Unit 2

Fraction Equivalence and Comparison

Unit Goals

Unit Narrative

In this unit, students extend their prior understanding of equivalent fractions and comparison of fractions.

In grade 3, students partitioned shapes into parts with equal area and expressed the area of each part as a unit fraction. They learned that any unit fraction results from a 1 partitioned into equal parts. Students used unit fractions to build non-unit fractions, including fractions greater than 1, and represented them on fraction strips and tape diagrams. The denominators of these fractions were limited to 2, 3, 4, 6, and 8. Students also worked...

Section A

Section Goals

Section Narrative

In this section, students revisit ideas and representations of fractions from grade 3, working with denominators that now include 5, 10, and 12. Students use physical fraction strips, diagrams of fraction strips, tape diagrams, and number lines to make sense of the size of fractions and fractional relationships.

Students reason about the relationship between fractions where one denominator is a...

Let’s name some fractions and represent them visually.

Let’s name some other fractions and represent them with diagrams.

Let’s compare fractions with the same numerator or the same denominator.

Let’s find some fractions that are the same size.

Let’s investigate equivalent fractions on a number line.

Let’s compare the size of fractions to \(\frac{1}{2}\) and to 1.

Section A Practice Problems

to access Section Checkpoints.

Section A

Let’s name some fractions and represent them visually.

Let’s name some other fractions and represent them with diagrams.

Let’s compare fractions with the same numerator or the same denominator.

Let’s find some fractions that are the same size.

Let’s investigate equivalent fractions on a number line.

Let’s compare the size of fractions to \(\frac{1}{2}\) and to 1.

Section B

Section Goals

Section Narrative

In this section, students develop their ability to reason about and generate equivalent fractions. They begin by using number lines as a tool for finding equivalent fractions and verifying equivalence of two fractions.

number line. 6 evenly spaced tick marks. First tick mark, 0. Point at second tick mark, 1 fifth. Last tick mark, 1.

Number line from 0 to 1. Evenly spaced by tenths. Point at 2 tenths.

Through repeated reasoning, students notice regularity in the visual representations and begin to make sense of a numerical way to determine equivalence and generate equivalent fractions (MP8)....

Let’s find some equivalent fractions.

Let’s use number lines to reason about equivalent fractions.

Let’s talk about how we know whether two fractions are equivalent.

Let’s look at a way to find equivalent fractions without using diagrams.

Let’s find equivalent fractions by working with numerators and denominators.

Section B Practice Problems

to access Section Checkpoints.

Section B

Let’s find some equivalent fractions.

Let’s use number lines to reason about equivalent fractions.

Let’s talk about how we know whether two fractions are equivalent.

Let’s look at a way to find equivalent fractions without using diagrams.

Let’s find equivalent fractions by working with numerators and denominators.

Section C

Section Goals

Section Narrative

By the time they reach this section, students have an expanded set of understandings and strategies for reasoning about the size of fractions. Here, they further develop these skills and work to compare fractions with different numerators and different denominators.

To make comparisons, students may use visual representations, equivalent fractions, and their understanding of the size of fractions (for instance,...

Let’s compare some fractions.

Let’s compare fractions by writing an equivalent fraction.

Let’s solve different kinds of fraction comparison problems.

Let’s compare fractions by writing equivalent fractions with the same denominator.

Let’s put some fractions in order.

Let’s create a game about locating and comparing fractions on the number line.

Section C Practice Problems

to access Section Checkpoints.

Section C

Let’s compare some fractions.

Let’s compare fractions by writing an equivalent fraction.

Let’s solve different kinds of fraction comparison problems.

Let’s compare fractions by writing equivalent fractions with the same denominator.

Let’s put some fractions in order.

Let’s create a game about locating and comparing fractions on the number line.

to access End-of-Unit Assessments.

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Fraction Equivalence and Comparison

Unit Goals

Unit Narrative

Section Goals

Section Narrative

Section A Practice Problems

Section Goals

Section Narrative

Section B Practice Problems

Section Goals

Section Narrative

Section C Practice Problems

Unit 2 Resources

About Unit 2

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Section Goals

Section Narrative

Section A Practice Problems

Section Goals

Section Narrative

Section C Practice Problems

Section Goals

Section Narrative

Section B Practice Problems