Section B Section B Checkpoint

Problem 1

3 diagrams of equal length. 5 equal parts. 1 part shaded. Total length, 1.

Explain how the diagram shows $3 \div 5$ .
Explain how the diagram shows $3 \times \frac{1}{5}$ .
What is the value of $3 \div 5$ ? Explain or show your reasoning.

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Solution

Sample response: There are 3 whole rectangles and 1 out of 5 equal shares of the rectangles is shaded. So, that’s $3 \div 5$ .
Sample response: There are 3 shaded parts and each is $\frac{1}{5}$ of a whole rectangle. So, that's $3 \times \frac{1}{5}$ .
$\frac{3}{5}$ . Sample response: There are 3 shaded pieces and each is $\frac{1}{5}$ of a whole rectangle.

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Sample Response

Sample response: There are 3 whole rectangles and 1 out of 5 equal shares of the rectangles is shaded. So, that’s $3 \div 5$ .
Sample response: There are 3 shaded parts and each is $\frac{1}{5}$ of a whole rectangle. So, that's $3 \times \frac{1}{5}$ .
$\frac{3}{5}$ . Sample response: There are 3 shaded pieces and each is $\frac{1}{5}$ of a whole rectangle.

Problem 2

Explain or show how each expression represents the shaded parts of the diagram.

$2 \times (4 \div 3)$
$4 \times \frac{2}{3}$
$4 \times 2 \times \frac{1}{3}$

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Solution

Sample responses:

Each rectangle is divided into 3 equal parts and 2 of them are shaded. So, that’s $2 \times (4 \div 3)$ .
There are 4 groups of $\frac{2}{3}$ of a rectangle. So, that’s $4 \times \frac{2}{3}$ .
There are 4 groups of 2 small parts and each one is $\frac{1}{3}$ of a rectangle. So, that’s $4 \times 2 \times \frac{1}{3}$ .

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Sample Response

Sample responses:

Each rectangle is divided into 3 equal parts and 2 of them are shaded. So, that’s $2 \times (4 \div 3)$ .
There are 4 groups of $\frac{2}{3}$ of a rectangle. So, that’s $4 \times \frac{2}{3}$ .
There are 4 groups of 2 small parts and each one is $\frac{1}{3}$ of a rectangle. So, that’s $4 \times 2 \times \frac{1}{3}$ .