Grade 7 is a pivotal year for Massachusetts math students. The MCAS assessment at this level draws heavily on the Massachusetts Curriculum Frameworks, which require students to reason with ratios and proportional relationships, operate with rational numbers, write and solve equations and inequalities, apply geometry to real-world measurement, and interpret data and probability. The word problems in this post target each of those domains, giving you realistic practice in the format you will see on the actual test.
ViewMath is not affiliated with or endorsed by the Massachusetts Department of Elementary and Secondary Education (DESE). MCAS® is a registered trademark of DESE. For official information, use the DESE MCAS page, the released items and practice tests page, and the current Massachusetts curriculum frameworks.
What MCAS Grade 7 Math Covers
The Massachusetts Curriculum Framework for Grade 7 Mathematics organizes content into five major domains:
- Ratios and Proportional Relationships (7.RP): Unit rates, proportional relationships, percent problems, percent change
- The Number System (7.NS): Operations with rational numbers including negative fractions and decimals, absolute value
- Expressions and Equations (7.EE): Writing, simplifying, and solving equations and inequalities; multi-step real-world problems
- Geometry (7.G): Area of triangles and special quadrilaterals; surface area and volume of 2D and 3D figures; circles; scale drawings
- Statistics and Probability (7.SP): Random sampling, comparing populations, probability models, compound events
15 MCAS-Style Grade 7 Word Problems
Ratios and Proportional Relationships
Problem 1. A bicycle shop sells 3 red bikes for every 5 blue bikes. If the shop sold 45 blue bikes last month, how many red bikes did it sell?
Problem 2. Maya earns $13.50 per hour working at a bookstore. She worked 18 hours last week. Her friend Dani worked 15 hours at the same hourly rate. How much more did Maya earn than Dani last week?
Problem 3. A pair of sneakers that normally costs $85 is on sale for 20% off. What is the sale price?
Problem 4. Last year, a school had 620 students. This year enrollment increased by 15%. How many students are enrolled this year?
The Number System
Problem 5. At 6:00 a.m. the temperature was −8°F. By noon it had risen 17 degrees. What was the temperature at noon?
Problem 6. A submarine is at −240 feet relative to sea level. It rises 3/4 of the way to the surface. What is its new position relative to sea level?
Problem 7. Evaluate: (−3/4) × (−2 2/3). Express your answer as a fraction or mixed number in simplest form.
Expressions and Equations
Problem 8. Carlos has $150. He buys several paperback books that cost $8.50 each. He wants to have at least $30 left over. Write and solve an inequality to find the maximum number of books Carlos can buy.
Problem 9. The perimeter of a rectangle is 58 cm. The length is 5 cm more than twice the width. Write and solve an equation to find the dimensions.
Problem 10. A school store sells pencils for $0.25 each and notebooks for $1.75 each. On Monday, the store sold twice as many pencils as notebooks and collected $27.00 in total. How many notebooks were sold?
Geometry
Problem 11. A triangular garden has a base of 12 meters and a height of 7.5 meters. What is the area of the garden in square meters?
Problem 12. A cylindrical water tank has a diameter of 6 feet and a height of 9 feet. What is the volume of the tank? Use π ≈ 3.14 and round to the nearest tenth.
Problem 13. On a scale drawing, 1 inch represents 25 miles. Two cities are 3.4 inches apart on the map. What is the actual distance between the cities?
Statistics and Probability
Problem 14. A bag contains 5 red marbles, 3 blue marbles, and 2 green marbles. If you randomly draw one marble without looking, what is the probability of drawing a blue or green marble?
Problem 15. A class surveyed 30 students about their favorite season. The results showed: Spring 10, Summer 12, Fall 5, Winter 3. Based on this sample, if the school has 450 students, how many would you predict prefer Summer?
Answer Key with Explanations
1. 27 red bikes. Set up the proportion 3/5 = r/45; r = 3 × 9 = 27.
2. $40.50 more. Maya earned 18 × $13.50 = $243. Dani earned 15 × $13.50 = $202.50. Difference = $40.50.
3. $68. 20% of $85 = $17. $85 − $17 = $68.
4. 713 students. 15% of 620 = 93. 620 + 93 = 713.
5. 9°F. −8 + 17 = 9.
6. −60 feet. 3/4 of 240 = 180 feet risen. −240 + 180 = −60.
7. 2. (−3/4) × (−8/3) = 24/12 = 2.
8. 8.50b ≤ 120; b ≤ 14.1 → maximum 14 books. (150 − 30 = 120 available; 120 ÷ 8.50 ≈ 14.1.)
9. Width = 8 cm, length = 21 cm. Let w = width, l = 2w + 5. Perimeter: 2(w + 2w + 5) = 58 → 6w + 10 = 58 → w = 8; l = 21.
10. 12 notebooks. Let n = notebooks, 2n = pencils. 1.75n + 0.25(2n) = 27.00 → 2.25n = 27.00 → n = 12 notebooks.
11. 45 square meters. Area = (1/2) × 12 × 7.5 = 45.
12. 254.3 cubic feet. Radius = 3 ft. V = π r² h = 3.14 × 9 × 9 = 254.34 ≈ 254.3 ft³.
13. 85 miles. 3.4 × 25 = 85 miles.
14. 1/2. 3 blue + 2 green = 5 favorable out of 10 total. P = 5/10 = 1/2.
15. 180 students. 12/30 = 2/5 prefer Summer. 2/5 × 450 = 180.
Tips for MCAS Grade 7 Success
The MCAS is not timed, so students have as much time as they need within the school day. The most productive preparation habits for Grade 7 are: practicing multi-step word problems regularly (many MCAS items require two or more calculations), reviewing negative number operations carefully (a common source of errors), and working through geometry formulas until they are automatic. Also practice writing inequalities from word problems — many students can solve the algebra but struggle to set it up.
ViewMath offers comprehensive Grade 7 practice books covering every MCAS domain with graduated difficulty, full answer explanations, and test-taking strategies. Visit viewmath.com/shop to explore practice sets built specifically for Massachusetts Grade 7 math.
