Explain Equivalence

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Lesson Plans and Worksheets for Grade 3
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Common Core For Grade 3

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Examples. videos, and solutions to help Grade 3 students learn how to explain equivalence by manipulating units and reasoning about their size.

Common Core Standards: 3.NF.3a, 3.NF.3b, 3.NF.3c

New York State Common Core Math Grade 3, Module 5, Lesson 27

Worksheets for Grade 3

Application Problem
The branch of a tree is 2 meters long. Monica chops the branch for firewood. She cuts pieces that are 1/6 meter long. Draw a number line to show the total length of the branch. Partition and label each of Monica’s cuts.
a. How many pieces does Monica have altogether?
b. Write 2 equivalent fractions to describe the total length of Monica’s branch.

Concept Development
Each rectangle represents 1 whole. Divide each rectangle into thirds.

How can we double the number of units in the second rectangle?
We cut each third in 2.
What’s our new unit?

Repeat this process for the third rectangle.
Instead of double, triple the original

Help the students explain equivalence by looking at the different units and sizes. Also, help them to see that the more you cut up a whole, the smaller the pieces get.


  1. Use the tape diagram to model equivalent fractions. Fill in the blanks and answer the following questions. 2 tenths is equal to _____ fifths.
    The whole stays the same.
    What happened to the size of the equal
    parts when there were less equal parts?
    1 third is equal to _____ ninths.
    The whole stays the same.
    What happened to the size of the equal
    parts when there were less equal parts?
  2. 8 students want to share 2 pizzas that are the same size, represented by the 2 circles below. They notice that the first pizza is cut into 4 equal slices, and the second is cut into 8 equal slices. How can the 8 students share the pizzas equally, without breaking any of the pieces?
  3. When the whole is the same, why does it take 4 copies of 1 tenth to show 2 copies of 1 fifth? Draw a model to support your answer.
  4. When the whole is the same, how many eighths does it take to make 1 fourth? Draw a model to support your answer.
  5. Mr. Pham cuts a cake into 8 equal slices. Then he cuts every slice in half. How many of the small slices does he have? Use words and numbers to explain your answer.

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