Fraction Equivalence Ordering and Operations Session Objectives Examination of the development of mathematical understanding across the module with a focus on the Concept Development within the ID: 718094
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Slide1
A Story of Units
Grade 4 – Module 5
Fraction Equivalence, Ordering, and OperationsSlide2
Session Objectives
Examination of the development of mathematical understanding across the module
with a
focus
on the
Concept Development within the
lessons
Introduction to mathematical models and instructional strategies to support implementation of
A Story of
UnitsSlide3
Agenda
Introduction to the Module
Concept Development
Module ReviewSlide4
Curriculum Overview of A Story of UnitsSlide5
Module Overview
R
ead the Narrative, Standards, Lesson Objectives, and Vocabulary.
What is
familiar
to you and your students?
What will be new learning?Slide6
Mid-Module Assessment
Study this document, and the End Module Assessment, prior to teaching the Lessons.
Provides a snapshot of the concepts taught over the next 21 Lessons.
Scan the Mid-Module Assessment to get an idea of what topic we are about to cover.
Topics A - DSlide7
Agenda
Introduction to the Module
Concept Development
Module ReviewSlide8
Topic A: Decomposition and Fraction Equivalence
6 lessons to show fraction equivalence through decomposition of fractions
Tools: number bond, folding paper strips, tape diagram, area model
4.NF.3b, 4.NF.4aSlide9
Decomposition of Fractions
Lesson 1, Concept Development
Use a strip of paper to represent, for example, thirds and sixths.
Show how a non-unit fraction is the sum of unit fractions.
Extend learning to show that non-
unxxit
fractions can be expressed as the sum of two or more fractions (unit or non-unit).Slide10
Decomposition of Fractions
Extend learning to fractions representing numbers greater than one.
Use tape diagrams to represent fractional parts.
Discover that there are multiple ways to decompose fractions.
Lesson 1, Concept DevelopmentSlide11
Lesson 2, Concept Development
Debrief: How is decomposing a non-unit fraction similar to decomposing whole numbers in Kindergarten and Grade 1? Slide12
Decomposition of Fractions
Express a non-unit fraction as a whole number times a unit fraction.
Lesson 3, Concept DevelopmentSlide13
Decomposition of Fractions
Decompose fractions into sums of smaller unit fractions.
Draw and label to show the equivalence of fractions.
Lesson 4, Concept DevelopmentSlide14
Decomposition of Fractions
Lesson 5, Application ProblemSlide15
Decomposition of Fractions
Show fraction equivalence using an area model.
Model equivalence by drawing an area model.
Lesson 5, Concept DevelopmentSlide16
Decomposition of Fractions
Create equivalent fractions by drawing an area model and then dividing it into smaller parts.
Lesson 6, Concept DevelopmentSlide17
Decomposition of Fractions
Turn and Talk to those sitting at your table
:
H
ow can decomposing fractions lead to better understanding of the representation of non-unit fractions and to fraction equivalence?
How do number bonds, tape
diagrams, and area models aid in
the understanding of the
decomposition of fractions?
Topic A DebriefSlide18
Topic B: Fraction Equivalence Using Multiplication and Division
5 lessons to show fraction equivalence using multiplication and division.
New Terms: numerator, denominator
Tools: tape diagrams, area model, number line
4.NF.1Slide19
Fraction Equivalence
Lesson 7, Application ProblemSlide20
Fraction Equivalence
Decompose the area model to show equivalence.
Create equivalent fractions by multiplying the numerator and denominator by the same number.
Lessons 7 and 8, Concept DevelopmentSlide21
Fraction Equivalence
Lesson 11, Application ProblemSlide22
Fraction Equivalence
Compose larger fractional units.
Discover that the numerator and denominator can be divided by the same number to model equivalence.
Lesson 9, Concept DevelopmentSlide23
Fraction Equivalence
Lesson 10, Concept Development
Use knowledge of common factors to show equivalent fractions.
Show equivalence using the greatest common factor.Slide24
Fraction Equivalence
Use a number line to show equivalence.
Lesson 11, Concept DevelopmentSlide25
Fraction Equivalence
Turn and Talk to those sitting at your table
:
How does the modeling used within this Topic help students to conceptually understand fractional equivalence?
Topic B Slide26
Topic C: Fraction Comparison
4
lessons to show comparison of fractions using benchmark numbers and common units
New Term: benchmarks
Tools: number line, tape diagrams, area models, number bonds
4.NF.2Slide27
Fraction Comparison
Think about fractions in relation to 0, ½ , and 1, first in isolation and then in fraction comparison.
Lesson 12, Concept DevelopmentSlide28
Fraction Comparison
Compare two fractions greater than one using benchmarks.
Lesson 13, Concept DevelopmentSlide29
Fraction Addition and Subtraction
Subtraction of a fraction from a whole using different methods
Lesson 17, Concept DevelopmentSlide30
Fraction Comparison
Common numerators
Numerators with related units
Lesson 14, Concept DevelopmentSlide31
Fraction Comparison
Denominators with related units
Lesson 14, Concept DevelopmentSlide32
Fraction Comparison
Denominators with unrelated units
Use of the area model to create common units for comparison
Use of number bonds to ‘pull out’ a whole and then compare the parts
Lesson 15, Concept DevelopmentSlide33
Fraction Comparison
Turn and Talk:
What methods of fraction comparison are familiar?
What methods of fraction comparison are new?
How can each of the methods be used to help students as they compare fractions?
Topic C Slide34
Topic D: Fraction Addition and Subtraction
6 lessons to show addition and subtraction of fractions with an emphasis on common units
New Terms: common denominators, mixed units
Tools: number line, tape diagram, number bond
4.NF.3a, 4.NF.4dSlide35
Fraction Addition and Subtraction
Unit language is used to relate addition and subtraction of fractions to addition and subtraction of whole numbers.
Lesson 16, Concept DevelopmentSlide36
Fraction Addition and Subtraction
Conversion from a fraction greater than one to a mixed number using a number bond
Lesson 16, Concept DevelopmentSlide37
Fraction Addition and Subtraction
Students work in groups to find multiple ways of solving
Lesson 18, Concept DevelopmentSlide38
Fraction Addition and Subtraction
Lesson 19, Application Problem
m
easuring inches
cooking a recipe
telling time
buying deli meat
money
measuring turns
gas gauge
m
easuring spoons and cupsSlide39
Fraction Addition and Subtraction
Lesson 19, Concept Development
Students use multiple solution strategies to solve.
Use RDW to solve. Try solving 2 ways.Slide40
Fraction Addition and Subtraction
Adding with related units
Lesson 20, Concept DevelopmentSlide41
Fraction Addition and Subtraction
Lesson 21, Concept DevelopmentSlide42
Fraction Addition and Subtraction
Turn and Talk:
How is subtracting fractions similar to subtracting whole numbers?
Discuss the progression and the importance of the number bond model across grades.
Topic DSlide43
Topic E:
Extending Fraction Equivalence to Fractions Greater Than One
7
lessons working with fractions greater than one to rename, order, and compare.
New Terms: line plot
Tools: number line, tape diagram, number bond, line plot
4.NF.1, 4.NF.2, 4.NF.3Slide44
Extending Fraction Equivalence to Fractions
>1
Lesson 22, Concept DevelopmentSlide45
Extending Fraction Equivalence to Fractions >1
Lesson 23, Concept DevelopmentSlide46
Extending Fraction Equivalence to Fractions >1
Rename fractions as mixed units using decomposition
Convert using multiplication
Lesson 24, Concept DevelopmentSlide47
Extending Fraction Equivalence to Fractions >1
Use RDW to solve:
Lesson 25, Application ProblemSlide48
Extending Fraction Equivalence to Fractions >1
Convert a mixed number to a fraction greater than one.
Lesson 25, Concept DevelopmentSlide49
Extending Fraction Equivalence to Fractions >1
Compare fractions greater than one by reasoning
using benchmark numbers.
Lesson 26, Concept DevelopmentSlide50
Extending Fraction Equivalence to Fractions >1
Comparison with related denominators
Comparison with unrelated denominators
Lesson 27, Concept DevelopmentSlide51
Extending Fraction Equivalence to Fractions >1
Plot fractions on a line plot and then use the line plot to help solve word problems.
Lesson 28, Concept DevelopmentSlide52
Extending Fraction Equivalence to Fractions >1
Turn and Talk:
How does the content of this Topic build on the learning of Topics A-D? How does the content of A-D help students realize success with this Topic?
Which of the strategies from this module have you previously taught?
Topic ESlide53
Topic F
:
Addition and Subtraction of Fractions by Decomposition
6 lessons working with fractions greater than one to estimate and find sums and differences
Tools: number line, number bond
4.NF.3c, 4.NF.3d, 4.MD.4Slide54
Addition & Subtraction of Fractions by Decomposition
Lesson 29, Concept Development
Rounding is used to establish an estimated sum or difference.Slide55
Addition
& Subtraction of Fractions by Decomposition
Use different strategies to add fractions
Lesson 30, Concept DevelopmentSlide56
Addition
& Subtraction
of Fractions by Decomposition
Lesson 30, Concept DevelopmentSlide57
Addition & Subtraction of Fractions by Decomposition
Addition of mixed numbers using different strategies
Lesson 31, Concept DevelopmentSlide58
Addition & Subtraction of Fractions by Decomposition
Lesson 32, Concept Development
Subtraction of a fraction from a mixed number using different strategiesSlide59
Addition & Subtraction of Fractions by Decomposition
Lesson 32, Concept Development
Subtraction of a fraction from a mixed number using different strategiesSlide60
Addition & Subtraction of Fractions by Decomposition
Subtract a mixed number from a mixed number using multiple strategies
Lesson 33, Concept DevelopmentSlide61
Addition & Subtraction of Fractions by Decomposition
Subtract with mixed numbers
Lesson 34, Concept DevelopmentSlide62
Addition & Subtraction of Fractions by Decomposition
Turn and Talk:
What from this Topic was new learning?
What advantages can you see in introducing multiple strategies to students?
Topic FSlide63
Topic G:
Repeated
Addition of Fractions
as Multiplication
6 lessons focusing on addition of fractions as multiplication
Tools: number line, tape diagram, number bond, line plot
4.NF.4abc, 4.MD.4Slide64
Repeated Addition of Fractions as Multiplication
Represent the multiplication of
n
times
a/b
as (
n×a
)/b
using
the associative
property and visual models
.
Lesson 35, Concept DevelopmentSlide65
Repeated Addition of Fractions as Multiplication
Patti needs 6 pieces of yarn that are each 3 eighths meter long. How much yarn does Patti
need?
Lesson 36, Concept DevelopmentSlide66
Repeated Addition of Fractions as Multiplication
Lesson 37, Application ProblemSlide67
Repeated Addition of Fractions as Multiplication
Lesson 37 and 38, Concept DevelopmentSlide68
Repeated Addition of Fractions as Multiplication
Solve multiplicative comparison word problems.
Lesson 39, Concept DevelopmentSlide69
Repeated Addition of Fractions as Multiplication
Solve word problems involving the multiplication of a whole number and a fraction including those involving line plots.
Lesson 40, Concept DevelopmentSlide70
Repeated Addition of Fractions as Multiplication
Turn and Talk:
How do the strategies taught within this Topic help students to be successful when solving problems involving a whole number times a mixed number?
Topic GSlide71
Topic H: Exploration
F
ind and use a pattern to calculate the sum of all fractional parts between zero and one.
Students work together to solve and
critique the thinking of others.
4.OA.5Slide72
Complete the End-of-Module Assessment.
Now with all of the mathematical knowledge and understanding of the models, review the assessment.
You may work alone or with your table to discuss challenges or successes students and teachers may face.
How do the Topics in this Module help to prepare students for success?
End-of-Module Assessment Slide73
Agenda
Introduction to the Module
Concept Development
Module ReviewSlide74
Biggest Takeaway
Turn and Talk:
What questions were answered for you?
What new questions have surfaced?Slide75
Key Points
The learning of fractions follows the same instructional sequence as the learning of whole numbers.
Fractional units behave just as all other units do, and can be manipulated like whole numbers.
Decomposing fractions strengthens the part-whole relationship.
Fraction equivalence and comparison are supported by visual models.