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
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.
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.
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