests/2013/answer_sheet_for_released_tests.pdf

http://www.doe.virginia.gov/testing/sol/released_tests/archive.shtml

http://www.interactiveachievement.com/teacher-login/

http://exchange.smarttech.com/

http://www.harveyshomepage.com/Harveys_Homepage/Welcome.html

http://portfolio.fcps1.org/itrt/ElemMatrix/myweb/Navigation/3_math_home.html

http://www.woodlands-junior.kent.sch.uk/maths/index.html

http://www.bbc.co.uk/skillswise/numbers/wholenumbers/

http://www.harcourtschool.com/menus/math2004/math2004_menu.html

http://guest.portaportal.com/bridgewatereagles

http://pinterest.com/ohostetter/technology-enhanced-items/

http://www.internet4classrooms.com/skills-3rd-mathbuilders.htm

https://googledrive.com/host/0B2w2sv-hoeskUEVuUm1oSkcyRUk/3MathReviewaddsubt.notebook

https://googledrive.com/host/0B2w2sv-hoeskUEVuUm1oSkcyRUk/SmarterThan3rdgrademath.ppt

135 Revised: 8/20/16

12. SOL Math Review PowerPoint

13. SOL Released Test PowerPoint

The following Student Response Activities (formatted in Notebook but can be used with Active Inspire/Expressions). See ITRT if you need assistance.

14. 2008 Senteo (SMART Response) Computation & Estimation SOL Test

15. 2008 Senteo (SMART Response) Measurement and Geometry Test

16. 2008 Senteo (SMART Response) Number Sense Test

17. 2008 Senteo (SMART Response) Patterns, Functions, & Algebra Test

18. 2008 Senteo (SMART Response) SOL Probability & Statistics Test

19. Several good Math Notebook files

20. 2001 SOL Math 3 Senteo (SMART Response) Part 1

21. 2001 SOL Math 3 Senteo (SMART Response) Part 2

22. 2007 SOL Math 3 Senteo (SMART Response)

23. SOL Decimal Review Senteo (SMART Response)

24. SOL 3rd Grade Math Notebook on SMART Exchange

25. SOL 3rd Grade Math Study Guide (Word format)

More TEI Practice Items (From Interactive Assessments Allenteacher.com)

https://googledrive.com/host/0B2w2sv-hoeskUEVuUm1oSkcyRUk/3Math.ppt

http://web.archive.org/web/20040512082022/http:/web.dps.k12.va.us/dps/Instruction/SOL_reviews/third/3MathReview.ppt

https://googledrive.com/host/0B2w2sv-hoeskUEVuUm1oSkcyRUk/32008ReleasedComputationEstimation.notebook

https://googledrive.com/host/0B2w2sv-hoeskUEVuUm1oSkcyRUk/32008ReleasedMeasurementGeometry.notebook

https://googledrive.com/host/0B2w2sv-hoeskUEVuUm1oSkcyRUk/32008ReleasedNumberNumberSense.notebook

https://googledrive.com/host/0B2w2sv-hoeskUEVuUm1oSkcyRUk/32008ReleasedPatternsFunctionsAlgebra.notebook

https://googledrive.com/host/0B2w2sv-hoeskUEVuUm1oSkcyRUk/32008ReleasedProbablilityStatistics.notebook

http://www.willoughby-eastlake.k12.oh.us/classroom/technology/smart_board_3rd_grade_ma.htm

https://googledrive.com/host/0B2w2sv-hoeskUEVuUm1oSkcyRUk/2001math3part1.notebook

https://googledrive.com/host/0B2w2sv-hoeskUEVuUm1oSkcyRUk/2001math3part2.notebook

https://googledrive.com/host/0B2w2sv-hoeskUEVuUm1oSkcyRUk/2007Math3Senteo.notebook

https://googledrive.com/host/0B2w2sv-hoeskUEVuUm1oSkcyRUk/Decimal3SenteoReview.notebook

http://exchange.smarttech.com/details.html?id=1886868d4435ad7d602b93d0ea861b8aa466101c3b82d17dbdbe3723bd292611

https://googledrive.com/host/0B2w2sv-hoeskUEVuUm1oSkcyRUk/3MathReview.doc

http://www.interactiveassessment.com/mathematics/grade-3/

136 Revised: 8/20/16


Student Links

Practice Test Items



ABCya

Fun 4 the Brain

Room Recess

Sheppard Software

StarrMatica

Turtle Diary

DOE Practice Items

DOE Released Test

IQ Practice Tests

Jefferson Lab


Quia


Interactivate


Manipulatives

NCTM Illuminations




Promethean Planet


Worksheet Fun

























Documents

Math Curriculum - dinwiddie.k12.va.us Curriculum . 2 ... read, write, identify place value in 3‐digit numeral; b) ... leave the digit in the rounding place as it is, and