Section A Practice Problems

Problem 1

What is the length of the pencil in centimeters? Show your reasoning.

Pencil measured by ruler in centimeters.

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Solution

9 cm. Sample response:

26 - 17 = 9

Problem 2

Here are the lengths of some snakes at the pet store in inches. Use the data to create a line plot.

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Solution

Problem 3

Find the value of each sum or difference. Explain or show your reasoning.

$374 + 455$
$259 - 186$

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Solution

829. Sample response:

$300 + 400 = 700$
$70 + 50 = 120$
$4 + 5 = 9$
$700 + 120 + 9 = 829$
73. Sample response:

$186 +70 = 256$
$256 + 3 = 259$
$70 + 3 = 73$

Problem 4

Write the time shown on each clock.

_______________
_______________
_______________

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Solution

9:00
4:10
8:55

Problem 5

Find the value of each expression.

$8 \times 9$
$16 \times 6$
$72 \div 8$
$92 \div 4$

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Solution

Problem 6

Find the length of each pencil.

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Solution

$3\frac{1}{2}$ or $\frac{7}{2}$ inches
4 or $\frac{8}{2}$ inches

Problem 7

Partition the ruler into halves of an inch and then quarters of an inch.
What is the length of the rectangle? Explain or show your reasoning.

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Solution

Ruler is partitioned into halves and quarters of an inch.
$2\frac{1}{4}$ inches. Sample response: The rectangle goes beyond 2 inches and it’s really close to the first quarter inch mark I put in after 2.

Problem 8

Here are the lengths of some pieces of pasta in inches.

Which lengths are the same? Explain or show your reasoning.

$3\frac{2}{4}$
2
$3\frac{1}{2}$
$\frac{4}{2}$

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Solution

$3 \frac{2}{4} = 3 \frac{1}{2}$ . Sample response: $\frac{1}{2}$ and $\frac{2}{4}$ are equivalent.
$2 = \frac{4}{2}$ . Sample response: There are 2 halves in a whole, so there are 4 halves in 2 wholes.

Problem 9

The line plot shows the width of some postcards in inches.

<p>Dot plot from 0 to 7 by ones. P<span>ostcard widths, inches. </span>Beginning at 4 and a half, the number of X’s above each increment are 2, 5, 2, 3, 2, 1.</p>

How many postcards measured $5 \frac{1}{2}$ inches?
How many postcards measured 6 inches or more?
How many postcards were measured for the line plot?

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Solution

2 postcards
6 postcards
15 postcards

Problem 10

Here are the lengths of some straws in inches. Represent the data on a line plot.

$4\frac{3}{4}$
$5\frac{1}{2}$
$4\frac{1}{4}$
$5\frac{2}{4}$
$4\frac{1}{2}$
$3\frac{3}{4}$
$5\frac{1}{4}$
$4\frac{2}{4}$
5
$4\frac{1}{4}$
$4\frac{1}{2}$

Dot plot from 0 to 6 by ones. Hash marks by fourths. Horizontal axis, <span>straw lengths, inches.</span>

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Solution

Problem 11

You will need a ruler marked in $\frac{1}{4}$ inches for this problem.

Find an object in the classroom or at home that you think will be close to each length.
- $1\frac{1}{2}$ inches
- 7 inches
- 33 inches
Measure each object using a ruler marked in $\frac{1}{4}$ inches. Was each estimate too high, too low, or just right?

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Solution

Sample responses:

an eraser, a pen, the length of my desk
The eraser was shorter—it was only $1 \frac{1}{4}$ inches. The pen was shorter— it was only $5 \frac{3}{4}$ inches. The desk was longer— it was $35\frac{1}{2}$ inches.

Problem 12

Choose a collection of objects to measure at school or at home. Show your measurement data on a line plot.

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Solution

Sample response: I measured the lengths of several ribbons. I started my plot at 7 inches and went to 10 inches because there were no lengths less than 7 inches and none more than 10 inches.