Curriculum  /  Math  /  3rd Grade  /  Unit 6: Fractions  /  Lesson 4

Fractions

Lesson 4

Math

Unit 6

3rd Grade

Lesson 4 of 24

Objective

Identify fractions of a whole that is not partitioned into equal parts.

Common Core Standards

Core Standards

  • 3.NF.A.1 — Understand a fraction 1/b as the quantity formed by 1 part when a whole is partitioned into b equal parts; understand a fraction a/b as the quantity formed by a parts of size 1/b.

Foundational Standards

  • 2.G.A.3

Criteria for Success

  1. Partition a whole into fractional units in more than one way.
  2. Understand that equal shares of identical wholes need not have the same shape.
  3. Determine the fraction that parts of a whole represent when those pieces are not equal in shape or size by partitioning them further to identify their equal parts.

Tips for Teachers

Too often, when students are asked questions about what fraction is shaded, they are shown regions that are portioned into pieces of the same size and shape. The result is that students think that equal shares need to be the same shape, which is not the case. On the other hand, sometimes visuals do not show all of the partitions” (Van de Walle, Teaching Student-Centered Mathematics, Grades 3–5, vol.2, p. 211). Thus, this lesson tries to address both of these potential misconceptions and deepen students’ conceptual understanding of fractions. Having students explain what it meant by “equal parts” also provides opportunities for students to attend to precision (MP.6) (NF Progression, p. 7).

Lesson Materials

  • Square-sized paper (1 piece per student)
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Anchor Tasks

25-30 minutes

Problem 1

Using a square sheet of paper, make folds as explained in each part below to construct a new shape. Explain how you know the shape you constructed has the specified area.

a.   Construct a square with exactly $$\frac{1}{4}$$ the area of the original square. Convince yourself and then your partner that it is a square and has $$\frac{1}{4}$$ of the area.

b.   Construct a triangle with exactly $$\frac{1}{4}$$ of the area of the original square. Convince yourself and then your partner that it has $$\frac{1}{4}$$ of the area.

c.   Construct another triangle, also with $$\frac{1}{4}$$ the area, that is not the same shape as the first one you constructed. Convince yourself and then your partner that it has $$\frac{1}{4}$$ of the area.

d.   Construct a square with exactly $$\frac{1}{2}$$ the area of the original square. Convince yourself and then your partner that it is a square and has $$\frac{1}{2}$$ of the area.

Guiding Questions

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Student Response

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References

youcubed Paper Folding

Paper Folding is made available by youcubed under the CC BY 4.0 license. Accessed March 29, 2019, 12:31 p.m..

Modified by Fishtank Learning, Inc.

Problem 2

Below is an image of a tangram set. Determine what fraction of the overall set each shape is.

Guiding Questions

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Student Response

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Problem Set

15-20 minutes

Discussion of Problem Set

  • Which circles have $$\frac{1}{2}$$ shaded? How do you know?
  • How did you determine the fractional part of each square in #2? In Part (f), did you need to make every single piece the same size or were you able to determine the fractional part of some pieces without breaking the whole into the smallest possible shape that could tile the whole square?
  • What shape did you draw for #3? How do you know the shaded part represents $$\frac{3}{8}$$ of the whole?
  • What made finding the fraction of each whole that each color represents in #4 different from the fraction of each whole that each region represents in #2? Was it easier or more difficult to do that?
  • How did you solve #5?

Target Task

5-10 minutes

Problem 1

Are each of the fractional pieces below $$\frac{1}{2}$$ of the whole square? Explain why or why not.

Student Response

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Problem 2

Determine the fraction of the whole square each piece represents.

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.

Word Problems and Fluency Activities

Word Problems and Fluency Activities

Help students strengthen their application and fluency skills with daily word problem practice and content-aligned fluency activities.

Next

Draw the whole when given the unit fraction.

Lesson 5
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Lesson Map

A7CB09C2-D12F-4F55-80DB-37298FF0A765

Topic A: Understanding Unit Fractions and Building Non-Unit Fractions

Topic B: Fractions on a Number Line

Topic C: Equivalent Fractions

Topic D: Comparing Fractions

Topic E: Line Plots

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