Grade 7 math in New Jersey covers some of the most practically useful math topics students will encounter: proportional relationships, working with negative numbers, multi-step equations, geometry, statistics, and probability. NJSLA-Adaptive mathematics questions can place these topics in real-world contexts, so students need practice reading carefully, setting up equations, and working through multiple steps.
This page provides 12 original word problems aligned with the New Jersey Student Learning Standards for Grade 7. Every problem includes a complete step-by-step solution.
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Official source checked: NJDOE lists NJSLA-Adaptive mathematics for grades 3 through high school and gives April 27-May 29, 2026 as the Spring 2026 NJSLA-Adaptive window. NJDOE’s NJSLA-Mathematics companion guide describes the assessment as measuring grade- or course-level skills, knowledge, practices, and concepts, with objective and constructed-response items. See the NJDOE testing schedule and NJSLA-Mathematics companion guide.
NJSLA Grade 7 Math Topics
The major content areas for Grade 7 NJSLA math include:
- Ratios and proportional relationships (constant of proportionality, percent increase/decrease, simple interest)
- Operations with rational numbers (positive and negative fractions and decimals)
- Expressions and equations (multi-step, variables on both sides)
- Geometry: scale drawings, areas and circumference of circles, composite figures, surface area and volume of 3D shapes
- Statistics: random sampling, comparing two populations using measures of center and variability
- Probability: simple probability, compound events, experimental vs. theoretical probability
12 Grade 7 Math Word Problems
Proportional Relationships
Problem 1. A store sells 4 notebooks for $6.00. At the same rate, how much would 10 notebooks cost?
Solution: Unit price = $6.00 ÷ 4 = $1.50 per notebook. Cost of 10 = 10 × $1.50 = $15.00.
Problem 2. A jacket originally costs $80. It is on sale for 35% off. What is the sale price?
Solution: Discount = 35% × $80 = 0.35 × 80 = $28. Sale price = $80 − $28 = $52.
Problem 3. A bank account earns simple interest. The account has $500, the interest rate is 4% per year, and the money stays in for 3 years. How much interest is earned?
Solution: I = P × r × t = 500 × 0.04 × 3 = $60.
Rational Number Operations
Problem 4. The temperature at midnight was −8°F. By noon it had risen 15°F. What was the noon temperature?
Solution: −8 + 15 = 7°F.
Problem 5. A submarine descends 3/4 of a mile each hour. How deep is it after 5 hours?
Solution: 3/4 × 5 = 15/4 = 3¾ miles deep (or −3.75 miles relative to sea level).
Problem 6. A recipe calls for −2/3 cup adjustment in salt (meaning reducing salt by 2/3 cup). If the original recipe uses 1½ cups of salt and the chef makes the recipe 2 times, how much salt reduction is needed in total?
Solution: One batch: reduce by 2/3. Two batches: reduce by 2 × 2/3 = 4/3 = 1⅓ cups total reduction.
Expressions and Equations
Problem 7. Maria earns $12 per hour babysitting. After working some hours, she had earned $84. Write and solve an equation to find how many hours she worked.
Solution: 12h = 84. h = 84 ÷ 12 = 7 hours.
Problem 8. A school charges a $15 registration fee plus $25 per class. If a student paid $115, how many classes did they register for?
Solution: 25c + 15 = 115. 25c = 100. c = 4 classes.
Geometry
Problem 9. A circular garden has a radius of 7 meters. What is its circumference? (Use π ≈ 3.14.)
Solution: C = 2πr = 2 × 3.14 × 7 = 43.96 meters.
Problem 10. A scale drawing shows a room where 1 inch = 5 feet. If the room appears 4 inches by 3 inches on the drawing, what are the actual dimensions of the room?
Solution: Actual length = 4 × 5 = 20 feet. Actual width = 3 × 5 = 15 feet. 20 ft × 15 ft.
Probability
Problem 11. A bag contains 3 red marbles, 5 blue marbles, and 2 green marbles. What is the probability of randomly picking a blue marble?
Solution: Total marbles = 3 + 5 + 2 = 10. P(blue) = 5/10 = 1/2 = 0.5.
Problem 12. A student flips a fair coin 40 times and gets heads 18 times. What is the experimental probability of heads? How does this compare to the theoretical probability?
Solution: Experimental P(heads) = 18/40 = 9/20 = 0.45. Theoretical P(heads) = 1/2 = 0.50. The experimental probability is slightly lower than theoretical due to random variation — with a fair coin, more flips will bring the experimental probability closer to 0.50.
Common Mistakes on Grade 7 Word Problems
- Percent decrease vs. new total: When a $80 item is 35% off, the discount is $28. The sale price is $80 − $28 = $52, not $28. Many students confuse the discount amount with the final price.
- Sign errors with negative numbers: Adding a negative is subtraction: −8 + (−3) = −11. Subtracting a negative is addition: −8 − (−3) = −5. Keeping track of signs in multi-step problems is a top source of Grade 7 errors.
- Using diameter instead of radius in circle formulas: C = 2πr, not C = 2π(diameter). Always identify whether the problem gives the radius or the diameter before substituting.
- Forgetting the registration fee in two-part cost problems: In Problem 8, some students solve 25c = 115 and get c = 4.6. The fixed fee ($15) must be subtracted before dividing by the per-unit cost.
- Confusing experimental and theoretical probability: Theoretical probability is what should happen over infinite trials (based on the math). Experimental probability is what actually happened in a specific trial. They are often not equal and that is normal.
ViewMath Resources for NJ Grade 7 Math
ViewMath Grade 7 math books provide extensive word problem practice aligned with NJSLS Grade 7 standards. Each book includes full answer keys with step-by-step solutions. Browse the resources listed on this page to find practice test books and workbooks that target the exact content tested on the NJSLA Grade 7 assessment.
