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IAR: Grade 4 - Math

By Sara Cowley
Last updated over 1 year ago
31 Questions
1.
The area of the rectangular sandbox at Dave's school is 108 square feet.
The sandbox has a width of 9 feet as shown in the diagram.
What is the length, in feet, of the sandbox?
Enter your answer in the box.
_______ feet
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2.
Enter your answer in the box.

3,649\times6= _______
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3.
Ms. Sloan asked 117 fourth-grade students the question, “How many pets do you have?” She displayed the data she collected in the bar graph shown.


Part A
How many of the students that responded have 2 pets? _______

Part B
How many more students have 1 pet than students who have 3 pets? _______
Explain your answer in the Show Your work space.

Part C
Find the total number of pets the fourth-grade students have: _______
  • Explain how you used the bar graph to solve the problem.
  • Show your work using equations.
Enter your explanation and your work in the Show Your Work space.
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4.

Drag and drop each number that is a multiple of 8 into the box.

  • 1
  • 2
  • 4
  • 8
  • 20
  • 24
  • 36
  • 58
  • 64
  • 80
  • Multiples of 8
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5.

Which fractions complete the number sentences shown to make true comparisons?
Complete each number sentence so that it is a true comparison.
Drag and drop a fraction into each box.

  • 20/100
  • 6/10
  • 1/2
  • 2/12
  • 2/3
  • 40/100
  • \frac{2}{5}=
  • \frac{3}{5}<
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6.

Which numbers make the comparison true?

27,768< ?

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7.
Part A
Alex ran 0.5 mile.

Using a denominator of 10, what is the fractional equivalent of this distance, in miles?


Enter your answer in the box: _______

Part B
Christy ran 4/10 mile on Monday and 7/100 mile on Tuesday. She said that she ran a total of 47/100 mile. Christy told Alex that she ran a greater distance than he ran, because 47 is more than 5.
  • Identify the incorrect reasoning in Christy's statement.
  • Explain how Christy can correct her reasoning.
  • Use >, <, or = to give a correct comparison between the distances that Alex and Christy ran.
Enter the incorrect reasoning, your explanation, and the correct comparison in the Show Your Work space.
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8.
Each student in a class chose one sport to play. This table shows the fractions of all students who chose each sport.


Part A
Enter the correct fractions and operation symbols into the blanks to create an equation that can be used to find s, the fraction of all students who chose to play either soccer or basketball.

Answer choices:
1/10 2/10 3/10 4/10 + - \times \div

_______ _______ _______ = s

Part B
Enter the fraction of all the students who chose to play either soccer or basketball.
Enter your answer in the space provided, and enter only your answer: _______
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9.

The rectangle is divided into eight equal sections.
Jodi colors 4 sections. Then she colors 3 more sections.
Which two of these represent the fraction of the rectangle that Jodi colors in all?
Select the two correct answers.

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10.
Enter your answer in the box.
522\div9= _______
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11.

The value of the digit 4 in the number 42,780 is 10 times the value of the digit 4 in which number?

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12.
Henry cut a piece of yarn that was 11/6 feet long into two pieces. List two different pairs of fractions that could show the lengths, in feet, of the two pieces. Explain how you found your pairs of fractions.

Enter your fraction pairs below, and your explanation in the Show Your Work space.

Pair 1: _______ and _______
Pair 2: _______ and _______
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13.
Rachana has a set of 10 mugs. The set is made up of three different kinds of mugs.

1/2 of the mugs have pictures on them.

2/5 of the mugs have words on them.

1/10 of the mugs have flowers on them.

Part A
Place the fractions above in order, from least to greatest. Enter each fraction in its correct box below:

Least: _______
Neither least nor greatest: _______
Greatest: _______

Part B
Enter a fraction equal to 2/5, with a denominator of 10, to show the fraction of the set of mugs that have words on them. _______
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14.

Which angle has a measure of 65\degree?

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15.
Select the correct symbol from each drop-down menu to compare the measurements.

0.4 meter __________ 0.04 meter
0.3 meter __________ 0.5 meter
0.65 meter __________ 0.61 meter
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16.

A basketball team scored a total of 747 points for the season. This was 9 times the number of points scored in the first game. How many points were scored during the first game?

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17.
The table shows the number of yards Ed ran in each of the first three football games of the season.

After the first three games of the season, Rico had exactly 3 times the total number of running yards that Ed had.

How many more total running yards did Rico have than Ed after the first three games of the season? _______

Show your work using equations in the Show Your Work space.
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18.
Four teachers offer an after-school chess club. The table shows the number of students who joined.


Part A
The teachers will divide the total group of students who joined into teams of no more than 6 students.
What is the least number of teams that will include all of the students?
Enter your answer in the box.
_______ teams

Part B
The chess club started with 18 chess sets. The teachers ordered 3 cases of 15 chess sets. They will divide the total number of chess sets so that each teacher receives an equal number. Then they will give any extra sets to the school library.

What is the greatest number of chess sets each of the 4 teachers should get?
Enter your answer in the box.
_______ chess sets
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19.

Which two equations represent the statement "48 is 6 times as many as 8?"
Select the two correct answers.

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20.

Select the three choices that are factor pairs for the number 28.

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21.
Enter your answer in the box.
7,564+8,239=_______
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22.
Two figures are shown. In Figure 1, the measure of angle MSG is 105\degree.
The measures of angle MSK, angle KSP, and angle PSG are shown in Figure 2. The measure of angle MSG is still 105\degree.
Part A
Enter the correct numbers and symbols into the blanks to complete an equation that can be used to find the value of y. Each symbol may be used more than once or not at all.
y + - \times \div 105 32 44
_______ _______ _______ _______ _______ =105

Part B
What is the value of y?
Enter your answer in the box: _______
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23.
Hayley has 272 beads. She buys 38 more beads. She will use 89 beads to make bracelets and the rest to make necklaces. She will use 9 beads for each necklace.

What is the greatest number of necklaces Hayley can make?

Enter your answer in the box.
_______ necklaces
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24.

Part A
Shaun plotted a point on the number line by drawing 5 equally spaced marks between 0 and 1 and placing a point on the third mark. He claims that the point represents the fraction 2/3 because each mark represents 1/5, so the third mark represents 3/5.

  • Explain why Shaun's reasoning is incorrect.
  • Explain how you can use the number line to determine the fraction that Shaun's point represents.
  • Determine the fraction that Shaun's point represents.
Enter your explanations and your answer in the Show Your Work space.

Part B
Shaun wants to write a fraction that is equivalent to the fraction 2/3.
Describe how Shaun can find a fraction that is equivalent to 2/3.
Enter your description in the Show Your Work space.

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25.

Which statement about angles is true?

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26.

Which expression is equivalent to 6\times\frac{2}{3}?

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27.

Jian’s family sells honey from beehives. They collected 3,311 ounces of honey from the beehives this season. They will use the honey to completely fill 4-ounce jars or 6-ounce jars.

Jian’s family will sell 4-ounce jars for $5 each or 6-ounce jars for $8 each.

Jian says if they use only 4-ounce jars, they could make $4,140 because 3,311\div4=827 R 3. That rounds up to 828, and 828 multiplied by $5 is $4,140.

Part A
Explain the error that Jian made when finding the amount of money his family could make if they use only 4-ounce jars.

Enter your explanation in the Show Your Work space.

Part B
Explain how to determine the money Jian's family could make if they use only 6-ounce jars. Include the total amount of money and the total number of 6-ounce jars in your explanation.

Enter your answers and your explanation in the Show Your Work space.

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28.
The length of a desktop is 4 feet. How many inches is the length of the desktop?

Enter your answer in the box.
_______ inches
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29.
A team runs a race. There are 4 people on the team, and each person runs the same distance. The team runs a total distance of 5,280 feet.

What is the distance, in feet, that each person runs?

Enter your answer in the box.
_______ feet
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30.
Part A
Sean buys 5 packages of fish. There is 7/8 pound of fish in each package.
What is the total weight, in pounds, of fish that Sean buys?
Enter your answer in the space provided. Enter only your answer.
_______

Part B
Sean cooks 1 package of the fish. He eats 3/8 pound of the fish from the package.
What is the total weight, in pounds, of the cooked fish that is left after Sean eats 3/8 pound?
Enter your answer in the space provided. Enter only your answer.
_______
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31.

For each figure pictured in the table, select the box for any statement that describes the figure. You may select more than one box for each figure.

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