Section B Practice Problems

Problem 1

Locate and label $\frac{1}{4}$ on the number line. Explain your reasoning.
Locate and label $\frac{1}{6}$ on the number line. Explain your reasoning.

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Solution

Sample response: It is $\frac{1}{4}$ because there are 4 equal parts and it's the first tick.
Sample response: It is $\frac{1}{6}$ because there are 6 equal parts and it's the first tick.

Problem 2

Locate and label $\frac{1}{8}$ on the number line.
Locate and label $\frac{1}{3}$ on the number line.

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Solution

Problem 3

Locate and label $\frac{4}{8}$ on the number line.
Locate and label $\frac{7}{6}$ on the number line.
Diego marks and labels fourths on the number line like this:

Do you agree with Diego? Explain your reasoning.

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Solution

No. Sample response: Diego skipped the tick mark labeled 1.

Problem 4

Label the tick marks on the number line.
Which fractions on the number line share the same locations as whole numbers? Explain how you know.

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Solution

$\frac{4}{4}$ , $\frac{8}{4}$ , $\frac{12}{4}$ . Sample response: $\frac{4}{4}$ is 1 because there are 4 fourths in a whole. Then $\frac{8}{4}$ is the same as 2 and $\frac{12}{4}$ is the same as 3.

Problem 5

Locate and label 1 on the number line. Explain your reasoning.

Number line. Tick marks labeled 0 and 5 thirds.

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Solution

Sample response: Since there are 5 one-thirds in $\frac{5}{3}$ , I split the space from 0 to $\frac{5}{3}$ into 5 equal pieces and each of those is $\frac{1}{3}$ . The third tick is 1 because there are 3 thirds in a whole.

Problem 6

How are the fraction strip and the number line alike? How are they different?

Diagram. Rectangle partitioned into 8 equal parts, each labeled one eighth.

<p>Number line. Scale 0 to 1 by eighths. Evenly spaced tick marks. First tick mark, 0. Last tick mark, 1.</p>

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Solution

Sample responses: Both the fraction strip and the number line are divided into 8 equal pieces, and both are labeled using eighths. The fraction strip shows only $\frac{1}{8}$ pieces. It does not show $\frac{2}{8}$ or $\frac{3}{8}$ . Also the $\frac{1}{8}$ labels are in the middle of each piece. On the number line, the labels are for the tick marks or the points on the number line.

Problem 7

Han says that he can find 1 on the number line, without finding $\frac{1}{8}$ . What could be Han’s method?

Number line. Two tick marks labeled 0 and 15 eighths.

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Solution

Sample response: He can find $\frac{5}{8}$ by cutting $\frac{15}{8}$ into 3 equal pieces. He can find $\frac{3}{8}$ by cutting $\frac{15}{8}$ into 5 equal pieces. Putting these together gives $\frac{8}{8}$ or 1.