Lesson 5 | Fraction Equivalence and Ordering | 4th Grade Mathematics

Objective

Recognize and generate equivalent fractions with smaller units using tape diagrams.

Common Core Standards

Core Standards

The core standards covered in this lesson

4.NF.A.1 — Explain why a fraction a/b is equivalent to a fraction (n × a)/(n × b) by using visual fraction models, with attention to how the number and size of the parts differ even though the two fractions themselves are the same size. Use this principle to recognize and generate equivalent fractions.

Number and Operations—Fractions

4.NF.A.1 — Explain why a fraction a/b is equivalent to a fraction (n × a)/(n × b) by using visual fraction models, with attention to how the number and size of the parts differ even though the two fractions themselves are the same size. Use this principle to recognize and generate equivalent fractions.

Foundational Standards

The foundational standards covered in this lesson

3.NF.A.3

Number and Operations—Fractions

3.NF.A.3 — Explain equivalence of fractions in special cases, and compare fractions by reasoning about their size.
4.OA.A.1

Operations and Algebraic Thinking

4.OA.A.1 — Interpret a multiplication equation as a comparison, e.g., interpret 35 = 5 × 7 as a statement that 35 is 5 times as many as 7 and 7 times as many as 5. Represent verbal statements of multiplicative comparisons as multiplication equations.

Criteria for Success

The essential concepts students need to demonstrate or understand to achieve the lesson objective

Understand that equivalent fractions are fractions that refer to the same whole and are the same size.
Generate equivalent fractions with smaller units using visual models, namely tape diagrams (MP.5).
Show that two fractions are equivalent using visual models, and explain why the models demonstrate their equivalence (MP.3).
Understand that equivalence is valid only when two fractions refer to the same whole.

Tips for Teachers

Suggestions for teachers to help them teach this lesson

Students are familiar with equivalent fractions and how to recognize and generate simple ones from Grade 3 (3.NF.3).
Depending on students’ comfort level with fraction representations from Grade 3, particularly tape diagrams/fraction strips and number lines, Lessons 5 and 6 can be combined.
The standards state that work with fractions in Grade 4 is limited to fractions with denominators 2, 3, 4, 5, 6, 8, 10, 12, and 100, but in this lesson and throughout the unit, students are exposed to and asked to work with fractions whose denominators may not be included in that list. Bill McCallum notes that “The restrictions in the standards are intended to both restrict what can be put on an assessment, and to put the brakes on over-enthusiastic focus on one part of the standards; they aren’t intended to forbid the use of examples that time and common sense allow” (General questions about the Mathematics standards, Mathematical Musings); thus more denominators are used in order to not limit students’ understanding.
As a supplement to the Problem Set, students can play a game to practice finding equivalent fractions with smaller units using tape diagrams, such as “Show Me 2” from Games with Fraction Strips and Fraction Cards on The Max Ray Blog.
There are no problems in this Problem Set, or any hereafter, that are related to the idea that “comparisons are valid only when the two fractions refer to the same whole” (4.NF.2). (Note that the idea of equivalence is a type of comparison.) This is because this is also part of the third-grade expectations regarding fraction equivalence and comparison, so students should understand this idea already. However, if they would benefit from some additional practice, here are some sources of good problems aligned to this aspect of the standard:
- Smarter Balanced Assessment Consortium: Item and Task Specifications Math Item Specifications, Claim 3, Grades 3-8 and High School (G3-5_Claim3_Spec_v4) — Example Item 3C.1d
- EngageNY Mathematics Grade 3 Mathematics > Module 5 > Topic C > Lesson 11 — Problem Set and Homework
- Illustrative Mathematics Comparing Fractions with a Different Whole — (Could be modified to present an argument that two fractions are equivalent rather than greater/less than)
- Massachusetts Department of Elementary and Secondary Education Model Curriculum Unit, "Fractions: Size Matters"

Lesson Materials

Strips of paper (2 per student) — These should be identical in size, perhaps 4.25" by 11"

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Anchor Tasks

Tasks designed to teach criteria for success of the lesson, and guidance to help draw out student understanding

Problem 1

Would you rather have the leftover king-sized candy bar in Scenario A or Scenario B? The original candy bars were the same size.

Scenario A

Scenario B

Guiding Questions

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Problem 2

Find two fractions that are equivalent to each of the following:

a. $$\frac{1}{3}$$

b. $$\frac{3}{4}$$

c. $$\frac{3}{2}$$

Guiding Questions

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Problem 3

Use pictures to explain why the following fractions are equivalent.

a. $${{1\over2}={3\over6}}$$

b. $${{2\over3}={8\over12}}$$

c. $${{4\over3}={8\over6}}$$

Guiding Questions

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Problem Set

Problem Set

Answer Keys

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Discussion of Problem Set

How many pieces did you shade in #3? Why?
What answer did you choose in #4? What made these equivalent fractions different from the others we’ve looked at today?
Look at #5c. What did your picture look like for $${{5\over2}}$$? What about $${{15\over6}}$$? What made these fractions different from the others?

Target Task

A task that represents the peak thinking of the lesson - mastery will indicate whether or not objective was achieved

Problem 1

The model below is shaded to represent a fraction.

Which model below represents an equivalent fraction?

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Problem 2

Use the pictures to explain why the two fractions represented above are equivalent.

Student Response

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Additional Practice

The Extra Practice Problems can be used as additional practice for homework, during an intervention block, etc. Daily Word Problems and Fluency Activities are aligned to the content of the unit but not necessarily to the lesson objective, therefore feel free to use them anytime during your school day.

Extra Practice Problems

Extra Practice Problems

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Word Problems and Fluency Activities

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Lesson 4

Lesson 6

Lesson Map

Topic A: Factors and Multiples

Identify multiples and determine if a whole number is a multiple of another number.

4.OA.B.4

Explore patterns in multiples of various whole numbers.

4.OA.B.4

Find factor pairs for numbers to 100 and recognize that a whole number is a multiple of each of its factors.

4.OA.B.4

Determine whether a given number is prime or composite.

4.OA.B.4

Topic B: Equivalent Fractions

Recognize and generate equivalent fractions with smaller units using tape diagrams.

4.NF.A.1

Recognize and generate equivalent fractions with smaller units using number lines.

4.NF.A.1

Recognize and generate equivalent fractions with smaller units using area models.

4.NF.A.1

Recognize and generate equivalent fractions with smaller units using multiples.

4.NF.A.1

Recognize and generate equivalent fractions with larger units using visual models.

4.NF.A.1

Recognize and generate equivalent fractions with larger units using factors.

4.NF.A.1

Topic C: Comparing and Ordering Fractions

Compare two fractions where one numerator or denominator is a factor of the other by replacing one fraction with an equivalent one.

4.NF.A.2

Compare two fractions by replacing both fractions with equivalent ones.

4.NF.A.2

Compare two fractions using one whole as a benchmark.

4.NF.A.2

Compare two fractions using one half as a benchmark.

4.NF.A.2

Compare and order fractions using various strategies.

4.NF.A

Fraction Equivalence and Ordering

Objective

Common Core Standards

Core Standards

Number and Operations—Fractions

Foundational Standards

Number and Operations—Fractions

Operations and Algebraic Thinking

Criteria for Success

Tips for Teachers

Lesson Materials

Anchor Tasks

Problem 1

Guiding Questions

Problem 2

Guiding Questions

Problem 3

Guiding Questions

Problem Set

Discussion of Problem Set

Target Task

Problem 1

Problem 2

Student Response

Additional Practice

Extra Practice Problems

Word Problems and Fluency Activities

Lesson Map

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