Knowledge and Skills - files.mrschoice.webnode.comfiles.mrschoice.webnode.com/200000008-d4ef5d5e93/GR… · Web viewRepresent relationships in word problems 2 – 4 days Unit 8:

Knowledge and Skills

Baltimore City Schools

Dr. Andrés Alonso

Chief Executive Officer

Dr. Sonja Santelises

Chief Academic Officer

Linda Eberhart

Executive Director Teaching and Learning

Curriculum Writers

Thanks to all City Schools teachers who wrote, revised, and provided feedback for this curriculum. A special thanks to the following curriculum writers:

Kim Alexander

Margo Berish

Julia Bonkowski

Megan Bovill

Thomas Coleman

Megan Cooper

Matthew Damseaux

Kimberly David

Melanie Davison

Chritian Fisher

Geneve Garcia

Beth Goldscher

Andrew Hlavka

Gil Laqui

Maggie Lasaga-Flister

Benjamin Lawrence

Luis Lima

Genevieve Mason

Scott Messinger

Kevin Older

Elizabeth Renwick

Estelito Reyes

Katherine Schlee

Weston Schreiber

Levi Straight

Odessa Tamayo

Siriporn Vinijkul

Smitha Viswanathan

Shanekwa Winfield

Math Works Homework

Homework can be an effective part of your math program - giving students the practice they need to master skills. Below are some Math Works methods for utilizing homework.

Suggested Homework Procedures:

· Check homework every night

· Give students an opportunity to revise homework

· Start the homework assignment together at the beginning or end of class.

· Dedicate 10 minutes to going over 2-5 problems that students are having trouble with (they pick some, you pick some). Model how you work through the problems on the board.

· Reward students for doing homework and revising it.

Homework Tips:

· Homework should consist primarily of skills that students have already been exposed to. Skills should cycle in and out depending on what your students have been taught AND what they have mastered.

· Require students to show their work on homework problems, not just write the answer. Give credit only when there is work.

· Circulate throughout the classroom while talking about homework problems to be sure students are writing down what you are talking about and are showing work.

· At the beginning of the year, homework should consist of skills taught in the previous grade level.

Grade 4 Homework

Other Useful Links

· MSA Daily Reviews

· Mathematics Study Guide

· Vocabulary Activities

· Math Templates

· Structuring Your Math Block -

Weekly Planning Grid

· Sample Lesson Plan Template

Grade 4 Math Curriculum Sequence

School Year 2010-2011

QUARTER 1 (Aug 30 – Nov 5)

45 days

Suggested Time Frame

BENCHMARK A

(same skills as June Benchmark in previous grade)

Sept 7 - Sept 17 testing window

UNIT 1: Whole Number Concepts

(7-12 days)

*Common Core

· Read, Write, Represent Whole Numbers

· Represent numbers with models through the millions

· Represent numbers in numeric and word form through the millions

· Create equivalent representations through the millions

· Represent numbers in expanded form through the millions

2 – 4 days

*Common Core

· Place Value and Expanded Form of Whole Numbers

· Identify the value of a digit through the millions using the base ten model

3 – 5 days

*Common Core

· Compare and Order Whole Numbers

· Compare numbers through the millions

· Order numbers through the millions

2 – 3 days

UNIT 2: Whole Number Computation 1

(7-11 days)

*Common Core

· Add Whole Numbers

· Add up to 4-digit whole numbers with regrouping

1 – 2 days

*Common Core

· Subtract Whole Numbers

· Subtract up to 4-digit minus 4-digit regrouping once

· Subtract up to 4-digit minus 4-digit regrouping twice

· Subtract up to 4-digit minus 4-digit regrouping three times

3 – 4 days

*Common Core

· Estimate Sums and Differences

· Rounding whole numbers

· Estimating sums and differences

2 – 3 days

· Compare Values of Mixed Currency

· Identify value of mixed currency

· Compare money sets

1 – 2 days

Unit 3: Number Theory and Computation 2

(10-20 days)

· Multiples

· Identify multiples

1 – 2 days

· Factors

· Identify factors

· Create and interpret factor arrays

1 – 3 days

*Common Core

· Multiply Whole Numbers

· Multiply up to 3-digits by 1 digit no regrouping

· Multiply up to 3-digits by 1 digit with regrouping

· Multiply up to 4-digits by 1 digit with regrouping

2 – 4 days

*Common Core

· Divide Whole Numbers

· Divide 2-digits by 1-digit

· Divide 3-digits by 1 digit

· Divide 4-digits by 1 digit

3 – 5 days

· Estimate Products and Quotients

· Estimate products

· Estimate quotients

2 – 3 days

· Divisibility Rules

· Identify numbers divisible by 2



· Identify numbers divisible by a combination of 2, 5, or 10

1 – 3 days

UNIT 4: Algebra 1

(7–14 days)

· Numeric Patterns

· Identify the rule for and extend a number pattern

1 – 2 days

· Repeating Patterns

· Identify the rule for and extend a repeating pattern

1 - 2 days

· Growing Patterns

· Identify a rule for and extend a growing pattern

1 - 3 days

· Solve for Unknown Quantities

· Find the unknown using addition and subtraction

· Find the unknown using multiplication

2 – 3 days

· Function Tables

· Complete function tables using addition and subtraction

· Complete function tables using multiplication

· Complete function tables using division

2 - 4 days

QUARTER 2 (Nov 8 – Jan 21)

46 days


BENCHMARK B

(all Quarter 1 skills assessed)

Nov 1 – Nov 12 testing window

Unit 5: Fraction Concepts

(7-12 days)

· Proper Fractions and Mixed Numbers

· Read, write, represent fractions as part of a whole

· Read, write, represent fractions as part of a set

· Read, write, represent mixed numbers

2 - 3 days

· Compare and Order Fractions and Mixed Numbers

· Compare proper fractions and mixed numbers

· Order proper fractions and mixed numbers

1 – 2 days

· Fractional Number Lines

· Create fractional number lines

· Write fractions on number lines

· Identify locations on number lines

· Write and identify mixed numbers on number lines

2 – 4 days

*Common Core

· Add and Subtract Proper Fractions and Mixed Numbers

· Add proper fractions

· Subtract proper fractions

· Add mixed numbers

· Subtract mixed numbers

2 – 3 days

Unit 6: Statistics and Probability

(11-18 days)

· Probability

· Express object probability as a fraction

· Express spinner probability as a fraction

· Express conditional probability as a fraction

3 - 5 days

· Median, Mode and Range

· Determine the range of a set of data

· Determine the mode of a set of data

· Determine the median of a set of data

2 – 3 days

· Line Plots

· Create line plots

· Interpret line plots

3 – 5 days

· Coordinate Grids

· Identify locations on a coordinate grid given object

· Identify objects on a coordinate grid given location

1 – 2 days

· Line Graphs

· Interpret line graphs

2 – 3 days

UNIT 7: Algebra 2

(5-9 days)

· Write Expressions

· Write expressions using addition or subtraction

· Write expressions using multiplication or division

2 – 3 days

· Equivalent Expressions

· Write equivalent expressions

1 – 2 days

· Write Relationships

· Evaluate relationships with missing relational symbols

· Represent relationships in word problems

2 – 4 days

Unit 8: Geometry 1

(4-8 days)

· Angles

· Identify right angles

· Identify acute and obtuse angles

· Identify angles in shapes and objects

2 – 4 days

· Transformations

· Identify and create translations

· Identify and create reflections

· Identify and create rotations

2 – 4 days

QUARTER 3 (Jan 25 – Apr 7)

45 days


BENCHMARK C – Mock MSA

(all VSC assessed skills)

Jan 31 – Feb 11 testing window

Unit 9: Geometry 2

(6-9 days)

· Geometric Solids

· Identify cones and cylinders

· Identify and describe pyramids by the number of edges, faces, or vertices

· Identify and describe prisms by the number of edges, faces, or vertices

4 – 6 days

· Nets for Cubes and Pyramids

· Identify the number and arrangement of squares needed to create cubes

· Identify the number and arrangement of rectangles/triangles needed to create pyramids

2 – 3 days

Unit 10: Decimals

(8-16 days)

· Read, Write, Represent Decimals

· Read, write, represent decimals in the tenths

· Read, write, represent decimals in the hundredths

2 – 4 days

· Place Value and Expanded Form of Decimals

· Represent decimals in expanded form through the hundredths

1 – 3 days

· Compare and Order Decimals

· Compare decimals through the hundredths

· Order decimals through the hundredths

1 – 2 days

· Add Decimals

· Add decimals through the tenths

· Add decimals through the hundredths

1 – 2 days

· Subtract Decimals

· Subtract decimals through the tenths

· Subtract decimals through the hundredths

1 – 2 days

· Estimate Decimal Sums and Differences

· Round decimals

· Estimate sums to the tenths

· Estimate sums to the ones place

· Estimate differences to the tenths

· Estimate differences to the ones place

2 – 3 days

Unit 11: Measurement 1

(5-9 days)

· Measure Length

· Draw length to nearest ¼ inch

· Measure length to nearest ¼ inch

· Measure length to nearest mm

2 – 4 days

· Determine Equivalent Units of Length

· Convert yards to inches

· Convert inches to yards, feet

3 – 5 days

Unit 12: Measurement 2

(7-11 days)

· Perimeter

· Find perimeter given all sides

· Find perimeter with missing sides

2 – 3 days

· Area

· Find area on grid

· Find area using formula

2 – 3 days

· Start time, Elapsed Time, and End Time

· Find end time

· Find start time

· Find elapsed time

3 – 5 days

Maryland State Assessment

March 7 to March 16

POST-MSA CURRICULUM


Unit 13: Fraction Concepts 2

(10 - 15 days)

· Least Common Multiple

· Identify the least common multiple of 2 numbers

· Identify the least common multiple of 3 numbers

2 - 3 days

*Common Core

· Equivalent Forms of Fractions

· Concrete representations of equivalent fractions using visual models with attention to how the number and size of the parts differ even though the two fractions themselves are the same size

· Process of finding equivalent fractions

3 - 5 days

*Common Core

· Add and Subtract Proper Fractions with Unlike Denominators

· Add proper fractions with unlike denominators

· Subtract proper fractions with unlike denominators

5 - 7 days

Unit 14: Simplify & Compare Fractions

(10 - 14 days)

· Identify GCF and Simplify Fractions

· Identify the Greatest Common Factor

· Use the Greatest Common Factor to simplify fractions

5 - 7 days

*Common Core

· Compare and Order Fractions with Unlike Denominators

· Compare fractions with unlike denominators

· Order fractions with unlike denominators Compare mixed numbers with unlike denominators

· Order mixed numbers with unlike denominators

·

5 - 7 days

Unit 15: Decimal Notation for Fractions

7-13 days

*Common Core

· Express a fraction with denominator 10 as an equivalent fraction with denominator 100

2-4 days

*Common Core

· Use decimal notation for fractions with denominators 10 or 100

3-5 days

*Common Core

· Compare two decimals to hundredths by reasoning about their size

2-4 days

Unit 16: Whole Number Computation 2

(9 – 15 days)

*Common Core

· Multiply Whole Numbers

· Multiply 2-digit by 2-digit as multiple of ten

· Multiply 2-digit by 2-digit

3 – 5 days

*Common Core

· Divide Whole Numbers

· Divide with 2-digit divisor as multiple of ten with reminders

· Divide with 2-digit divisor with remainders

· Division word problems

3 – 5 days

BENCHMARK D – End of Year Benchmark

(all skills from Quarters 1-4 assessed)

May 16 – May 27 testing window

*Common Core - This skill will infuse the Maryland State Standards and the

Common Core.


TIME FRAME: 2-3 days

PREREQUISITE SKILLS

Proper Fractions and Mixed Numbers

· Fractions as part of a set

· Fractions as part of a whole

· Mixed numbers

· Fractions of a region (halves, thirds, fourths)

· Identify fractional sets (halves, thirds, fourths)

· Represent fractional sets (halves, thirds, fourths)

· Writing fractions

VSC OBJECTIVE (calculators allowed)

4.6.A.2.b Read, write, or represent proper fractions of a set which has the same number of items as the denominator using symbols, words, and models

ASSESSMENT LIMIT: Use denominators of 6, 8, and 10 with sets of 6, 8, and 10, respectively

4.6.A.2.a Read, write, and represent proper fractions of a single region using symbols, words, and models

ASSESSMENT LIMIT: Use denominators 6, 8, and 10

VOCABULARY

fraction

Numerator

Denominator

fraction bar

set

region

mixed number

ENDURING UNDERSTANDINGS

· Fractions represent parts of a whole or group.

· Fractions can be compared using a variety of models.

· Fractions express a relationship between two numbers.

ESSENTIAL QUESTIONS

· How are the numerator and denominator related?

· How can the fractional parts of a set be modeled?

· How can fractions be modeled using numerals, regions, sets, and number lines?

· When is it appropriate to use fractions?

CONCEPT KNOWLEDGE AND PROCESS

· A fraction is an EQUAL part of a whole or EQUAL part of a group.

· The numerator is the number of equal parts you have or want; the denominator is the TOTAL number of equal parts in the whole.

· A mixed number is a whole number and a fraction.

ERROR INTERVENTION

IF students confuse the numerator and denominator

THEN consider using the mnemonic that the denominator means down. Have students label and count the total number of equal pieces and write that in the denominator first before they write the numerator.

IF students misread what the question is asking for in the numerator

THEN consider requiring that students circle key words that identify what the question is asking for (e.g. highlight the difference between “How many pieces are shaded?” and “How many pieces are not shaded?”).

IF students do not recall that fractions must have equal pieces

THEN consider showing numerous examples of equal and non-equal pieces.

Suggested Learning Plan

Learning Activities and Strategies

Activity

Description

Materials

Visual

Spatial

Flagging Conversation

SF Grade 4 TE Lesson 9-1 (p. 500b)

The students learn about fractions as a part of a region by looking at boating signal flags.

*You can extend this activity by giving the students a fraction to represent and having them create their own signal flag with a meaning.

· Picture of signal flags with an explanation of their meanings.

Literature Connection

Visual

Spelling Fractions

The students shade parts of a region and determine the fraction of consonants or vowels in their spelling words.

· Spelling Fractions worksheet

· List of spelling words from Reading, Science or Social Studies

· Crayons or colored pencils

Visual

Social

What’s Your Favorite?

The students survey their classmates to find out their favorite pizza and create a pie chart to determine different fractional parts.

· Crayons

· What’s Your Favorite? worksheet #1

· What’s Your Favorite? worksheet #2

Visual

Spatial

Fractions in Paintings

SF Grade 4 TE Lesson 9-2 (p.502b)

The students identify fractional parts in a group in pictures and in artwork.

· Books or magazines with paintings or pictures

Social

Cooperative

How Many in the Group

SF Grade 4 TE Lesson 9-2 (p.502b)

The students write the fractions for different characteristics of the students in their tables or groups.

Visual

Kinesthetic

Food and Fractions

The students use food to replicate fractions as a part of a set.

· M&M’s, Skittles or Trail Mix

Visual

Kinesthetic

Mixed Number Bamboo Painting

The students use the integration of art to gain an understanding of mixed numbers. The students create a bamboo painting to represent a mixed number.

· Water Color Paints

· White Paper

· Bamboo Paint Brushes

· Bamboo Plant

Kinesthetic

Different Names, Same Number

SF Grade 4 TE Lesson 9-10 (p. 530a)

The students investigate the concept of mixed numbers using grid paper and by cutting wholes into parts.

· 10 x 10 grid paper

· Teaching Tool 5

· Scissors

DIFFERENTIATION

CROSS-CURRICULAR CONNECTIONS

Accommodations* G.A.T.E./Enrichment

Artful Teaching Literacy Integration


Resources

Sub-Skills

Teacher Created Materials

Adopted Textbooks

Technology

Fractions as part of a whole

· MW Exploring Fractions

· MW Exploring Fractions with tiles

· MW Fractional Regions

· SF Grade 4 TE Lesson 9-1 (pp. 500A-501)


· SF Grade 4 TE Lesson 9-10 (pp. 530-533)

· WEB: NLVM - Fraction Naming

Fractions as part of a set

· MW Fractional Sets

·

Mixed numbers

· MW Exploring Mixed Numbers

· MW Mixed Numbers

·

Writing in Math Other Resources

Assessments

TRACKING SHEET

CONCEPT

ASSESSMENT

MULTIPLE CHOICE QUESTION BANK

OTHER WAYS TO ASSESS


TIME FRAME: 1 – 2 days

PREREQUISITE SKILLS

Compare and Order Fractions and Mixed Numbers

· Compare proper fractions and mixed numbers

· Order proper fractions and mixed numbers

· Comparing numbers

· Ordering numbers

· Fractional number lines


4.6.A.2.g Compare and order fractions and mixed numbers with or without using the symbols (<, >, or =)

Assessment Limit: Use like denominators and no more than 3 numbers (0 to 20)

VOCABULARY

fraction

numerator

denominator

fraction bar

mixed number

whole number

compare

order

greater than

less than

equal to




· Fractions express a relationship between two numbers.

ESSENTIAL QUESTIONS

· How is the ordering of fractions the same as ordering whole numbers and how is it different?




· When is it appropriate to use fractions?


· A fraction is an EQUAL part of a whole or EQUAL part of a group.


· A mixed number is a whole number and a fraction.

ERROR INTERVENTION

IF students are having trouble visualizing the size of fractions

THEN consider using fraction tiles and have students compare and order fractions by laying out the tiles on their desks.

IF students overlook the value of the whole number when comparing/ordering fractions and mixed numbers

THEN consider requiring that students circle the whole numbers first and then compare/order the fractions. They should learn to compare the whole numbers first and then the numerators when the denominators are the same.

IF students read the relational symbol incorrectly

THEN consider having them draw teeth inside the > or < symbol because the sign wants to “eat” the greater fraction or mixed number.



Activity

Description

Materials

Kinesthetic

Visual

Spatial

Comparing Fraction Tiles

The students use fraction tiles to compare fractions and are able to visualize which fraction is greater or smaller.

· Fraction tiles *

· Blank paper

· Pencil

Cooperative

Visual

Kinesthetic

Place Your Order

The students work with their groups to represent and order fractions with like denominators.

· Index cards with fractions written on them

· Pencil or crayons

Visual

I Spy

The students spy on their classmates to determine fractions as a part of a group.

· I Spy! worksheet

· Pencil

DIFFERENTIATION





Resources

Sub-Skills


Adopted Textbooks

Technology

Compare proper fractions and mixed numbers

· MW Exploring Compare & Order Fractions

· MW Compare Fractions

· MW Exploring Compare Mixed Numbers

· MW Compare Mixed Numbers


· WEB: Greater Than, Less Than, or the Same

Order proper fractions and mixed numbers

· MW Order Fractions

· MW Order Mixed Numbers

·


Assessments

TRACKING SHEET

CONCEPT

ASSESSMENT





PREREQUISITE SKILLS

Proper Fractions and Mixed Numbers on a Number Line

· Create fractional number lines

· Write numbers on number line

· Identify locations on number line

· Write and Identify mixed numbers on number line

· Finding a fraction on a number line (up to fourths)

· Finding a location on a number line (up to fourths)


4.1.C.1.a Represent mixed numbers and proper fractions on a number line

Assessment Line: Use proper fractions with a denominators of 6, 8, or 10

VOCABULARY

fraction

numerator

denominator

fraction bar

mixed number

whole number




ESSENTIAL QUESTIONS



· How can fractions be modeled using numerals, regions, set, and number lines?


· A fraction is an equal part of a whole or part of a group (set).


ERROR INTERVENTION

IF students count the number of lines instead of the number of spaces

THEN consider having students highlight each space with a different color to find the denominator of the fraction.

IF students forget to label the whole number past 1 on a number line (mixed numbers on a number line)

THEN consider having students trace each whole number on a number line in a different color and write in the whole number before they actually write the mixed number/fraction.

IF students find the denominator by counting all of the equal spaces on a number line and not just the number of spaces between whole numbers

THEN consider modeling this common mistake and emphasizing that the denominator is only the number of equal spaces between two whole numbers.

IF students have trouble identifying a fraction/mixed number located between two other fractions

THEN consider requiring that students fill in all missing fractions on the number line before choosing the correct answer.



Activity

Description

Materials

Visual

Spatial

Concrete

Make a Number Line

The students use fraction tiles to create a number line.

· Fraction tiles *

Kinesthetic

In the Fold


The students create fractional number lines by folding strips of paper into equal sections and by labeling the fractions.

· Strips of paper that are at least 11 inches long

· Pencils

Kinesthetic

Visual

Pin the Fraction on the Number Line

The students place Post-it notes on number lines to begin to the connection between the denominator and the equal number of spaces on a number line.

· Post-it notes with various fractions written on them

· Blank number lines to accommodate fractions with different denominators

Kinesthetic

Visual

Number Line on a Floor

The students use the floor and create a class-size number line to plot specific points

· Fraction cards

· Students

· Sentence strip

DIFFERENTIATION





Resources

Sub-Skills


Adopted Textbooks

Technology

Create fractional number lines

· MW Create Fractional Number Line



· WEB: Identify Fractions

· WEB: Fractions on a Number Line – Drag and Drop

· WEB: Find Grammy

· WEB: Identify Mixed Fractions

Write numbers on number line

· MW Write Fractions on a Number Line

·

·

Find locations on number line

· MW Identify Locations on a Number Line

·

·

Mixed numbers on number line

· MW Mixed Numbers on a Number Line

·

·


Assessments

TRACKING SHEET

CONCEPT

ASSESSMENT





PREREQUISITE SKILLS

Add and Subtract Proper Fractions and Mixed Numbers

· Add proper fractions

· Subtract proper fractions

· Add mixed numbers

· Subtract mixed numbers

· Basic addition and subtraction facts

VSC OBJECTIVE (calculators not allowed)

4.6.C.1.e Add and subtract proper fractions and mixed numbers

Assessment Limits: Use 2 proper fractions with a single digit like denominators, 2 mixed numbers with a single digit,

like denominators a whole number and a proper fraction with a single digit denominator and numbers (0 to 20)

VOCABULARY

fraction

numerator

denominator

fraction bar

mixed number

whole number

proper fraction


· Operation strategies with fractions are similar to those used with whole numbers.



ESSENTIAL QUESTIONS

· What strategies can be developed to show computation with fractions?

· How are models used to show how fractional parts are combined or separated?



· A fraction is an equal part of a whole or part of a group (set).


ERROR INTERVENTION

IF students add both the numerator and denominator

THEN consider emphasizing repeatedly that the denominator stays the same when you are adding and subtracting like denominators.

IF students add both the numerator and denominator

THEN consider having the students show the work with fraction tiles.

IF students have trouble adding and subtracting a whole number with a fraction (e.g. 3 – ½)

THEN consider requiring that students draw a picture before adding or subtracting. If subtracting, they should cross out the part that needs to be taken away.

IF students have trouble knowing what parts of a mixed number and fraction to add together or subtract

THEN consider having students line up the problem vertically with one column for the fraction and one column for the whole number. This should help them stay organized.



Activity

Description

Materials

VisualConcrete

Adding Fraction Tiles

The students use fraction tiles to visualize the concept of adding fractions with like denominators.

· Fraction tiles *

Linguistic

Quilt Story


The students create stories and illustrate them to demonstrate adding fractions.

· Centimeter grid paper

DIFFERENTIATION





Resources

Sub-Skills


Adopted Textbooks

Technology

Add proper fractions

· MW Exploring Fraction Computation

· MW Add Proper Fractions



Subtract proper fractions

· MW Subtraction Proper Fractions

·

Add mixed numbers

· MW Exploring Mixed Number Computation

· MW Add Mixed Numbers

·

Subtract mixed numbers

· MW Subtract Mixed Numbers

·


Assessments

TRACKING SHEET

CONCEPT

ASSESSMENT





PREREQUISITE SKILLS

Probability

· Express object probability as a fraction

· Express spinner probability as a fraction

· Express conditional probability as a fraction

· Object probability (describing using words)

· Spinner probability (describing using words)

· Fractions


4.5.B.1.a Express the probability as a fraction

Assessment Limit: Use a sample space of no more than 6 outcomes

VOCABULARY

probability

favorable outcomes

total outcomes

possible outcomes

numerator

denominator

fraction bar

event

likely

unlikely

equally likely

impossible

certain

fair

unfair


· The likelihood of an event depends on the possible outcomes.

· Probability can be represented numerically and graphically.

ESSENTIAL QUESTIONS

· How can the possible outcomes for an event be determined?

· How is probability represented numerically?

· How is the likelihood of an event determined and communicated?


· Probability is the chance or likelihood of something happening.

· Probability can be written in terms of certain [WILL ALWAYS HAPPEN], impossible [WILL NEVER HAPPEN], less likely, more likely, or equally likely.

ERROR INTERVENTION

IF students forget to write probability as a fraction (e.g., they simply write the number of favorable outcomes)

THEN consider modeling this error for them and create a process chart for finding the probability with probability itself written as a fraction. Example: proba

Bility

IF students forget that adding or taking away objects changes the denominator and may change the numerator

THEN consider requiring that students draw pictures to show items that are added or taken away.

IF students write the fraction as the number of favorable outcomes over the number of remaining objects instead of the number of total outcomes

THEN consider requiring that students label and count the total number of objects and write that in the denominator first. Students should then circle the objects that make up the favorable outcomes.



Activity

Description

Materials

Kinesthetic

Visual

Concrete

Food and Probability

The students use food to explore the probability of a certain outcome. The students also discover how conditions can change the probability of an event.

· Skittles, M&Ms, Trail Mix or Fruit Loops

· Pencil and paper

Visual

Concrete

Raffle Jar

The students win raffle tickets in class and participate in a weekly drawing in order to learn the concept of events and outcomes.

· Raffle jar *

· Raffle tickets or strips of paper

Linguistic

Literature

Connection

Hundred Penny Box


The students find the probability of picking a penny with certain years printed on them after reading the story Hundred Penny Box.

· Book Hundred Penny Box by Sharon Bell Mathis

Kinesthetic

Coin Toss


The students flip coins to determine the possible outcomes and the probability of flipping heads or tails.

· Play money or

· Teaching Tool 7

· Coins

Social

Cooperative

Probability Design


The students develop a set of index cards and determine the probability of picking certain favorable outcomes.

· Index Cards

Visual

Concrete

Fractions = Probability


The students create a spinner and express the probability of landing on different colors as a fraction.

· Spinner *

· Teaching Tool 20 with six sections

· Crayons

DIFFERENTIATION





Resources

Sub-Skills


Adopted Textbooks

Technology

Object probability

· MW Exploring Probability

· MW Object Probability




· US: “Understanding: Probability and Odds”

· WEB: NLVM - Spinners

· US: “Discovering Math: Probability”

Spinner probability

· MW Spinner Probability

·

Conditional probability

· MW Conditional Probability


Assessments

TRACKING SHEET

CONCEPT

ASSESSMENT




TIME FRAME: 2 -3 days

PREREQUISITE SKILLS

Median, Mode, and Range

· Determine the range of a set of data

· Determine mode of a set of data

· Determine median of a set of data

· Interpreting tables

· Ordering numbers


4.4.B.2.a Determine median, mode, and range

ASSESSMENT LIMIT: Use no more than 8 pieces of data and whole numbers (0 to 100)

VOCABULARY

statistics

data

median

mode

range


· The type of data determines how data sets can be organized, displayed, and analyzed.

· Statistical measures provide a numeric picture of the shape of the data.

ESSENTIAL QUESTIONS

· In what ways can sets of data be represented by statistical measures?

· How can the mean, median, mode, and range be used to describe the shape of the data?

· How can range, median, and mode be computed and compared?


· Median is the middle number in a set of ordered data.

· Mode is the number that occurs the most often in a set of data.

· Range is the difference between the greatest number and the least number in a set of data.

ERROR INTERVENTION

IF students attempt to find the median, mode, and range without ordering the numbers from least to greatest

THEN consider requiring that they order the numbers from least to greatest before they solve the problem.

IF students do not remember the definitions of median, mode, and range

THEN consider thinking of creative ways to teach the meanings of the words:

Median: the median is the middle barrier on a street; draw three shirts (small, medium, and large) and label the middle one with an M for median and middle.

Mode: most often in data; relate the mode to what’s in style. Median, mode, and range rap

IF students have trouble finding the median when there is an event amount of data

THEN consider having them “spread out” the missing numbers between the two middle numbers and then find the median.



Activity

Description

Materials

Social

Kinesthetic

Pet Summary

SF Grade 4 TE Lesson 4-12 (p. 226A)

The students are introduced to mode, median, and range by taking a survey of how many pets that they have.

· Index cards

Kinesthetic

Visual

Comparing Cubits

SF Grade 4 TE Lesson 4-12 (p. 226B)

The students work in groups to visualize what mode, median, and range look like.

· Adding machine tape or other strips of paper

· Scissors

Kinesthetic

Visual

Concrete

Hands-on Activity

The students use data that is relevant to them and complete a hands-on activity in order to find the mode, median, and range of the data.

· Scissors

· Construction paper

· Crayons

· 1-inch graph paper

· Data on a transparency

Auditory

Mode, Median, Range Rap

The students learn the meaning of mode, median, and range by learning a rap.

· Song on overhead

· Teacher copy of the rap

· Student copy of the rap

DIFFERENTIATION





Resources

Sub-Skills


Adopted Textbooks

Technology

Determine the range of a group of data

· MW Exploring Median, Mode, and Range

· MW Range


· US: “Estimating a Range"

· WEB: "Rags to Riches"

· US: "Mean, Median, Mode, Range, and Overall Distribution"

· WEB: Maths: Handling Data - Mode, median, and mean

· US: Math Mastery: Graphs and Statistics

· WEB: BrainPOP: Spelling Test Scores

Determine mode of a group of data

· MW Mode

·

·

Determine median of a group of data

· MW Median

·

·


Assessments

TRACKING SHEET

CONCEPT

ASSESSMENT





PREREQUISITE SKILLS

Line Plots

· Create line plots

· Interpret line plots

· Interpreting tables

· Ordering numbers

· Range, median, and mode


4.4.B.1.a Interpret line plots

ASSESSMENT LIMIT: Use no more than 20 pieces of data with a range no more than 10 and whole numbers (0 to 100)

4.4.A.1.b Organize and display data in line plots and frequency tables using a variety of categories and sets of data

ASSESSMENT LIMIT: Use line plots with no more than 20 pieces of unorganized data and a range of no more than 10 and whole numbers (0 – 100)

VOCABULARY

statistics

graph

data

title

key

horizontal axis

median

mode

range

outlier

gap

cluster

line plot


· Representation of data depends on the characteristics of that data.


ESSENTIAL QUESTIONS

· What data display is appropriate for a given set of data?

· How does the type of data influence the choice of graph?

· What kinds of questions can be answered using different data displays?


· Line plots show the frequency and spread of data.

ERROR INTERVENTION

IF students randomly guess an answer in a multiple choice problem or miss a data point

THEN consider requiring that students draw the data in a line plot before matching it with the best answer.

IF students confuse line plots and line graphs

THEN consider making the connection between a line plot and planting seeds in which they plot one or more seeds on a direct line.

IF students confuse the meaning of the Xs

THEN consider having students design a large class line plot and then place individual cut-out X’s on the plot. They will then see that one X represents one person.

IF students have trouble finding the median, mode, and range by simply looking at a line plot

THEN consider requiring that they translate the Xs into a list of numerical data from least to greatest.

IF students have trouble understanding the difference between “3 or more” and “more than 3”

THEN consider having them circle the data on the graph. This helps visual learners understand the meaning of the question.

IF students do not understand the meaning of the question

THEN consider having them underline key words and ask themselves: “Is this question asking me to look at the Xs or to look at the horizontal axis?”



Activity

Description

Materials

Social

Cooperative

Line Up the Kids


The students interpret a line plot that is based on class survey results.

· Chalkboard or white board

· Chalk or dry erase markers

Kinesthetic

How Many Breaths per Minute?


The class collects data and displays it on a line plot. The students interpret the data on the line plot by looking at the number of “Xs” over each number.

· Clock with a second hand or stop watch

Verbal

Journal Idea

SF Grade 4 TE Lesson 4-7 (p. 207)

The students demonstrate that they are able to create a line plot based on data by completing a journal assignment where they have to describe the steps to create a line plot.

· Pencil

· Paper or journal notebook

Kinesthetic

Visual

Social

Human Line Plot *

The students create a line plot using information based on themselves and place their data on the horizontal axis.

· Chart paper or large poster board

· 1 paper X per student

· Tape or glue

· Markers

· Crayons

Kinesthetic

A Handful of Counters


The students create a line plot based on the number of counters that they grab in their hands.

· Counters or

· Teaching Tool 14

DIFFERENTIATION





Resources

Sub-Skills


Adopted Textbooks

Technology

Create line plots

· MW Create Line Plots


· WEB: Plop It!

Interpret line plots

· MW Exploring Interpret Line Plots

· MW Interpret Line Plots


Assessments

TRACKING SHEET

CONCEPT

ASSESSMENT





PREREQUISITE SKILLS

Coordinate Plane

· Identify locations on a coordinate grid given object

· Identify objects on a coordinate grid given location

· Number lines

· Identifying the X and Y axis


4.1.C.1.b Identify positions in a coordinate plane

ASSESSMENT LIMIT: Use the first quadrant and ordered pairs of whole numbers (0 to 20)

VOCABULARY

coordinate grid

coordinate plane

ordered pair

horizontal

vertical

plot

origin


· Ordered pairs show an exact location on a coordinate plane.

· Functional relationships can be represented graphically and symbolically.

ESSENTIAL QUESTIONS

· How is the location of a point on a grid described?

· How are graphs, tables, and symbols used to represent relationships?


· A coordinate grid describes the location of an object by its distance from a horizontal and vertical axis.

ERROR INTERVENTION

IF students mistakenly label points by writing the vertical point first and then the horizontal point

THEN consider teaching students a creative mnemonic to remember “over, then up.”

Examples: 1.) Superman runs before he flies.

2.) In basketball, you dribble the

ball before you shoot.

IF students forget to start at zero

THEN consider requiring that they put a star at zero before plotting any points.



Activity

Description

Materials

Kinesthetic

Classroom Coordinate Grid

Create a coordinate grid on the classroom floor and allow the students to slide horizontally and vertically to the ordered pair that they drew from the deck of cards.

· Blue painter’s tape *

· Deck of cards

Games

Treasure Map Bingo

The students choose five locations on a coordinate grid treasure map and win BINGO if all of their ordered pairs are called on their Treasure Map.

· 1-inch graph paper

· Deck of cards

· Markers

Visual

Spatial

What’s the Location?


The students compare a coordinate grid to a map and describe the ordered pairs as streets and avenues.

· Chalkboard or whiteboard

· Chalk or dry erase markers

· Ruler

DIFFERENTIATION





Resources

Sub-Skills


Adopted Textbooks

Technology

Identify locations on a coordinate grid given object

· MW Exploring Coordinate Grid

· MW Identify Locations Coordinate Grid


· US: "Coordinate Mapping"

· WEB: Plot Points on a Coordinate Grid

Identify objects on a coordinate grid given location

· MW Identify Objects Coordinate Grid

·


Assessments

TRACKING SHEET

CONCEPT

ASSESSMENT




TIME FRAME: 2 - 3 days

PREREQUISITE SKILLS

Interpret Line Graphs

· Interpret line graphs

· Addition

· Subtraction

· Range, median, mode


4.4.B.1.b Interpret line graphs

ASSESSMENT LIMIT: Use the x-axis representing no more than 6 time intervals, the y-axis consisting of no more than 10 intervals with scales as factors of 100 using whole numbers (0 to 100)

VOCABULARY

statistics

graph

data

title

scale

Interval

horizontal axis

vertical axis

Increase

decrease

no change

line graph


· Representation of data depends on the characteristics of that data.


ESSENTIAL QUESTIONS

· What data display is appropriate for a given set of data?

· How does the type of data influence the choice of graph?

· What kinds of questions can be answered using different data displays?


· Line graphs show how data changes over time.

· Horizontal axis will always be time.

ERROR INTERVENTION

IF students do not see where the greatest increase or decrease is

THEN consider having them subtract between each data point to show the change.

IF students do not recognize where a line graph increases, decreases, or stays the same

THEN consider using arm signals for up, down, and no change and having students draw arrows on each segment of the line graph.

IF students don’t understand the question

THEN make a list of typical questions and operations that could be used to answer a question.



Activity

Description

Materials

Linguistic

What Story Does the Graph Tell?


The students look at a line graph and create a story to describe how the data in the graph changed over time.


· Pencil

Concrete

Visual

How Am I Doing?

Students look at their own class work or tests to create a line graph and determine how their grades have changed over the school year.

· Student work samples

· Graph paper

· Rulers

· Pencils

Kinesthetic

Visual

Arm Signals

The students use movements of their arms to indicate whether the data increases, decreases or remains the same as time progresses.

· Example of a line graph on the overhead

· Overhead projector

Linguistic

What Story Does the Graph Tell?


The students look at a line graph and create a story to describe how the data in the graph changed over time.


· Pencil

DIFFERENTIATION





Resources

Sub-Skills


Adopted Textbooks

Technology

Interpret line graphs

· MW Interpret Line Graphs


· WEB: Create A Graph

· WEB: Print Your Own Graph Paper


Assessments

TRACKING SHEET

CONCEPT

ASSESSMENT





PREREQUISITE SKILLS

Write Expression

· Write expressions using addition and subtraction

· Write expressions using multiplication and division

· Writing expressions using addition

· Writing expressions using subtraction


4.1.B.1.a Represent numeric quantities using operational symbols (+, -, ×, ÷ with no remainders)

ASSESSMENT LIMIT: Use whole numbers (0 to 100)

VOCABULARY

operation

operational symbols


· Mathematical expressions and equations represent relationships among quantities.

· Symbolic notation is used to represent mathematical relationships.

ESSENTIAL QUESTIONS

· How does a mathematical expression differ from a number sentence?

· How is a number sentence like a balance scale?

· How are symbols used to represent mathematical relationships including operations, equality, and inequality?


· An expression names an amount.

ERROR INTERVENTION

IF students do not understand which operation to use to write or solve the problem

THEN consider making a list of addition, subtraction, multiplication, and division clue words. Students should then circle important numbers and underline clue words before determining the operation needed.


THEN consider having them draw a picture to represent the problem. They can then usually identify the correct operation.


THEN consider having them visualize the problem, determine if the answer is increasing (+ or x) or decreasing (- or ÷) in equal groups or non-equal groups, and then identify the correct operation.



Activity

Description

Materials

Verbal

Develop Clue Words *

The students create an ongoing list of clue words that will aid them in choosing the appropriate operational symbol to complete the expression.

· Chart paper

· Markers

· Teacher clue word sheet

· Student clue words sheets

Auditory

Kinesthetic

Visual

Name That Expression

The students use clue words to determine if the solution to an expression will be bigger or smaller and to determine the appropriate operational symbol to use in the expression.

· White board

· White board markers

· Overhead

· Pre-prepared word problems

Linguistic

Auditory

Read to Understand


Students identify clue words and record them on a chart as they read different phrases.

· Chart paper

DIFFERENTIATION





Resources

Sub-Skills


Adopted Textbooks

Technology

Write expressions using addition and subtraction

· MW Exploring Write Expression

· MW Write Expressions Addition and Subtraction


· SF Grade 4 TE lesson 3-12 (pp. 160A-163)

· WEB: Math Playground: Various Word Problems

· WEB: Four Square for Story Problems

Write expressions using multiplication and division

· MW Write Expressions Multiplication and Division

·

·


Assessments

TRACKING SHEET

CONCEPT

ASSESSMENT





PREREQUISITE SKILLS

Equivalent Expressions

· Write equivalent expressions

· Writing expressions for addition

· Writing expressions for subtraction


4.1.B.1.b Determine equivalent expressions

ASSESSMENT LIMIT: Use whole numbers (0 to 100)

VOCABULARY

equivalent

expression

equal

fact family




ESSENTIAL QUESTIONS





· An expression names an amount.

ERROR INTERVENTION

IF students assume that because two problems have the same numbers, they are equivalent (Example: students think that 5 + 3 = 5 x 3)

THEN consider requiring students to solve each expression before determining the correct answer. They will then see that 5 + 3 ≠ 5 x 3.

IF students do not understand what equivalent means

THEN consider underlining the “equ” in equivalent, equal, and equation.



Activity

Description

Materials

Visual

Kinesthetic

Cooperative

Balancing Act

The students use a number balance to determine whether their expressions are equivalent to their partner’s expression.

· Number balance *

· Calculator *

Kinesthetic

Visual

Equal Expressions

The students use white boards to compose an expression equivalent to an expression that is given.

· Whiteboards

· Dry erase markers

Concrete

How Many Ways to 12

The students learn about writing equivalent expressions by finding how many different ways they can make 12 using addition, subtraction, multiplication and division.

· Pencil

· Paper

· Calculator *

DIFFERENTIATION





Resources

Sub-Skills


Adopted Textbooks

Technology

Write equivalent expressions

· MW Exploring Write Equivalent Expressions

· MW Write Equivalent Expressions



· WEB: Can You Balance?

· WEB: Match Equivalent Expressions

· WEB: Cyberchase – Poodle Weigh In


Assessments

TRACKING SHEET

CONCEPT

ASSESSMENT




TIME FRAME: 2 – 4 days

PREREQUISITE SKILLS

Write Relationships

· Evaluate relationships with missing relational symbols

· Represent relationships in word problems

· Comparing expressions

· Evaluate relationships with addition and subtraction

· Represent relationships in addition and subtraction word problems


4.1.B.2.a Represent relationships using relational symbols (>, <, =) and operational symbols (+, -, ×, ÷) on either side

Assessment Limit: Use operational symbols (+, -, ×) and whole numbers (0 to 200)

VOCABULARY

expression

relational symbols

operational symbols

equal

balance

not equal

Inequality

equivalent




ESSENTIAL QUESTIONS





· A relationship where two expressions have the same value has an = sign.

· A relationship where two expressions do not have the same value has a > or < sign.

ERROR INTERVENTION

IF students become overwhelmed by the wordiness of the problem

THEN consider having them highlight the first expression in one color and the second expression in another color; write the first expression, then write the second expression; finally, compare the expressions.

IF students rush to input operational symbols

THEN consider requiring that they plug in all possible operational symbols before determining the correct answer.

IF students choose a relationship as correct just by looking at the numbers

THEN consider requiring that they solve each expression before determining the correct answer.



Activity

Description

Materials

Verbal

Develop Clue Words

The students create an ongoing list of clue words that will aid them in choosing the appropriate operational symbol to complete the expression.

· Chart paper

· Markers

· Student clue words sheets

Auditory

Kinesthetic

Visual

Name That Expression

The students use clue words to determine if the solution to an expression will be bigger or smaller and to determine the appropriate operational symbol to use in the expression.

· White board

· White board markers

· Overhead

· Pre-prepared word problems

Linguistic

Auditory

Read to Understand


Students identify clue words and record them on a chart as they read different phrases.

· Chart paper

Kinesthetic

Visual

Pinch Cards

The students use an index card with relational symbols on it to indicate the appropriate relationship between two expressions.

· Index Cards with > < = on them

· Markers

DIFFERENTIATION





Resources

Sub-Skills


Adopted Textbooks

Technology

Evaluate relationships with missing relational symbols

· MW Exploring Relationships

· MW Evaluate Relationships Missing Relationships


· WEB: BrainPOP: Inequalities Movie

Represent relationships in word problems

· MW Represent Relationships in word problems


Assessments

TRACKING SHEET

CONCEPT

ASSESSMENT





PREREQUISITE SKILLS

Angles

· Identify right angles

· Identify acute and obtuse angles

· Identify angles in shapes and objects

· Rays, lines, and line segments


4.2.A.1.b Identify, compare, classify, and describe angles in relationship to another angle

ASSESSMENT LIMIT: Use acute, right, or obtuse angles

VOCABULARY

geometry

point

Line

ray

line segment

vertex

angle

endpoint

right angle

acute angle

obtuse angle


· Objects can be described and compared using geometric attributes.

· A three dimensional figure can be analyzed in terms of its two-dimensional parts.

ESSENTIAL QUESTIONS

· How are angles classified?

· What makes one angle different from another?


· An angle is created from two rays that share an endpoint.

· A right angle forms the corner of a square.

· An acute angle is smaller than a right angle.

· An obtuse angle is bigger than a right angle.

ERROR INTERVENTION

IF students confuse acute angles, right angles, and obtuse angles

THEN consider using a mnemonic to distinguish between the types of angles:

An acute angle is “a cute” little baby angle.

An obtuse angle looks like an open book.

A right angle is “just right.” It makes a perfect L.

IF students have trouble identifying angles within shapes

THEN consider having students highlight the rays to better see the angle.

IF students have trouble identifying angles within shapes

THEN consider having them put a square in the angle.

IF students have trouble identifying angles that are turned

THEN consider encouraging students to turn their paper so that the angle looks “right side up.”



Activity

Description

Materials

Visual

Spatial

Geometry on the Geoboard

SF Grade 4 TE Lesson 8-3 (p. 440a)

The students use Geoboards to represent different types of angles by intersecting lines.

· Geoboard or

· Geoboard paper

· Rubber bands

Visual

Kinesthetic

Cooperative

Angles on the Floor

The students work in pairs to identify types of angles using a index card to see if the angle is bigger, smaller, or equal to a right angle.

· Blue painter’s tape

· Index cards *

Visual

Kinesthetic

I Spy Right Angles

The students identify right angles that they see within the classroom and mark them by creating a square inside the angle with blue painter’s tape.

· Blue painters tape

Visual

Kinesthetic

Game

Geometry Simon Says

The students play a game of Simon Says where they have to create angles and lines using arm signals.

DIFFERENTIATION





Resources

Sub-Skills


Adopted Textbooks

Technology

Identify right angles

· MW Exploring Angles

· MW Identify Right Angles


· WEB: Alphabet Geometry: Right Angles

· WEB: Alphabet Geometry: Acute Angles

· WEB: Alphabet Geometry: Obtuse Angles

Identify acute and obtuse angles

· MW Identify Acute Obtuse Angles

·

·

Identify angles in shapes and objects

· MW Identify Angles in Objects


Assessments

TRACKING SHEET

CONCEPT

ASSESSMENT





PREREQUISITE SKILLS

Transformations

· Identify translations

· Identify reflections

· Identify rotations

· Flips

· Turns

· Slides

· Congruence

· Symmetry


4.2.E. 1.a Identify and describe the results of translations, reflections, and rotations

ASSESSMENT LIMIT: Use a horizontal line translation, reflection over a vertical line, or rotation of 90° clockwise around a given point of a geometric figure or picture

4.2.D.1.a Identify and describe geometric figures as congruent

ASSESSMENT LIMIT: Identify the result in a transformation as being congruent to the original figure

VOCABULARY

geometry

congruent

transformation

translation

reflection

rotation


· A transformation is a specific movement of an object.

· Changing the position of an object does not affect its attributes.

ESSENTIAL QUESTIONS

· In what ways can the position of geometric figures be changed?

· What are translations, rotations, and reflections?


· A transformation moves a shape to a new spot without changing its size or shape

· You can transform (move) a shape three ways: by flipping it, sliding it, or turning it.

· A flip, or reflection, is a mirror image of a figure on the opposite side of a line.

· A slide, or translation, is a figure moved a certain distance in a given direction.

· A turn, or rotation, moves a figure around a point.

ERROR INTERVENTION

IF students confuse translations, reflections, and rotations

THEN consider emphasizing the similar letters

SLide is a tranSLation.

TuRn is a RoTation.

FLip is a reFLection.

IF students confuse translations, reflections, and rotations

THEN consider doing hand movements to help them identify the transformations.

IF students have trouble identifying a rotation

THEN consider having them actually turn their paper and observe how the figure looks as it turns.

IF students forget that transformations must be congruent

THEN consider requiring that they trace the initial figure and then translate, rotate, or reflect it to check their work



Activity

Description

Materials

VisualKinesthetic

Finger Painting *

The students learn about translations by using finger paints and their hands as the object being transformed.

· Three large pieces of paper folded in half (per student)

· Finger paints

Visual

Kinesthetic

Spatial

Letter Cut Outs *

The students use letter cut-outs to translate, reflect, and rotate over a dotted line.

· Large pieces of construction paper

· Letter cut outs of the first letter of the first name of each student in the class.

Kinesthetic

Auditory

“Transformation Shuffle”

The students translate, reflect and rotate to the tune of a popular hip-hop song.

· Words to transformation shuffle

· Song “Cupid Shuffle” by Cupid

DIFFERENTIATION





Resources

Sub-Skills


Adopted Textbooks

Technology

Identify translations

· MW Identify Translations


· WEB: NLVM - Playing with Translations

· WEB: NLVM - Playing with Reflections

· WEB: NLVM - Playing with Rotations

· WEB: Alphabet Geometry: Transformations

Identify reflections

· MW Identify Reflections

·

·

Identify rotations

· MW Identify Rotations

·

·


Assessments

TRACKING SHEET

CONCEPT

ASSESSMENT



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Documents

Knowledge and Skills - files.mrschoice.webnode.comfiles.mrschoice.webnode.com/200000008-d4ef5d5e93/GR… · Web viewRepresent relationships in word problems 2 – 4 days Unit 8: