Fractions

Lesson 3

Objective

Partition a whole into equal parts, identifying and counting unit fractions using pictorial area models and tape diagrams, identifying the unit fraction numerically.

Common Core Standards

Core Standards

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  • 3.G.A.2 — Partition shapes into parts with equal areas. Express the area of each part as a unit fraction of the whole. For example, partition a shape into 4 parts with equal area, and describe the area of each part as 1/4 of the area of the shape.

  • 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

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  • 2.G.A.3

Criteria for Success

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  1. Understand a unit fraction to be a fraction that refers to just one equal part.
  2. Write a unit fraction using unit form and fraction notation (e.g., “1 fourth” and “$$\frac{1}{4}$$", respectively).
  3. Partition a pictorial area or length model to represent a unit fraction (MP.5).
  4. Explain whether or not a pictorial area or length model represents a particular unit fraction or not (MP.3).
  5. Determine the unit fraction represented by an abstract description of a situation (MP.2).
  6. Count unit fractions up to a whole.

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Anchor Tasks

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Problem 1

Each shape below represents one whole. What fraction of each shape is shaded?

  1.  

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Guiding Questions

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Problem 2

Make a model in which the shaded part represents the corresponding unit fraction.

a.  $$\frac{1}{3}$$

b.  $$\frac{1}{2}$$

c.  $$\frac{1}{6}$$

 

Guiding Questions

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Problem 3

Kai says that each part of the shape below represents $$\frac{1}{2}$$. Do you agree or disagree? Explain your thinking.

Guiding Questions

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Problem Set & Homework

Discussion of Problem Set

  • Are the fractions in #2 unit fractions? How do you know?
  • How did you determine the correct answer in #3? How did you know that was correct even though we’ve never discussed ninths as a class?
  • Which two answer choices were you able to eliminate immediately in #4? How did you decide between the two remaining answer choices?
  • How did you partition the cake in #6? Is there more than one correct way to do so?
  • How did you determine the correct answer in #7 without an image?

Target Task

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Problem 1

Which figure is $$\frac{1}{2}$$ shaded?

A.

B.

C.

D.

References

EngageNY New York State Testing Program Grade 3 Common Core Mathematics Test Released Questions with Annotations August 2014#134030001_4 (p. 4)

From EngageNY.org of the New York State Education Department. New York State Testing Program Grade 3 Common Core Mathematics Test Released Questions with Annotations August 2014. Internet. Available from https://www.engageny.org/resource/new-york-state-common-core-sample-questions/file/103126; accessed Nov. 6, 2018, 1:35 p.m..

Problem 2

A rectangle is shown below.

  1. Draw line segments on the rectangle to divide the rectangle into 8 equal parts.
  2. What fraction of the area of the whole rectangle is the area of each part?

References

Massachusetts Department of Elementary and Secondary Education Spring 2016 Grade 3 Mathematics TestQuestion #13

Spring 2016 Grade 3 Mathematics Test is made available by the Massachusetts Department of Elementary and Secondary Education. © 2017 Commonwealth of Massachusetts. Accessed Oct. 15, 2018, 4:58 p.m..

Mastery Response

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