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Illinois State Assessments · IAR Math

Illinois IAR Math Practice Test

Build Illinois mathematics readiness with five focused 10-question practice sets covering number, algebra, geometry, measurement, data, probability, and problem solving.

Illinois IAR Math practice sets

This Illinois IAR Math Practice Test page provides five short practice sets with 10 original multiple-choice questions each. The sets cover number and operations, expressions and equations, geometry and measurement, data and probability, and integrated multi-step problem solving.

IAR Math skills

The Illinois State Board of Education describes IAR mathematics as an assessment for Grades 3–8 that requires students to reason about quantities and relationships in real-world situations. These supplemental sets practice computation, fractions and decimals, algebraic thinking, geometry, measurement, statistics, probability, and mathematical reasoning.

How to use this page

Complete one 10-question set at a time. Show your work, check units and labels, then review the explanation after each response.

This is supplemental State Test Practice, State Assessment Practice, and Standardized Test Practice. It does not replace current Illinois State Board of Education guidance, official materials, accommodations, tool policies, or testing procedures.

For broader grade-level study paths, explore Elementary School Tests, Middle School Tests, and High School Tests.

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5. Test

Illinois IAR Math Practice Questions

A 10-question Illinois IAR Math practice set on integrated iar math review, with answers and explanations.

Read each problem, graph, table, or model carefully, choose one answer, and review the explanation after responding.

10 Questions
0/10 Questions0 %
Correct 0
Incorrect 0
Unanswered 10
1. QuestionMultiple choice

A class plants 7 trays with 6 seeds in each tray. How many seeds are planted?

Please select an answer first.

Correct answer: A

The correct answer is 42.

  1. Read the IAR math task: Identify the quantities, operation, representation, or relationship the problem asks you to use.
  2. Show the reasoning: Multiply 7 trays by 6 seeds: 7 × 6 = 42.
  3. Check the result: Confirm that the answer is reasonable and that units, labels, and conditions are included.

Multiply 7 trays by 6 seeds: 7 × 6 = 42.

2. QuestionMultiple choice

A hiker walks 4.25 miles in the morning and 3.5 miles in the afternoon. How far does the hiker walk altogether?

Please select an answer first.

Correct answer: B

The correct answer is 7.75 miles.

  1. Read the IAR math task: Identify the quantities, operation, representation, or relationship the problem asks you to use.
  2. Show the reasoning: Add 4.25 and 3.50 to get 7.75 miles.
  3. Check the result: Confirm that the answer is reasonable and that units, labels, and conditions are included.

Add 4.25 and 3.50 to get 7.75 miles.

3. QuestionMultiple choice

A rectangular sign is 3 meters wide and 1.5 meters tall. What is its area?

Please select an answer first.

Correct answer: C

The correct answer is 4.5 square meters.

  1. Read the IAR math task: Identify the quantities, operation, representation, or relationship the problem asks you to use.
  2. Show the reasoning: Area equals 3 × 1.5 = 4.5 square meters.
  3. Check the result: Confirm that the answer is reasonable and that units, labels, and conditions are included.

Area equals 3 × 1.5 = 4.5 square meters.

4. QuestionMultiple choice

A student saves 9 dollars each week. Which expression gives the amount saved after w weeks?

Please select an answer first.

Correct answer: D

The correct answer is 9w.

  1. Read the IAR math task: Identify the quantities, operation, representation, or relationship the problem asks you to use.
  2. Show the reasoning: Nine dollars per week multiplied by w weeks is 9w.
  3. Check the result: Confirm that the answer is reasonable and that units, labels, and conditions are included.

Nine dollars per week multiplied by w weeks is 9w.

5. QuestionMultiple choice

A set of scores is 70, 80, 80, 90, and 100. What is the mode?

Please select an answer first.

Correct answer: A

The correct answer is 80.

  1. Read the IAR math task: Identify the quantities, operation, representation, or relationship the problem asks you to use.
  2. Show the reasoning: The value 80 appears twice and every other value appears once.
  3. Check the result: Confirm that the answer is reasonable and that units, labels, and conditions are included.

The value 80 appears twice and every other value appears once.

6. QuestionMultiple choice

A tank holds 150 liters and 45 liters are used. How many liters remain?

Please select an answer first.

Correct answer: B

The correct answer is 105 liters.

  1. Read the IAR math task: Identify the quantities, operation, representation, or relationship the problem asks you to use.
  2. Show the reasoning: Subtract the amount used: 150 − 45 = 105 liters.
  3. Check the result: Confirm that the answer is reasonable and that units, labels, and conditions are included.

Subtract the amount used: 150 − 45 = 105 liters.

7. QuestionMultiple choice

A triangle has a base of 12 units and a height of 5 units. What is its area?

Please select an answer first.

Correct answer: C

The correct answer is 30 square units.

  1. Read the IAR math task: Identify the quantities, operation, representation, or relationship the problem asks you to use.
  2. Show the reasoning: Triangle area is 1/2 × 12 × 5 = 30 square units.
  3. Check the result: Confirm that the answer is reasonable and that units, labels, and conditions are included.

Triangle area is 1/2 × 12 × 5 = 30 square units.

8. QuestionMultiple choice

A student says 5/6 is greater than 3/4 because 5 is greater than 3. What is the best way to compare them?

Please select an answer first.

Correct answer: D

The correct answer is Use a common denominator or convert both to decimals..

  1. Read the IAR math task: Identify the quantities, operation, representation, or relationship the problem asks you to use.
  2. Show the reasoning: Five sixths is about 0.833 and three fourths is 0.75, so a common representation gives a valid comparison.
  3. Check the result: Confirm that the answer is reasonable and that units, labels, and conditions are included.

Five sixths is about 0.833 and three fourths is 0.75, so a common representation gives a valid comparison.

9. QuestionMultiple choice

A machine makes 24 parts in 4 hours at a constant rate. How many parts does it make per hour?

Please select an answer first.

Correct answer: A

The correct answer is 6 parts.

  1. Read the IAR math task: Identify the quantities, operation, representation, or relationship the problem asks you to use.
  2. Show the reasoning: Divide 24 parts by 4 hours to get 6 parts per hour.
  3. Check the result: Confirm that the answer is reasonable and that units, labels, and conditions are included.

Divide 24 parts by 4 hours to get 6 parts per hour.

10. QuestionMultiple choice

What is the best general strategy for an Illinois IAR Math practice question?

Please select an answer first.

Correct answer: B

The correct answer is Read carefully, choose a useful representation, calculate, and check the answer..

  1. Read the IAR math task: Identify the quantities, operation, representation, or relationship the problem asks you to use.
  2. Show the reasoning: Reading the conditions, selecting a method, calculating, and checking helps reduce avoidable errors.
  3. Check the result: Confirm that the answer is reasonable and that units, labels, and conditions are included.

Reading the conditions, selecting a method, calculating, and checking helps reduce avoidable errors.

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Choose your next study path

Illinois State Test Practice

Review integrated Illinois IAR and ISA-style reading, math, science, data, and evidence questions.

Illinois IAR ELA Practice Test

Practice Illinois IAR reading, vocabulary, language, evidence, revision, and writing skills.

Elementary School Tests

Build foundational reading, math, science, and social studies skills for Grades 1–5.

Middle School Tests

Review grade-level ELA, math, science, and social studies skills for Grades 6–8.

High School Tests

Explore course and assessment preparation for Grades 9–12.

Pomodoro Timer

Use focused study intervals to work through your next practice set.

Frequently asked questions about Illinois IAR Math Practice

Which grades are covered by Illinois IAR Math?

The Illinois State Board of Education states that IAR mathematics is available in Grades 3–8. Check the official IAR page for current assessment information.

Which math skills are included?

The practice sets include number and operations, fractions and decimals, expressions and equations, geometry, measurement, data, statistics, probability, and multi-step reasoning.

Are these official IAR questions?

No. These are original supplemental practice questions. Check the official Illinois State Board of Education IAR page for current practice items, tool policies, accommodations, and testing procedures.