ILEARN Grade 7 math word problems usually test more than computation. Students must recognize ratios, percent change, rational number operations, equations, scale drawings, geometry, probability, and data interpretation in real situations. The strongest review plan mixes topics instead of practicing only one chapter at a time.
Use this set as a diagnostic, tutoring lesson, classroom review, or home practice. Each problem is original and designed to match the type of reasoning Indiana Grade 7 students need for standards-based math review.
ViewMath is not affiliated with or endorsed by the Indiana Department of Education. IDOE describes ILEARN mathematics as a computer-adaptive assessment aligned to Indiana Academic Standards, with mostly discrete mathematics questions and some technology-enhanced real-world tasks. See the official ILEARN page for current information.
How to Use These Problems
Have students solve the problems on paper, then mark each missed answer with one error label: concept, setup, computation, or pacing. Grade 7 students often know the arithmetic but choose the wrong model. The error label shows what to reteach.
Ratio and Proportional Reasoning
1. A printer prints 84 pages in 6 minutes. At the same rate, how many pages can it print in 15 minutes?
Solution: Unit rate = 84 divided by 6 = 14 pages per minute. In 15 minutes: 14 x 15 = 210 pages.
2. A map uses a scale of 1 inch = 12 miles. Two towns are 4.5 inches apart on the map. What is the actual distance?
Solution: 4.5 x 12 = 54 miles.
3. A recipe uses 5 cups of flour for every 2 cups of sugar. If a baker uses 15 cups of flour, how much sugar is needed?
Solution: 5 to 2 is equivalent to 15 to 6, so 6 cups of sugar are needed.
Percent Applications
4. A backpack originally costs $48. It is on sale for 30% off. What is the sale price?
Solution: Discount = 0.30 x 48 = $14.40. Sale price = $48 – $14.40 = $33.60.
5. A town had 8,000 residents. The population increased to 8,600. What was the percent increase?
Solution: Increase = 600. Percent increase = 600/8,000 = 0.075 = 7.5%.
Rational Numbers
6. The temperature at 6 a.m. was -3 degrees. By noon it rose 11 degrees. What was the noon temperature?
Solution: -3 + 11 = 8 degrees.
7. A submarine is 120 meters below sea level. It rises 35 meters, then descends 18 meters. What is its final position?
Solution: Start at -120. Then -120 + 35 – 18 = -103 meters. The submarine is 103 meters below sea level.
Expressions and Equations
8. A music club charges a $20 sign-up fee plus $8 per month. If a student paid $68 total, how many months did the student pay for?
Solution: 20 + 8m = 68. Then 8m = 48, so m = 6 months.
9. Three less than twice a number is 17. What is the number?
Solution: 2n – 3 = 17. Then 2n = 20, so n = 10.
Geometry and Measurement
10. A circle has a radius of 6 inches. Use 3.14 for pi. What is the circumference?
Solution: C = 2 x 3.14 x 6 = 37.68 inches.
11. A rectangular garden is 14 feet long and 9 feet wide. A path around the garden adds 2 feet to each side. What is the area of the larger rectangle including the path?
Solution: Adding 2 feet to each side increases each dimension by 4 feet total. Larger rectangle: 18 by 13. Area = 18 x 13 = 234 square feet.
Probability and Data
12. A spinner has 10 equal sections: 3 red, 4 blue, 2 green, and 1 yellow. What is the probability of landing on blue?
Solution: 4/10 = 2/5.
13. A student scores 82, 90, 76, 88, and 94 on five quizzes. What is the mean score?
Solution: Sum = 430. Mean = 430 divided by 5 = 86.
Mixed Challenge Problems
14. A store buys a bike for $160 and marks it up by 25%. It later discounts the marked price by 10%. What is the final sale price?
Solution: Marked price = 160 x 1.25 = $200. Final price = 200 x 0.90 = $180.
15. A class has 28 students. The ratio of students who prefer science to students who prefer history is 4:3. How many students prefer science?
Solution: Total ratio parts = 4 + 3 = 7. Each part is 28 divided by 7 = 4. Science = 4 parts = 16 students.
What to Review After This Set
| If the Student Missed | Review This |
|---|---|
| Problems 1-3 | Unit rates, proportions, scale factors, and ratio tables |
| Problems 4-5 or 14 | Percent change, discounts, markup, and choosing the original amount |
| Problems 6-7 | Integer operations and number-line models |
| Problems 8-9 | Writing and solving one-step and two-step equations |
| Problems 10-11 | Geometry formulas and careful reading of dimensions |
| Problems 12-13 | Probability, mean, median, and data interpretation |
How to Turn Missed Problems into Practice
For every missed word problem, have the student rewrite the problem with smaller numbers and solve the simpler version first. A discount problem with $48 can become a discount problem with $10. A scale drawing with 4.5 inches can become a drawing with 2 inches. Once the structure is clear, return to the original numbers. This habit helps students separate the reasoning from the arithmetic.
ViewMath Indiana Grade 7 Resources
Use the Indiana ILEARN Grade 7 study guide for examples, the workbook for repeated practice, the Step-by-Step book for guided explanations, quizzes for short checkpoints, and practice tests when the student is ready for mixed review. Browse the collection at viewmath.com/books/grade-7-math/grade-7-math-indiana-ilearn-ias/.
