Washington Grade 7 students preparing for the Smarter Balanced Assessment (SBA) need more than isolated computation drills. The hardest questions often ask students to read a situation, choose a model, and connect ratios, percent, expressions, equations, geometry, or probability to a real context.
OSPI identifies Smarter Balanced math as part of Washington state testing, and the Washington testing portal describes the summative Smarter Balanced assessments as including a computer adaptive test and a performance task. This practice set is original ViewMath review, not official SBA material.
ViewMath is an independent publisher and is not affiliated with or endorsed by OSPI, Smarter Balanced, Cambium Assessment, or any Washington state assessment program. For official information, visit OSPI Mathematics Assessment and the Washington State Testing Portal.
What Grade 7 Word Problems Usually Require
- Ratios and unit rates: compare prices, speeds, recipes, and rates.
- Proportional relationships: identify constant of proportionality from tables, graphs, and equations.
- Percent problems: tax, tips, discounts, markups, percent change, and simple interest.
- Expressions and equations: translate words into algebra and solve multi-step equations.
- Geometry: scale drawings, area, circumference, angle relationships, and volume.
- Statistics and probability: sample data, probability models, and comparisons between groups.
Washington SBA Grade 7 Mixed Practice
1. A cyclist rides 18 miles in 1.5 hours. At the same rate, how far will the cyclist ride in 4 hours?
2. A recipe uses 5 cups of rice for 8 servings. How many cups are needed for 20 servings?
3. A shirt costs $36 before tax. The sales tax is 8.5%. What is the total cost?
4. A $64 jacket is discounted by 25%. What is the sale price?
5. A table shows x: 2, 4, 6 and y: 9, 18, 27. Is the relationship proportional? If so, what is the constant of proportionality?
6. Solve: 3(x – 4) = 24.
7. A movie theater charges $8 per ticket plus a $3 online fee for the whole order. Write an expression for the cost of t tickets.
8. A scale drawing uses 1 inch to represent 6 feet. A room is 3.5 inches long on the drawing. What is the actual length?
9. A circle has radius 7 cm. Use 22/7 for pi. What is the circumference?
10. A rectangular prism is 5 inches long, 4 inches wide, and 9 inches tall. What is the volume?
11. The probability of choosing a blue marble is 3/8. If there are 24 marbles total, how many are blue?
12. A data set is 12, 14, 14, 16, 19. What is the mean?
13. A phone plan charges $18 per month plus $0.12 for each text message. Write an expression for the monthly cost if m text messages are sent.
14. A store increases the price of a backpack from $40 to $46. What is the percent increase?
15. A map scale says 2 centimeters represents 15 miles. Two towns are 7 centimeters apart on the map. What is the actual distance?
16. A spinner has 5 equal sections: 2 red, 1 blue, and 2 green. What is the probability of landing on blue or green?
17. The angles in a triangle measure x degrees, 2x degrees, and 3x degrees. Find the three angle measures.
18. A student says 4/5 divided by 2 equals 4/3 because “dividing makes the answer bigger.” Explain the error and find the correct answer.
Answer Key with Explanations
1. 18 / 1.5 = 12 miles per hour. In 4 hours: 12 x 4 = 48 miles.
2. 5/8 cup per serving. For 20 servings: 20 x 5/8 = 12.5 cups.
3. Tax = 0.085 x 36 = 3.06. Total = $39.06.
4. Discount = 0.25 x 64 = 16. Sale price = $48.
5. Yes. y/x = 9/2 = 18/4 = 27/6 = 4.5.
6. 3(x – 4) = 24, so x – 4 = 8 and x = 12.
7. Ticket cost is 8t and the fee is 3, so the expression is 8t + 3.
8. 3.5 x 6 = 21 feet.
9. C = 2 x pi x r = 2 x 22/7 x 7 = 44 cm.
10. V = 5 x 4 x 9 = 180 cubic inches.
11. 3/8 x 24 = 9 blue marbles.
12. Sum = 75. Mean = 75 / 5 = 15.
13. The fixed charge is 18 and each message adds 0.12, so the expression is 18 + 0.12m.
14. Increase = 46 – 40 = 6. Percent increase = 6/40 = 0.15 = 15%.
15. 7 cm is 3.5 times 2 cm. Actual distance = 3.5 x 15 = 52.5 miles.
16. Favorable sections are 1 blue + 2 green = 3 sections. Probability = 3/5.
17. x + 2x + 3x = 180, so 6x = 180 and x = 30. The angles are 30 degrees, 60 degrees, and 90 degrees.
18. Dividing by a whole number can make a positive fraction smaller. Half of 4/5 is 2/5. The setup is 4/5 / 2 = 4/5 x 1/2 = 4/10 = 2/5.
Common Grade 7 Word-Problem Traps
Trap 1: using the wrong base in a percent problem. In Problem 14, the percent increase compares the increase to the original $40, not to the new $46. A good habit is to write “change over original” before calculating.
Trap 2: treating every ratio table as proportional. A proportional relationship must have the same y/x value in every row and usually passes through the origin when graphed. If a problem includes a starting fee, like Problem 13, it is linear but not proportional.
Trap 3: skipping units. Scale, circumference, volume, and probability problems often use familiar arithmetic, but the answer is incomplete without miles, centimeters, cubic inches, or a probability statement.
How to Review Missed Word Problems
For each missed item, ask the student to label the error type:
- Reading error: the student missed a condition or unit.
- Setup error: the wrong equation, ratio, or formula was chosen.
- Computation error: the setup was correct but arithmetic went wrong.
- Explanation error: the answer was correct, but the reasoning was unclear.
This matters because the fix is different. A computation error needs fluency practice. A setup error needs examples and comparison problems.
For SBA-style review, the written correction matters as much as the new answer. Have students rewrite one missed problem in this format: “The question asks for ____. I chose ____ because ____. My corrected equation is ____.” This short routine turns a wrong answer into evidence about reading, modeling, or calculation.
Two-Week SBA Grade 7 Review Plan
| Days | Focus | Practice Type |
|---|---|---|
| 1-2 | Ratios, rates, and proportional relationships | Tables, graphs, equations, and unit-rate word problems |
| 3-4 | Percent and rational numbers | Discounts, tax, tips, markups, and integer operations |
| 5-6 | Expressions and equations | Translate, solve, and check multi-step equations |
| 7-8 | Geometry and scale | Area, circumference, volume, and scale drawings |
| 9-10 | Mixed review | Timed sets and written corrections |
During the final two review days, mix easy, medium, and challenging problems instead of studying one topic at a time. Students need practice deciding whether a problem is about a unit rate, percent change, an equation, a scale factor, or a geometry formula before they start calculating.
ViewMath Washington Grade 7 Resources
ViewMath Washington Grade 7 books include study guides, workbooks, quizzes, 30-day review, and full practice tests for students preparing for Washington SBA math and grade-level standards.
Browse the collection at ViewMath Washington Grade 7 Math.
