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

Fractions

Lesson 3

Math

Unit 6

3rd Grade

Lesson 3 of 24

Objective

Partition a whole into equal parts using area models and tape diagrams, identifying and writing non-unit fractions in fraction notation.

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. Understand non-unit fractions are built from unit fractions.
  2. Understand the denominator of a fraction to be the fractional unit and the numerator of a fraction to be the number of units.
  3. Identify a non-unit fraction of a whole and write it using fraction notation.
  4. Partition and shade a pictorial area or length model to represent a non-unit fraction (MP.5).
  5. Explain whether or not a pictorial area or length model represents a particular non-unit fraction (MP.3).
  6. Determine the non-unit fraction represented by an abstract description of a situation (MP.2).

Tips for Teachers

  • This is a dense lesson so you may decide to split it over two days. It covers a variety of non-unit fractions, including those equivalent to and greater than 1. As the Progressions state, “there is no need to introduce ‘proper fractions’ and ‘improper fractions’ initially; $$\frac{5}{3}$$ is what you get by combining 5 parts when a whole is partitioned into 3 equal parts”, so addressing them in the same lesson helps students see that all fractions are built from unit fractions. However, if you’d like to split this lesson over two days, you could use Anchor Tasks 1 and 2 on the first day, and save Anchor Task 3 which involves fractions greater than 1 for the second day. The Problem Set and Extra Practice Problems can be split similarly, since all problems involving fractions greater than 1 are at the end of each resource. 
  • While there is no need to introduce “proper fractions” and “improper fractions” as mentioned above, it of course might come up in discussion. If it does, it’s a good idea to avoid using the term “improper fraction”, since it implies that there’s something wrong with this way of writing a number, when in fact sometimes it’s the preferred way to write it. Instead, use the term “fraction greater than one” with students, which after this task, makes sense to them.
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Anchor Tasks

25-30 minutes

Problem 1

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

a.   

b.   

c.   

 

d.   

Guiding Questions

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Student Response

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Problem 2

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

a.    

$$\frac{3}{4}$$

b.    

$$\frac{5}{6}$$

c.    

$$\frac{7}{9}$$

Guiding Questions

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Student Response

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Problem 3

a.   Each shape below represents 1 whole. What fraction is represented by the shaded parts? Be prepared to explain your reasoning.

  1.  

b.   Draw a model to represent the fraction $$\frac{5}{2}$$.

Guiding Questions

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Student Response

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Problem Set

15-20 minutes

Discussion of Problem Set

  • How would you change each of the incorrect statements in #2 to make them true statements?
  • What were the two reasons why Gregory was incorrect in #5? How would you change Gregory’s claim and/or the model to make him correct?
  • How did you determine how Nadia needed to finish the math problem in #7? How was this problem different from some of the others on the Problem Set?
  • How did you determine the correct answer in #8 without an image?
  • Did students eat $$\frac{10}{8}$$ or $$\frac{10}{16}$$ of a pan in #12? How do you know? What does $$\frac{10}{16}$$ represent?

  • How many pizzas should Jeremy order in #13? How do you know? How can you tell just by looking at the numbers involved that it will be more than one pizza?

Target Task

5-10 minutes

Problem 1

Which figure is $$\frac{2}{3}$$ shaded?

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Student Response

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Problem 2

Draw a visual fraction model that represents each fraction below. Be sure to indicate what represents 1 whole.

a.   $$\frac{6}{6}$$

b.   $$\frac{5}{4}$$

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

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

Lesson 4
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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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