Unit 5

Fractions as Numbers

Unit Goals

Unit Narrative

In this unit, students make sense of fractions as numbers, using various diagrams to represent and reason about fractions, compare their sizes, and relate them to whole numbers. The denominators of the fractions explored here are limited to 2, 3, 4, 6, and 8.

In grade 2, students partitioned circles and rectangles into equal parts and used the language “halves,” “thirds,” and “fourths.” Students begin this unit in a similar way, by reasoning about the sizes of shaded parts in shapes. Next, they create fraction strips by folding strips of...

Section A

Section Goals

Section Narrative

In this section, students use shaded diagrams and fraction strips to learn about fractions, building on their prior knowledge of halves, thirds, and fourths.

Students partition rectangles into 6 or 8 equal parts and describe each part as a “sixth” or an “eighth” respectivey, and write the notation or , respectively.

They learn that the notation refers to a unit...

Let’s name parts of a whole.

Let’s use fractions to describe parts.

Let’s learn about non-unit fractions.

Let’s build other fractions from unit fractions.

Section A Practice Problems

to access Section Checkpoints.

Section A

Let’s name parts of a whole.

Let’s use fractions to describe parts.

Let’s learn about non-unit fractions.

Let’s build other fractions from unit fractions.

Section B

Section Goals

Section Narrative

In this section, students reason about fractions on the number line. This work relies on two prior experiences: locating whole numbers on the number line, and partitioning a whole into equal parts.

Students previously have learned that numbers can be represented as distances from 0 on the number line. Here students learn that the same is true about fractions. Students...

Let’s learn about fractions on the number line.

Let’s partition the number line to locate unit fractions.

Let’s locate non-unit fractions on the number line.

Let’s work with fractions and whole numbers on the number line.

Let’s locate numbers on the number line when we are given the location of 1 fraction.

Section B Practice Problems

to access Section Checkpoints.

Section B

Let’s learn about fractions on the number line.

Let’s partition the number line to locate unit fractions.

Let’s locate non-unit fractions on the number line.

Let’s work with fractions and whole numbers on the number line.

Let’s locate numbers on the number line when we are given the location of 1 fraction.

Section C

Section Goals

Section Narrative

In this section, students learn that equivalent fractions are fractions that are the same size.

They first identify equivalent fractions by noticing parts that are of equal length on fraction strips and tape diagrams.

For example, the shaded third in the first diagram is the same size as the two shaded sixths in the second diagram, so and are equivalent....

Let’s identify equivalent fractions.

Let’s generate equivalent fractions.

Let’s find fractions at the same location.

Let’s find fractions and whole numbers that are equivalent.

Section C Practice Problems

to access Section Checkpoints.

Section C

Let’s identify equivalent fractions.

Let’s generate equivalent fractions.

Let’s find fractions at the same location.

Let’s find fractions and whole numbers that are equivalent.

Section D

Section Goals

Section Narrative

In this section, students compare fractions, using any representation or reasoning strategies that make sense to them. They learn that comparisons are valid only if the fractions being compared refer to the same whole.

Students begin by deciding if two fractions are equivalent. They use diagrams, number lines, and the meaning of fractions to support their reasoning.

Next students compare...

Let’s represent and compare fractions.

Let’s compare 2 fractions with the same denominator.

Let’s compare 2 fractions with the same numerator.

Let’s compare more fractions in different situations.

Let’s use what we know about fractions to plan a 3-mile fun run.

Section D Practice Problems

to access Section Checkpoints.

Section D

Let’s represent and compare fractions.

Let’s compare 2 fractions with the same denominator.

Let’s compare 2 fractions with the same numerator.

Let’s compare more fractions in different situations.

Let’s use what we know about fractions to plan a 3-mile fun run.

to access End-of-Unit Assessments.

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Fractions as Numbers

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

Section Goals

Section Narrative

Section D Practice Problems

Unit 5 Resources

About Unit 5

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Section Goals

Section Narrative

Section B Practice Problems

Section Goals

Section Narrative

Section C Practice Problems

Section Goals

Section Narrative

Section D Practice Problems

Section Goals

Section Narrative

Section A Practice Problems