🦉
Fred
Hi! I'm Fred the Owl, your math coach. This is an Iowa / ITBS-style Grade 7 Math practice built by FlyingMinds — proportional reasoning, rational numbers, expressions & equations, circles & geometry, probability and statistics, plus an Iowa Computation section. Pick an answer to see how to solve it.
Font: Speed:
Iowa Assessments · ITBS · Math · Grade 7

Math — Grade 7

FlyingMinds Iowa Test Prep — original, advanced practice built by FlyingMinds to help you become a critical thinker and pass the test
Grade 7Ratios & PercentRational NumbersEquations & InequalitiesGeometryProbability & Statistics
📋 Test Overview
Test
Iowa / ITBS-style Math practice
Grade level
Grade 7
Length
practice + Iowa Computation + challenge + 4 explain prompts — more practice than Testing Mom's Grade 7 math sets
Skills
Ratios & proportional relationships · percent & percent change · rational numbers · expressions · two-step equations & inequalities · circles · area, surface area & volume · scale & similar figures · probability · statistics · Iowa Computation (mark N if not given)
How it's upgraded
Each idea is taught first; every answer gets a worked explanation; arithmetic is verified
Standards
7.RP · 7.NS · 7.EE · 7.G · 7.SP
⭐ 0 / 92 stars · ✍️ 0 / 4 explanations
📖 Learn 🎯 Practice 🏆 Challenge ✍️ Explain
Before you practice: Grade 7 math is built on proportional reasoning, negative numbers, and algebra. Learn each idea, then practice.
📌 FlyingMinds rule: Show each step, label your answer, and check that it makes sense.

➗ Ratios, rates & percent

A proportion sets two ratios equal — cross-multiply to solve. A unit rate is per ONE. Percent change = (change ÷ original) × 100. Discounts and tax adjust a price.

± Rational numbers

Add same signs and keep the sign; different signs subtract and take the larger sign. Two negatives multiply/divide to a positive. |x| is distance from 0.

🅰️ Expressions & equations

Use the distributive property and combine like terms. Solve two-step equations by undoing in reverse order. For inequalities, FLIP the sign when you multiply or divide by a negative.

⭕ Circles & geometry

Circumference = πd = 2πr; area = πr² (π ≈ 3.14). Triangle area = ½bh; prism volume = base area × height; surface area sums all faces.

📐 Scale & similar figures

Similar figures have equal side ratios and equal angles. A scale factor multiplies every length; area scales by the factor squared.

🎲 Probability & statistics

Probability = favorable ÷ total (0 to 1); complements add to 1. Mean = add and divide; median = middle; an outlier pulls the mean most. Use samples to predict about a population.

🔮 WARM-UP · NOT SCORED
🦉 Fred asks: How would you solve the proportion 3/4 = x/20?
Starter: I would __________ because __________ .

🎯 Practice score: 0 / 80

🟢 Part A — Ratios & proportional relationships

A proportion sets two equal ratios. A unit rate is the amount for ONE. The constant of proportionality is the unit rate (y = kx).

7.RP · RatiosRATIO
1. A car travels 180 miles in 3 hours. Its unit rate is —
7.RP · RatiosRATIO
2. If 5 pens cost $4, then 15 pens cost —
7.RP · RatiosRATIO
3. Solve the proportion: 3/4 = x/20.
7.RP · RatiosRATIO
4. A recipe uses 2 cups of flour for 3 cups of milk. For 9 cups of milk, you need —
7.RP · RatiosRATIO
5. In y = kx, k is called the —
7.RP · RatiosRATIO
6. 8 apples cost $6. The cost per apple is —
7.RP · RatiosRATIO
7. A map scale is 1 inch = 25 miles. Then 6 inches represents —
7.RP · RatiosRATIO
8. Which ratio is equivalent to 6:9?

🔵 Part B — Percent & percent change

Percent means per 100. Percent change = (change ÷ original) × 100. Tax and discount adjust a price.

7.RP · PercentPERCENT
9. What is 30% of 90?
7.RP · PercentPERCENT
10. A $50 jacket is 20% off. The sale price is —
7.RP · PercentPERCENT
11. A price rises from $40 to $50. The percent increase is —
7.RP · PercentPERCENT
12. A $20 meal has an 8% tax. The tax is —
7.RP · PercentPERCENT
13. 15 is what percent of 60?
7.RP · PercentPERCENT
14. A population falls from 200 to 150. The percent decrease is —
7.RP · PercentPERCENT
15. A shirt costs $24 after a 25% discount was taken off the original. The discount amount was —
7.RP · PercentPERCENT
16. Write 0.45 as a percent.

🟡 Part C — Rational numbers

Add, subtract, multiply, and divide positive and negative numbers. Same signs → positive product; different signs → negative.

7.NS · Rational numbersNUMBER
17. −8 + 5 =
7.NS · Rational numbersNUMBER
18. −6 − (−4) =
7.NS · Rational numbersNUMBER
19. (−3) × (−7) =
7.NS · Rational numbersNUMBER
20. (−24) ÷ 6 =
7.NS · Rational numbersNUMBER
21. −2 + (−9) =
7.NS · Rational numbersNUMBER
22. Which is greater: −0.5 or −0.75?
7.NS · Rational numbersNUMBER
23. −1/2 + 1/4 =
7.NS · Rational numbersNUMBER
24. The value of |−9| − |4| is —

🟣 Part D — Expressions & two-step equations

Combine like terms and use the distributive property. Solve by undoing operations in reverse order.

7.EE · Expressions/EquationsEQUATION
25. Simplify: 3(x + 4).
7.EE · Expressions/EquationsEQUATION
26. Combine like terms: 5x + 2 − 3x.
7.EE · Expressions/EquationsEQUATION
27. Solve: 2x + 3 = 11.
7.EE · Expressions/EquationsEQUATION
28. Solve: 5x − 4 = 16.
7.EE · Expressions/EquationsEQUATION
29. Solve: x/3 + 2 = 5.
7.EE · Expressions/EquationsEQUATION
30. Evaluate 4a − 2b when a = 3 and b = 5.
7.EE · Expressions/EquationsEQUATION
31. Which expression equals 2(3x − 1)?
7.EE · Expressions/EquationsEQUATION
32. Solve: 7 = 3x − 2.

⚪ Part E — Inequalities

An inequality (>, <, ≥, ≤) shows a range of values. Solve like an equation, but FLIP the sign if you multiply or divide by a negative.

7.EE · InequalitiesINEQUALITY
33. Solve: x + 5 > 9.
7.EE · InequalitiesINEQUALITY
34. Solve: 2x ≤ 10.
7.EE · InequalitiesINEQUALITY
35. When you divide both sides of an inequality by −2, you must —
7.EE · InequalitiesINEQUALITY
36. Which value is a solution to x − 3 < 2?
7.EE · InequalitiesINEQUALITY
37. Solve: −3x < 12.
7.EE · InequalitiesINEQUALITY
38. 'At least 18' is written as —

🟢 Part F — Circles

Circumference = π × diameter (or 2πr). Area = π × r². Use π ≈ 3.14.

7.G · CirclesGEOMETRY
39. Using π ≈ 3.14, the circumference of a circle with diameter 10 is —
7.G · CirclesGEOMETRY
40. Using π ≈ 3.14, the area of a circle with radius 5 is —
7.G · CirclesGEOMETRY
41. The radius of a circle is half of its —
7.G · CirclesGEOMETRY
42. Using π ≈ 3.14, the circumference of a circle with radius 3 is —
7.G · CirclesGEOMETRY
43. Using π ≈ 3.14, the area of a circle with radius 10 is —
7.G · CirclesGEOMETRY
44. Which formula gives the AREA of a circle?

🔵 Part G — Area, surface area & volume

Triangle area = ½bh. Volume of a prism = area of base × height. Surface area adds up all the faces.

7.G · GeometryGEOMETRY
45. The area of a triangle with base 12 and height 5 is —
7.G · GeometryGEOMETRY
46. The volume of a rectangular prism 4 × 3 × 6 is —
7.G · GeometryGEOMETRY
47. The area of a trapezoid is found with —
7.G · GeometryGEOMETRY
48. A cube has edges of 4. Its surface area is —
7.G · GeometryGEOMETRY
49. A triangular prism's volume equals —
7.G · GeometryGEOMETRY
50. The volume of a cube with side 5 is —
7.G · GeometryGEOMETRY
51. The area of a parallelogram with base 9 and height 4 is —
7.G · GeometryGEOMETRY
52. A box has volume 60 and a base area of 12. Its height is —

🟣 Part H — Scale, proportion & similar figures

Similar figures have equal ratios of matching sides. A scale factor multiplies every length.

7.G · ScaleGEOMETRY
53. A model uses a scale of 1 cm = 4 m. A 5 cm length represents —
7.G · ScaleGEOMETRY
54. Two similar triangles have a scale factor of 3. A side of 5 becomes —
7.G · ScaleGEOMETRY
55. If 4/6 = 6/x, then x =
7.G · ScaleGEOMETRY
56. On a blueprint, 1 inch = 8 feet. A wall 24 feet long is drawn as —
7.G · ScaleGEOMETRY
57. A photo is enlarged by a scale factor of 2. Its area becomes —
7.G · ScaleGEOMETRY
58. Similar figures always have —

⚪ Part I — Probability

Probability = favorable outcomes ÷ total outcomes, a number from 0 (impossible) to 1 (certain).

7.SP · ProbabilityPROBABILITY
59. A fair coin is flipped. P(heads) is —
7.SP · ProbabilityPROBABILITY
60. A die (1–6) is rolled. P(rolling a 4) is —
7.SP · ProbabilityPROBABILITY
61. A bag has 3 red and 2 blue marbles. P(red) is —
7.SP · ProbabilityPROBABILITY
62. A probability of 0 means an event is —
7.SP · ProbabilityPROBABILITY
63. A die is rolled. P(an even number) is —
7.SP · ProbabilityPROBABILITY
64. If P(rain) = 0.7, then P(no rain) is —

🟢 Part J — Statistics

Mean = add and divide. Median = middle of ordered data. The range and spread describe variability.

7.SP · StatisticsSTATISTICS
65. Find the mean of 6, 8, 10, 12.
7.SP · StatisticsSTATISTICS
66. Find the median of 4, 8, 6, 10, 2 (ordered: 2,4,6,8,10).
7.SP · StatisticsSTATISTICS
67. Find the range of 15, 4, 9, 20.
7.SP · StatisticsSTATISTICS
68. The mean of 6 numbers is 12. Their total is —
7.SP · StatisticsSTATISTICS
69. A sample is used to make a prediction about a —
7.SP · StatisticsSTATISTICS
70. Which is most affected by an outlier?

🧮 Part — Iowa format: Computation

Iowa style: Work out the exact answer. If your answer is not one of the first three choices, mark N — not given.

7.NS · ComputationCOMPUTATION
71. 4,237 + 3,895 = ?
7.NS · ComputationCOMPUTATION
72. 9,001 − 4,678 = ?
7.NS · ComputationCOMPUTATION
73. 58 × 34 = ?
7.NS · ComputationCOMPUTATION
74. 1,512 ÷ 9 = ?
7.NS · ComputationCOMPUTATION
75. (−12) + 7 = ?
7.NS · ComputationCOMPUTATION
76. (−6) × (−9) = ?
7.NS · ComputationCOMPUTATION
77. 40% of 250 = ?
7.NS · ComputationCOMPUTATION
78. 2/3 + 1/6 = ?
7.NS · ComputationCOMPUTATION
79. 7.5 × 0.4 = ?
7.NS · ComputationCOMPUTATION
80. 144 ÷ 0.12 = ?
🏆 Challenge score: 0 / 18
🏆 Challenge round. Multi-step reasoning for sharp Grade 7 thinkers.
Grade 7 MathCHALLENGE
81. A $60 coat is marked 25% off, then 10% off the sale price. The final price is —
Grade 7 MathCHALLENGE
82. A car uses 12 gallons to go 360 miles. To go 540 miles it needs —
Grade 7 MathCHALLENGE
83. Solve: 3(x − 2) = 18.
Grade 7 MathCHALLENGE
84. A recipe's ratio of sugar to flour is 2:5. With 15 cups of flour, sugar needed is —
Grade 7 MathCHALLENGE
85. Using π ≈ 3.14, the area of a circle with diameter 8 is —
Grade 7 MathCHALLENGE
86. A temperature changes from −4°F to 11°F. The change is —
Grade 7 MathCHALLENGE
87. The mean of 5 scores is 80. Four scores are 70, 85, 90, 75. The fifth is —
Grade 7 MathCHALLENGE
88. A bag has 4 red, 3 blue, 5 green marbles. P(blue) is —
Grade 7 MathCHALLENGE
89. A box 5 × 4 × 3 is filled with unit cubes. How many cubes fit?
Grade 7 MathCHALLENGE
90. Solve the proportion: 8/x = 2/5.
Grade 7 MathCHALLENGE
91. A jacket's price rose from $80 to $100. The percent increase is —
Grade 7 MathCHALLENGE
92. Evaluate −2(3 − 7) + 5.
7.SP · ChallengeCHALLENGE
93. A spinner has 8 equal sections numbered 1 through 8. On one spin, the probability of landing on a number greater than 5 is —
7.SP · ChallengeCHALLENGE
94. You flip a fair coin and roll a standard number cube. The probability of getting heads AND a number greater than 4 is —
7.SP · ChallengeCHALLENGE
95. Six houses on a street are worth (in thousands) 180, 190, 200, 210, 220, and 900. Which statement is true?
7.SP · ChallengeCHALLENGE
96. In a random sample of 50 students, 18 said they ride the bus. Based on this sample, about how many of the 800 students in the school ride the bus?
7.RP · ChallengeCHALLENGE
97. A town's population grew 20% one year and then fell 10% the next year. Starting from 5,000 people, the population after the two years is —
7.RP · ChallengeCHALLENGE
98. A printer prints 14 pages in 4 minutes at a steady rate. At that rate, the number of pages printed in 10 minutes is —
✍️ Write it. Explain your thinking. Fred checks length, key words, and mechanics.
✍️ EXPLAIN #1 · SCORED
🦉 Fred asks: A store sells 5 notebooks for $4. Explain how to find the cost of 15 notebooks.
Sentence starter: To find the cost of 15 notebooks, I would __________ because __________ .

✍️ EXPLAIN #2 · SCORED
🦉 Fred asks: Explain the rule for the sign when you multiply two negative numbers, with an example.
Sentence starter: When you multiply two negatives, the answer is __________, for example __________ .

✍️ EXPLAIN #3 · SCORED
🦉 Fred asks: Write and solve a two-step equation for: 'Three times a number plus 2 is 17.' Show your steps.
Sentence starter: The equation is __________ and the answer is __________ because __________ .

✍️ EXPLAIN #4 · CHALLENGE · SCORED
🦉 Fred asks: A jacket goes from $40 to $50. Explain how to find the percent increase.
Sentence starter: To find the percent increase, I would __________ because __________ .

Scroll to explore the full test
← Back to Fred · All Iowa Tests
✅ Google Classroom opened in a new tab. Sign in, pick "", and click Assign.