Word problems are where Grade 7 Florida FAST math gets real. Students must apply ratios, proportions, percent concepts, algebraic expressions, geometry formulas, and statistical reasoning not in isolation but wrapped inside realistic scenarios that require reading comprehension alongside math skill. This post gives you a focused set of word problems aligned to the Grade 7 B.E.S.T. (Benchmarks for Excellent Student Thinking) standards, with worked solutions and a prep plan for the Florida FAST assessment.
ViewMath is not affiliated with or endorsed by the Florida Department of Education or the Florida Statewide Assessments program. Visit fldoe.org for official FAST information.
Grade 7 FAST Math: Key B.E.S.T. Standards Overview
The Florida B.E.S.T. standards for Grade 7 math are organized into five strands. Word problems appear across all of them:
- Number Sense and Operations: Operations with rational numbers (positive and negative fractions, mixed numbers, decimals). Converting between forms of rational numbers.
- Ratios and Proportional Relationships: Proportional relationships, percent applications (percent change, simple interest, markups, markdowns, tax, tip), unit rates with complex fractions.
- Algebraic Reasoning: Writing and solving multi-step equations and inequalities with rational coefficients; representing proportional relationships with equations.
- Geometric Reasoning: Scale drawings, angle relationships, cross-sections of 3D figures, area and circumference of circles, surface area and volume of prisms, pyramids, and composite figures.
- Data Analysis and Probability: Random sampling, making inferences about populations, simple and compound probability, data distributions.
Ratios and Proportions Word Problems
Problem 1
A store is selling 3 notebooks for $4.50. At the same rate, how much would 8 notebooks cost?
Solution: Unit rate = $4.50 ÷ 3 = $1.50 per notebook. Cost of 8 = 8 × $1.50 = $12.00.
Problem 2
A recipe calls for 2/3 cup of sugar for every 1 1/2 cups of flour. If you use 4 cups of flour, how much sugar do you need?
Solution: Ratio = (2/3) ÷ (3/2) = 4/9 cups of sugar per cup of flour. Sugar = (4/9) × 4 = 16/9 = 1 7/9 cups. Alternatively: set up the proportion (2/3)/( 3/2) = x/4 → x = 4 × (2/3)/(3/2) = 16/9 ≈ 1.78 cups.
Problem 3 — Percent Change
A jacket originally costs $80. It is marked down by 25%. What is the sale price? Then a 6% sales tax is added. What is the final price?
Solution: Discount = 25% × $80 = $20. Sale price = $80 − $20 = $60. Tax = 6% × $60 = $3.60. Final price = $60 + $3.60 = $63.60.
Problem 4 — Simple Interest
Maria puts $500 in a savings account that earns 3% simple interest per year. How much interest will she earn after 4 years? What is the total in the account?
Solution: I = P × r × t = 500 × 0.03 × 4 = $60. Total = $500 + $60 = $560.
Algebraic Reasoning Word Problems
Problem 5
A plumber charges a $45 service fee plus $60 per hour of work. The total bill was $225. How many hours did the plumber work?
Solution: 45 + 60h = 225 → 60h = 180 → h = 3 hours.
Problem 6 — Inequality
A student needs to score at least 75 points on the next test to have an average of 80 or more across 4 tests. The first three test scores were 78, 82, and 85. Write and solve an inequality.
Solution: (78 + 82 + 85 + x)/4 ≥ 80 → (245 + x)/4 ≥ 80 → 245 + x ≥ 320 → x ≥ 75. The student needs at least 75 points.
Problem 7
Two friends are saving money. Carlos has $120 and saves $15 per week. Destiny has $40 and saves $25 per week. After how many weeks will they have the same amount?
Solution: 120 + 15w = 40 + 25w → 80 = 10w → w = 8 weeks.
Geometry Word Problems
Problem 8 — Scale Drawing
On a map, 1 inch represents 15 miles. Two cities are 4.5 inches apart on the map. What is the actual distance?
Solution: 4.5 × 15 = 67.5 miles.
Problem 9 — Circle
A circular fountain has a diameter of 14 feet. What is the area of the water surface? (Use π ≈ 3.14)
Solution: r = 7 ft. Area = π × r² = 3.14 × 49 ≈ 153.86 sq ft.
Problem 10 — Surface Area
A rectangular prism has a length of 8 cm, width of 5 cm, and height of 3 cm. What is the total surface area?
Solution: SA = 2(lw + lh + wh) = 2(40 + 24 + 15) = 2(79) = 158 cm².
Number Sense Word Problems (Rational Numbers)
Problem 11
The temperature in a city was −8°F on Monday. By Wednesday it had risen 13°F. What was the temperature on Wednesday?
Solution: −8 + 13 = 5°F.
Problem 12
A submarine descends 45.5 feet, then rises 18.25 feet, then descends another 12.75 feet. What is the submarine’s final depth relative to the surface?
Solution: −45.5 + 18.25 − 12.75 = −40 feet (40 feet below the surface).
Data Analysis and Probability Word Problems
Problem 13
A bag contains 3 red marbles, 5 blue marbles, and 2 green marbles. What is the probability of drawing a blue marble? If a blue marble is drawn and not replaced, what is the probability of drawing another blue marble?
Solution: P(blue) = 5/10 = 1/2. After removing one blue: P(blue) = 4/9.
Problem 14
A school randomly surveyed 40 students about their favorite subject. 12 said math. The school has 600 students. About how many students in the school prefer math?
Solution: 12/40 = x/600 → x = 12 × 15 = 180 students.
Common Grade 7 Word Problem Mistakes
- Percent change direction: “A 20% increase then a 20% decrease” does NOT return to the original price. (100 → 120 → 96.) Always apply percents to the current value, not the original.
- Mixing up positive and negative signs with rational number operations: Subtracting a negative number is equivalent to adding. −5 − (−3) = −5 + 3 = −2. Use a number line for any subtraction involving negatives.
- Writing equations without a variable: Students sometimes compute the answer mentally and skip writing the equation. On the FAST test, the work matters — and equations make checking easier.
- Scale drawing conversion direction: If 1 inch = 15 miles and you want the real distance, multiply the map measurement. If you want the map measurement, divide the real distance. Always identify which direction you are converting before computing.
3-Week FAST Grade 7 Math Prep Plan
Week 1: Rational Numbers, Ratios, and Percents
Begin with operations on rational numbers — fractions, mixed numbers, and decimals with positive and negative values. Use number lines to anchor negative operations. Then move to proportional relationships: setting up and solving proportions, finding unit rates with complex fractions, and solving percent problems (percent change, tax, tip, discount, simple interest).
Week 2: Algebraic Reasoning and Geometry
Focus on writing and solving multi-step equations and inequalities. Practice word problem to equation translation — identify the unknown, define a variable, write the equation before computing. Then cover geometric reasoning: scale drawings, angle relationships, circle area and circumference, surface area, and volume.
Week 3: Probability, Statistics, and Mixed Review
Review probability (simple and compound) and statistical inference from random samples. Complete a full 20-question mixed word problem set. Identify the two or three problem types with the most errors and do one targeted session per type before the assessment window.
Florida Grade 7 FAST Math Resources
ViewMath offers Grade 7 math practice books aligned to the Florida B.E.S.T. standards, designed to help students build fluency with the word problem types that appear most often on the FAST assessment. Each book includes full practice tests and complete answer explanations. Browse the Grade 7 Florida collection in the sidebar.
ViewMath is an independent publisher. Our materials are not official FAST or Florida DOE products.
