Grade 7 CAASPP math is not just about harder numbers — it’s about more sophisticated reasoning. Students are expected to move between representations, work with negative values, solve multi-step equations, and interpret results in context. This collection of word problems covers the most-tested Grade 7 CA CCSS domains and includes full worked solutions for every question.
What Grade 7 CAASPP Math Tests
The highest-priority domains for Grade 7 California math, based on CA CCSS, are:
- Ratios and proportional relationships (including percent problems)
- The number system (rational number operations)
- Expressions and equations (including two-step equations and inequalities)
- Geometry (area and circumference of circles, volume and surface area of 3D figures, scale drawings)
- Statistics and probability (sampling, probability of simple and compound events)
Section 1: Proportional Relationships and Percents (6 Problems)
1. A car travels 135 miles in 3 hours at a constant speed. At the same rate, how far will it travel in 7 hours?
Solution: Unit rate = 135 ÷ 3 = 45 miles per hour. Distance in 7 hours = 45 × 7 = 315 miles.
2. A shirt originally costs $45. It is on sale for 20% off. What is the sale price?
Solution: Discount = 20% × $45 = 0.20 × 45 = $9. Sale price = $45 − $9 = $36.
3. A class of 28 students includes 35% who prefer science over math. How many students prefer science?
Solution: 35% × 28 = 0.35 × 28 = 9.8, which rounds to 10 students. (Note: in context, 9.8 students is not realistic — this would typically be presented as a data set where a fractional answer indicates approximately 10.)
4. A gym increased its membership fee from $40 to $52 per month. What was the percent increase?
Solution: Increase = $52 − $40 = $12. Percent increase = (12/40) × 100 = 30%.
5. Two recipes use sugar in different ratios. Recipe A uses 2 cups of sugar for 5 cups of flour. Recipe B uses 3 cups of sugar for 8 cups of flour. Which recipe is sweeter (higher ratio of sugar to flour)?
Solution: Recipe A: 2/5 = 0.40. Recipe B: 3/8 = 0.375. Recipe A is sweeter.
6. If 12 apples cost $4.20, how much would 20 apples cost at the same price per apple?
Solution: Unit price = $4.20 ÷ 12 = $0.35 per apple. Cost of 20 = 20 × $0.35 = $7.00.
Section 2: Rational Number Operations (4 Problems)
7. The temperature at 6 AM was −8°F. By noon, it had risen 15°F. What was the noon temperature?
Solution: −8 + 15 = 7°F.
8. A submarine is at −240 feet below sea level. It descends another 75 feet. What is its new depth?
Solution: −240 + (−75) = −315 feet (315 feet below sea level).
9. Evaluate: −2/3 × (−9/4)
Solution: A negative times a negative is positive. (2/3) × (9/4) = 18/12 = 3/2 = 1.5.
10. On Monday, a bank account balance changed by −$38.50. On Tuesday it changed by +$120.00. On Wednesday it changed by −$67.25. What was the net change over three days?
Solution: −38.50 + 120.00 + (−67.25) = 120.00 − 38.50 − 67.25 = +$14.25.
Section 3: Expressions and Equations (5 Problems)
11. Solve: 3x − 7 = 14
Solution: 3x = 21; x = 7.
12. Solve: −2(x + 4) = 10
Solution: Distribute: −2x − 8 = 10. Add 8: −2x = 18. Divide: x = −9.
13. A babysitter charges $8 per hour plus a one-time fee of $5. Write and solve an equation for how many hours she worked if her total was $53.
Solution: Let h = hours. Equation: 8h + 5 = 53. Subtract 5: 8h = 48. Divide: h = 6 hours.
14. Solve and graph the inequality: 4x − 3 > 9
Solution: Add 3: 4x > 12. Divide: x > 3. Graph: open circle at 3, shaded to the right.
15. Two friends are saving money. Alex has $25 and saves $12 per week. Jordan has $70 and saves $7 per week. After how many weeks will they have the same amount?
Solution: 25 + 12w = 70 + 7w. Subtract 7w: 18 + 5w = 70. Wait — subtract 25: 12w − 7w = 70 − 25; 5w = 45; w = 9 weeks. Check: Alex = 25 + 108 = 133; Jordan = 70 + 63 = 133 ✓
Section 4: Geometry (3 Problems)
16. A circle has a radius of 7 cm. What is its circumference? (Use π ≈ 3.14)
Solution: C = 2πr = 2 × 3.14 × 7 = 43.96 cm.
17. Find the area of a circle with diameter 10 inches. (Use π ≈ 3.14)
Solution: Radius = 5 inches. A = πr² = 3.14 × 25 = 78.5 square inches.
18. A triangular prism has a base area of 24 cm² and a height of 10 cm. What is its volume?
Solution: V = Base Area × Height = 24 × 10 = 240 cm³.
Section 5: Probability (2 Problems)
19. A bag contains 4 red, 3 blue, and 5 green marbles. If you pick one marble without looking, what is the probability of picking a blue marble?
Solution: P(blue) = 3/12 = 1/4.
20. A fair coin is flipped and a standard die (1–6) is rolled. What is the probability of getting tails and a number greater than 4?
Solution: P(tails) = 1/2. P(>4) = 2/6 = 1/3. P(both) = 1/2 × 1/3 = 1/6.
How to Use These Problems for CAASPP Prep
After working through these 20 problems, note which sections gave you the most trouble. Any section with more than 2 missed problems deserves focused review time. For the CAASPP specifically, pay extra attention to:
- Percent problems that require more than one step (increase/decrease, then a second calculation)
- Equation word problems where you have to define the variable and write the equation yourself
- Geometry problems that combine the formula with a real-world context or diagram
California Grade 7 CAASPP Math Resources from ViewMath
ViewMath’s California Grade 7 series includes workbooks, study guides, and full-length CAASPP-aligned practice tests — all covering the CA CCSS Grade 7 domains in detail. Browse the Grade 7 California collection using the sidebar below.
ViewMath is an independent publisher. Our books are not official CAASPP or Smarter Balanced materials.
