Fishtank Learning

3rd Grade Math
Unit 6: Fractions
Lesson 13

Objective

Understand two fractions as equivalent if they are the same sized pieces of the same sized wholes, though not necessarily the same shape. Use this understanding to generate simple equivalent fractions.

Anchor Tasks - Problem 1

Mrs. Allen and Ms. Roll each got the same kind of chocolate bar at the grocery store. Mrs. Allen broke her chocolate bar into three equal-sized pieces and ate one of those pieces. Ms. Roll broke her chocolate bar into six equal-sized pieces and ate two of those pieces. Who ate more chocolate, Mrs. Allen or Ms. Roll? Use the models below to support your reasoning.

Two rectangles divided into equal parts, one with 1/3 shaded and the other with 2/6 shaded.

Guiding Questions

What are all of the possible ways Mrs. Allen and Ms. Roll could have partitioned their chocolate bars?
(Present the partitioned chocolate bars given in the notes section below.) I think Mrs. Allen and Ms. Roll did not eat the same amount of chocolate because their pieces are different shapes. Do you agree or disagree?
Would we be able to determine who ate more chocolate if we didn’t know that the chocolate bars were the same size? Why or why not?

Notes

Present the following options as possible partitions to help students see that equivalent fractions must be the same size though not necessarily the same shape:

$Fraction model showing 1/3 and 2/6 as equivalent fractions.$

Anchor Tasks - Problem 2

Jessie drew the following area model to represent a fraction.

Rectangle divided into 12 equal squares, 5 squares shaded.

Which of the following fractions are equivalent to the one represented above? Select all that apply.

Guiding Questions

Is the fraction $$\frac{6}{8}$$ the same as the fraction $$\frac{8}{6}$$? Why or why not?
Is $$\frac{6}{8}$$ equivalent to $$\frac{3}{4}$$? How do you know? How can you use the area model to support your reasoning?
Is $$\frac{6}{8}$$ equivalent to $$\frac{12}{16}$$? How do you know? How can you use the area model to support your reasoning?
Is $$\frac{6}{8}$$ equivalent to $$\frac{9}{12}$$? How do you know? What makes this slightly more challenging to support with the use of the area model?

A. $$\frac{3}{4}$$

B. $$\frac{6}{9}$$

C. $$\frac{8}{6}$$

D. $$\frac{9}{12}$$

E. $$\frac{12}{16}$$

Problem Set

View Problem Set

Discussion of Problem Set

In #1, which shapes were most difficult to match? Why?
Look at #2. What pattern do you notice between the three sets of models? How does this pattern relate to other parts of today’s lesson?
How did you determine the other models that were equivalent to Figure Y? Which one was the most difficult to figure out? Why?
In #8, how do you know the way you shaded Figure B was equivalent to the way you shaded Figure C?

Target Task - Problem 1

Shade the model below to create a fraction that is equivalent to $$\frac{4}{8}$$.

Grid divided into 8 equal squares, 4 squares shaded.

Target Task - Problem 2

Explain how you know the model above represents a fraction that is equivalent to $$\frac{4}{8}$$.

Word Problem

Vastimila has 4 boxes of action figures each with 7 action figures. She gives some action figures to her little sister and then has 16 remaining. How many action figures did she give to her sister?