Fractions

Lesson 15

Objective

Understand two fractions as equivalent if they are the same point on a number line referring to the same whole. Use this understanding to generate simple equivalent fractions.

Common Core Standards

Core Standards

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  • 3.NF.A.3.A — Understand two fractions as equivalent (equal) if they are the same size, or the same point on a number line.

  • 3.NF.A.3.B — Recognize and generate simple equivalent fractions, e.g., 1/2 = 2/4, 4/6 = 2/3). Explain why the fractions are equivalent, e.g., by using a visual fraction model.

Criteria for Success

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  1. Understand that equivalent fractions are fractions that are equal, i.e., they represent the same point on the number line.
  2. Generate simple equivalent fractions with the use of a number line (MP.5).
  3. Recognize that comparisons (which include the possibility of equivalence) are valid only when the two fractions refer to the same whole, which in the case of a number line, is the same length unit interval (MP.6).
  4. Explain the equivalence of fractions using an area model or other method (MP.3, MP.5).

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Anchor Tasks

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Problem 1

Ebony and Shaun both have the same length string. Ebony cuts her string into three equal-length pieces to make necklaces, and Shaun cuts his string into six equal-length pieces to make bracelets. Ebony uses two of her pieces of string and Shaun uses four of his pieces of string. Who used more string, Ebony or Shaun? Draw a picture to support your reasoning.

Guiding Questions

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Problem 2

  1. Place the following fractions on the number line below.

 

a.  $$\frac{2}{4}$$

b.  $$\frac{1}{2}$$

  1. Are these fractions equivalent? How do you know?
  2. Find another fraction that is equivalent to the fraction in Part (b).

Guiding Questions

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Problem 3

Scott drew this picture:


 

Then he said

This shows that $$ \frac{\mathbf{1}}{\mathbf{4}}$$ is equal to .$$\frac{\mathbf{4}}{\mathbf{8}}$$.

  1. What was his mistake?
  2. Replace either fraction with a different fraction so that they are equivalent to one another. Then draw a number line to support your answer.

Guiding Questions

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References

Illustrative Mathematics Comparing Fractions with a Different Whole

Comparing Fractions with a Different Whole, accessed on March 28, 2018, 1:21 p.m., is licensed by Illustrative Mathematics under either the CC BY 4.0 or CC BY-NC-SA 4.0. For further information, contact Illustrative Mathematics.

Modified by The Match Foundation, Inc.

Problem Set & Homework

Discussion of Problem Set

  • In #2c, did anyone list $$\frac{3}{6}$$? How do you know that is equivalent to 1 half even though the second number line was not partitioned into halves?
  • How did you complete the number sentence for #3? Can you write a non-fractional number that is equivalent to all of these fractions? How do you know it is equivalent?
  • What fractions did you write for #4b? What are all of the possibilities?
  • What fractions did you write for #4d? How do you know those fractions are equivalent to 1 whole?
  • What is another fraction that is equivalent to the fractions in #7 and #8? How do you know it is equivalent?

Target Task

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Find a fraction that is equivalent to $$\frac{2}{4}$$. Show or explain how you know they are equivalent using a number line.

Mastery Response

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