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Representations of Fractions (Part 1)

Grade 4: Unit 2: Lesson 1

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Lesson Purpose

The purpose of this lesson is for students to make sense of unit fractions with denominators 2, 3, 4,

5, 6, 8, 10, and 12, using physical and visual representations.

Lesson Narrative

In grade 3, students were introduced to fractions as numbers. They learned to name and represent

fractions, to recognize simple equivalent fractions, and to compare fractions with like numerators

and denominators (limited to 2, 3, 4, 6, and 8). They used fraction strips, area diagrams, tape

diagrams, and number lines to support their reasoning with fractions.

This lesson activates students’ prior knowledge of unit fractions and includes fractions with new

denominators 5, 6, 10, and 12. Students revisit the meaning of numerator and denominator, name

unit fractions, create representations for them, and recall some strategies and tools for reasoning

about fractions.

The idea of equivalence may naturally come up (and will help to prepare students for upcoming

work), but it is not the focus of this lesson.

Learning Goals

• Make sense of the numerator and denominator of unit fractions that have denominators 2, 3, 4,

5, 6, 8, 10, and 12.

• Use physical and visual representations to reason about fractions.

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Let’s name some fractions and represent them visually.

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What Do You Know About ...?

Warm-Up

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What do you know about this number? ?

½

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Let’s talk about it

What different ways can we represent ½ ?

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Fraction Strips

Activity 1

The purpose of this activity is for students to use fraction strips to represent halves, fourths, and

eighths. The denominators in this activity are familiar from grade 3. The goal is to remind students

of the relationships between fractional parts in which one denominator is a multiple of another.

Students should notice that each time the unit fractions on a strip are folded in half, there are twice

as many equal-size parts on the strip and that each part is half as large.

In the discussion, use the phrases “number of parts” and “size of the parts” to reinforce the

meaning of a fraction.

Materials to Gather:

• Straightedges

Materials to copy:

• Fraction Strips

• Each group of 2 needs 4 strips of equal-size paper (cut lengthwise from letter-size or larger

paper or use the provided blackline master).

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Fraction Strips

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Let’s talk about it..

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Fractions, Represented

Activity 2

MLR1: Stronger and Clearer Each Time

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If each full diagram represents 1, what fraction does each shaded part represent?

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Here are four blank diagrams. Each diagram represents 1. Partition each diagram and shade one part so that the shaded part represents the given fraction.

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Let’s talk about it..

• How did you know how to partition the diagrams in the second question?

• What relationships do you see between the fractions in this activity?

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Lesson Synthesis

In general, what does the denominator in a fraction represent?

What does the fraction tell us?

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Lesson Synthesis

What did you notice about the size of a fraction as the denominator gets larger? Why might that be?

What relationships did we see between the fractions that we studied today?

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What Do the Diagrams Show?

Cool-Down

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Cool-Down: What Do the Diagrams Show?

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Image Citations

https://giphy.com/search/fractions

https://giphy.com/stickers/transparent-4FOZeXigeiavvyAxEF

https://giphy.com/stickers/chat-message-vera-dement-Q5pH4UmOiQciITstXU

https://giphy.com/stickers/rice-ball-ricey-adamrice-I7dcSQ4oRlwM3xFkVp

https://giphy.com/stickers/UPMCHealthPlan-upmc-health-plan-mental-hXjheXXa5w0WR3jRqt

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