Section A Practice Problems

Problem 1

Partition the rectangle into 10 equal squares.

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Solution

Sample response:

Problem 2

Here are 2 equal-size squares. A part of each square is shaded.

Is the same amount of each square shaded? Explain or show your reasoning.

Diagram. Square partitioned into 4 equal parts, 1 part shaded.

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Solution

Yes. Sample response: Each picture shows one-quarter of the square shaded.

Problem 3

<p>Number line. First tick mark 0, last tick mark 100. 9 unlabeled tick marks between 0 and 100.</p>

Label the tick marks on the number line.
Locate and label 45 and 62 on the number line.

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Solution

Students do not need to plot the exact location of the numbers, but 45 should be between 40 and 50 and 62 should be between 60 and 70. Sample response:

Problem 4

Write $<$ or $>$ in each blank to compare the numbers.

$718\, \underline{\hspace{1cm}}\, 817$
$106\, \underline{\hspace{1cm}} \,89$
$806\, \underline{\hspace{1cm}} \,809$

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Solution

Problem 5

Partition the rectangle into 6 equal parts.

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Solution

Sample response:

Problem 6

What fraction of the whole rectangle is shaded?
Partition the rectangle into 8 equal parts.

What fraction of the whole rectangle does each part represent?

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Solution

$\frac{1}{6}$
$\frac{1}{8}$ . Sample response:

Problem 7

What fraction of the rectangle is shaded? Explain how you know.
Shade $\frac{4}{6}$ of the rectangle.

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Solution

$\frac{5}{8}$ . Sample response: There are 8 equal parts and 5 of them are shaded.
Sample response:

Problem 8

Jada walks across the street at a stoplight that is $\frac{5}{6}$ of the way from her home to the school. Represent the situation on the fraction strip. Explain your reasoning.

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Solution

Sample response: I divided the strip into 6 equal parts and shaded 5 of them, one for each $\frac{1}{6}$ of Jada's trip from home to school.

Problem 9

Write a situation represented by the diagram. Explain why the diagram represents your situation.

Diagram. Rectangle partitioned into 8 equal parts, 6 parts shaded.

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Solution

Sample response: Noah walked $\frac{6}{8}$ the length of the hallway. The diagram shows 8 equal pieces for the length of the hallway. Each piece is $\frac{1}{8}$ . The 6 shaded pieces represent the $\frac{6}{8}$ of the hallway Noah walked.

Problem 10

Lin shaded part of some fraction strips. What fraction did she shade in each strip? Explain how you know.

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Solution

$\frac{1}{2}$ . Sample response: There are two equal pieces, one shaded and one unshaded.
$\frac{5}{6}$ . Sample response: I lined up the fraction strip with those in my book, and the missing piece is $\frac{1}{6}$ , so $\frac{5}{6}$ are shaded.
$\frac{3}{8}$ . Sample response: I tried to line it up with my different fractions strips. It is more than $\frac{1}{4}$ or $\frac{1}{3}$ but less than $\frac{1}{2}$ , and it lined up with $\frac{3}{8}$ .