Proportional reasoning is the central thread of Grade 7 mathematics, and it shows up in virtually every domain on the Georgia Milestones End-of-Grade (EOG) assessment — from ratio tables and percent problems to equations, geometry with scale, and probability. Students who can set up and solve proportional relationships fluently are better positioned across all Grade 7 topics, not just the Ratios and Proportional Relationships domain.
This guide focuses on word problems — the format that trips up the most students on the Georgia Milestones — across all major Grade 7 domains, with complete answers and detailed explanations.
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Georgia Milestones Grade 7: Domain Overview
- Ratios and Proportional Relationships: Unit rates with fractions, identifying proportional relationships, equations in the form y = kx, percent problems
- The Number System: All four operations with rational numbers (negative fractions, decimals)
- Expressions and Equations: Multi-step equations, expanding expressions, word problem equation setup
- Geometry: Circles (circumference, area), composite figures, scale drawings, angle relationships
- Statistics and Probability: Random samples, population inference, compound probability, data comparisons
Word Problems: Ratios and Proportional Relationships
1. Maria earns $13.50 for every 3 hours she babysits. At this rate, how much will she earn in 8 hours?
Unit rate = $13.50 ÷ 3 = $4.50/hr. Earnings for 8 hr = 8 × $4.50 = $36.
2. A map uses a scale of 1 inch = 35 miles. Two cities are 4.8 inches apart on the map. What is the actual distance?
4.8 × 35 = 168 miles.
3. A store is running a 40% off sale. A jacket originally costs $95. What is the sale price? How much money is saved?
Discount = 0.40 × $95 = $38. Sale price = $95 − $38 = $57. Savings = $38.
4. After a 15% tip, the total cost of dinner was $69. What was the price before the tip?
1.15 × original = $69 → original = $69 ÷ 1.15 = $60.
5. James invests $1,400 at a simple interest rate of 3% per year. How much interest does he earn in 4 years? What is the total value of his investment?
I = prt = 1400 × 0.03 × 4 = $168. Total = $1,400 + $168 = $1,568.
6. A car’s value dropped from $18,000 to $15,300. What is the percent decrease?
Decrease = $2,700. Percent decrease = (2,700 ÷ 18,000) × 100 = 15%.
Word Problems: Equations and Rational Numbers
7. A rectangle has a perimeter of 68 cm. Its length is 5 cm more than twice its width. Write and solve an equation to find the dimensions.
Let w = width. Length = 2w + 5. Perimeter: 2(w + 2w + 5) = 68 → 2(3w + 5) = 68 → 6w + 10 = 68 → 6w = 58 → w ≈ 9.67 cm. Length ≈ 24.33 cm. (If integer answer required, try: 2(3w+5)=68 → w=9⅔.)
8. The temperature at midnight was −8°F. By noon it had risen 23°F. By evening it dropped 11°F. What was the evening temperature?
−8 + 23 − 11 = 4°F.
9. A submarine was at −240 feet relative to sea level. It rose ¼ of that distance. What is the new depth?
It rose ¼ × 240 = 60 feet. New depth: −240 + 60 = −180 feet.
10. Solve: −3(2x + 4) = 18
−6x − 12 = 18 → −6x = 30 → x = −5.
Word Problems: Geometry
11. A circular fountain has a radius of 8 feet. The city plans to build a fence around it. How much fencing is needed? (Use π ≈ 3.14)
C = 2πr = 2 × 3.14 × 8 = 50.24 feet.
12. The fountain in Problem 11 will also be tiled. What is the area of the fountain floor that needs tiling?
A = πr² = 3.14 × 64 = 200.96 sq ft.
13. Two angles are supplementary. One angle measures (3x + 20)°. The other measures (x + 40)°. Find both angle measures.
3x + 20 + x + 40 = 180 → 4x + 60 = 180 → 4x = 120 → x = 30. Angles: 3(30)+20 = 110° and 30+40 = 70°.
Word Problems: Statistics and Probability
14. A survey of 50 randomly chosen students found that 18 prefer online learning. Based on this sample, how many of the school’s 700 students would you predict prefer online learning?
18/50 = x/700 → x = 18 × 700/50 = 252 students.
15. Two number cubes (each numbered 1–6) are rolled. What is the probability that both show an even number?
P(even on one die) = 3/6 = 1/2. P(both even) = (1/2)(1/2) = 1/4.
16. A spinner has 5 equal sections: 2 red, 2 blue, 1 yellow. If you spin twice, what is the probability of getting red on the first spin and yellow on the second?
P(red) = 2/5. P(yellow) = 1/5. P(both) = (2/5)(1/5) = 2/25.
Common Georgia Grade 7 Milestones Word Problem Mistakes
- Percent of vs. percent off: “A shirt is 30% off” means you subtract 30% from the price. “A shirt’s price is 30% of the original” means you pay only 30%. These are very different, and many students confuse them under time pressure.
- Forgetting to account for all three values in multi-step number line problems: In temperature/depth problems with multiple changes, always write out each operation explicitly rather than trying to do it mentally.
- Treating compound probability as addition instead of multiplication: P(A and B) = P(A) × P(B) for independent events. Students who add get answers greater than 1, which is a reliable self-check signal that something is wrong.
- Losing the carry in multi-step equations: Distributing a negative sign — as in −3(2x + 4) — often produces errors when students write −6x + 4 instead of −6x − 12.
3-Week Georgia Grade 7 Milestones Prep Plan
Week 1: Proportional Relationships and Percents
Practice unit rates with fractions and decimals. Write y = kx equations from tables. Work through 15 percent word problems covering discount, markup, tip, interest, and percent change. Build a reference chart of percent-to-decimal conversions.
Week 2: Equations, Geometry, and Rational Numbers
Solve multi-step equations and inequalities. Practice with negative fractions and decimals. Work through circles (circumference, area), supplementary/complementary angles, and scale drawing problems. Focus on setting up equations from word problem language.
Week 3: Probability, Statistics, and Mixed Review
Practice simple and compound probability with spinners, dice, and cards. Use random sample data to make population predictions. Compare two data sets using mean, median, and MAD. Finish with a 20-question full-topic practice test and complete error review.
Georgia Grade 7 Math Resources
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