🦉
Fred
Hi! I'm Fred the Owl, your math coach. This is an Iowa / ITBS-style Grade 6 Math practice by FlyingMinds — ratios & percents, integers, expressions & equations, geometry, and statistics, plus an Iowa Computation section. Pick an answer to see how to solve it.
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Iowa Assessments · ITBS · Math · Grade 6

Math — Grade 6

FlyingMinds Iowa Test Prep — original, advanced practice built by FlyingMinds to help you become a critical thinker and pass the test
Grade 6Ratios & PercentIntegersExpressions & EquationsGeometryStatistics
📋 Test Overview
Test
Iowa / ITBS-style Math practice
Grade level
Grade 6
Length
practice + Iowa Computation + challenge + 4 explain prompts — more practice than Testing Mom's Grade 6 math sets
Skills
Ratios & rates · percents · integers & absolute value · factors, GCF & LCM · fraction & decimal operations · expressions · equations & inequalities · coordinate plane · area, surface area & volume · statistics (mean, median, mode, range) · 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
6.RP · 6.NS · 6.EE · 6.G · 6.SP
⭐ 0 / 98 stars · ✍️ 0 / 4 explanations
📖 Learn 🎯 Practice 🏆 Challenge ✍️ Explain
Before you practice: Grade 6 math moves into ratios, percents, 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 ratio compares amounts (2:3). A unit rate is per ONE (miles per hour). Percent means per 100: to find a percent of a number, multiply by its decimal (25% → 0.25).

± Integers

Negative numbers are less than 0. Adding a negative moves left; subtracting moves left too. Absolute value |x| is the distance from 0 — always 0 or positive.

🔢 Factors, GCF & LCM

GCF = greatest factor two numbers share. LCM = least multiple they share. A prime number has exactly two factors: 1 and itself.

🅰️ Expressions & equations

A variable stands for a number. Evaluate by substituting. Solve equations by undoing operations on both sides. Inequalities (>, <) describe a range of values.

📐 Geometry & the coordinate plane

Rectangle area = l×w; triangle = ½bh; box volume = l×w×h. Plot points (x, y): x across, y up/down; the axes meet at the origin (0,0).

📊 Statistics

Mean = add then divide; median = middle of ordered data; mode = most frequent; range = greatest − least. An outlier pulls the mean most.

🔮 WARM-UP · NOT SCORED
🦉 Fred asks: Explain in words how you would find 20% of a number.
Starter: To find 20% of a number, I would __________ because __________ .

🎯 Practice score: 0 / 86

🟢 Part A — Ratios & rates

A ratio compares two amounts (2:3). A unit rate is the amount for ONE (miles per hour). Scale up or down by multiplying.

6.RP · RatiosRATIO
1. A recipe uses 2 cups of flour to 3 cups of sugar. The ratio of flour to sugar is —
6.RP · RatiosRATIO
2. There are 12 boys and 8 girls. The ratio of girls to boys in simplest form is —
6.RP · RatiosRATIO
3. A car travels 150 miles in 3 hours. Its unit rate is —
6.RP · RatiosRATIO
4. If 4 pens cost $5, then 12 pens cost —
6.RP · RatiosRATIO
5. Tia reads 30 pages in 2 days. At that rate, in 5 days she reads —
6.RP · RatiosRATIO
6. The ratio of cats to dogs is 5:2. If there are 10 cats, the number of dogs is —
6.RP · RatiosRATIO
7. Which ratio is equivalent to 3:4?
6.RP · RatiosRATIO
8. A map scale reads 1 inch = 20 miles. Then 4 inches represents —

🔵 Part B — Percents

Percent means 'per 100.' To find a percent of a number, change the percent to a decimal and multiply.

6.RP · PercentPERCENT
9. What is 25% of 80?
6.RP · PercentPERCENT
10. What is 10% of 250?
6.RP · PercentPERCENT
11. Write 3/4 as a percent.
6.RP · PercentPERCENT
12. Write 0.6 as a percent.
6.RP · PercentPERCENT
13. 20 is what percent of 50?
6.RP · PercentPERCENT
14. A $40 shirt is 25% off. The discount is —
6.RP · PercentPERCENT
15. A class has 30 students; 60% are girls. The number of girls is —
6.RP · PercentPERCENT
16. What is 15% of 200?

🟡 Part C — Integers & absolute value

Negative numbers are less than 0. Absolute value is the distance from 0 (always 0 or positive).

6.NS · IntegersINTEGERS
17. Which is greater: −5 or −2?
6.NS · IntegersINTEGERS
18. What is |−7| (the absolute value of −7)?
6.NS · IntegersINTEGERS
19. −3 + 8 =
6.NS · IntegersINTEGERS
20. 4 + (−9) =
6.NS · IntegersINTEGERS
21. −6 − 4 =
6.NS · IntegersINTEGERS
22. Which number is farthest from 0: −8, 3, or 5?
6.NS · IntegersINTEGERS
23. A temperature drops from 2°C to −5°C. The change is —
6.NS · IntegersINTEGERS
24. Order from least to greatest: 0, −4, 2, −1

🟣 Part D — Factors, GCF & LCM

The GCF is the largest factor two numbers share. The LCM is the smallest multiple they share.

6.NS · FactorsFACTORS
25. The GCF of 12 and 18 is —
6.NS · FactorsFACTORS
26. The LCM of 4 and 6 is —
6.NS · FactorsFACTORS
27. Is 17 prime or composite?
6.NS · FactorsFACTORS
28. The GCF of 24 and 36 is —
6.NS · FactorsFACTORS
29. The LCM of 3 and 5 is —
6.NS · FactorsFACTORS
30. Which number is a multiple of BOTH 2 and 3?

⚪ Part E — Fractions & decimals

Add/subtract fractions with a common denominator. To divide by a fraction, multiply by its reciprocal. Line up decimal points.

6.NS · Fractions/DecimalsNUMBER
31. 1/2 + 1/4 =
6.NS · Fractions/DecimalsNUMBER
32. 2/3 − 1/6 =
6.NS · Fractions/DecimalsNUMBER
33. 3/4 × 2/3 =
6.NS · Fractions/DecimalsNUMBER
34. 1/2 ÷ 1/4 =
6.NS · Fractions/DecimalsNUMBER
35. 0.5 + 0.25 =
6.NS · Fractions/DecimalsNUMBER
36. 1.2 × 0.3 =
6.NS · Fractions/DecimalsNUMBER
37. Which is larger: 0.7 or 0.65?
6.NS · Fractions/DecimalsNUMBER
38. Write 2/5 as a decimal.

🟢 Part F — Expressions

A variable stands for a number. To evaluate, substitute the value and compute. Use the distributive property to expand.

6.EE · ExpressionsEXPRESSION
39. Evaluate 3x + 2 when x = 4.
6.EE · ExpressionsEXPRESSION
40. Write 'five more than a number n' as an expression.
6.EE · ExpressionsEXPRESSION
41. Which is equivalent to 2(x + 3)?
6.EE · ExpressionsEXPRESSION
42. Evaluate 2a − b when a = 5 and b = 3.
6.EE · ExpressionsEXPRESSION
43. The expression 4n means —
6.EE · ExpressionsEXPRESSION
44. Combine like terms: 3x + 5x =
6.EE · ExpressionsEXPRESSION
45. Evaluate (10 − 2) ÷ 4.
6.EE · ExpressionsEXPRESSION
46. Write 'the product of 6 and y.'

🔵 Part G — Equations & inequalities

To solve, undo the operation with its opposite. An inequality (>, <) shows a range of values.

6.EE · EquationsEQUATION
47. Solve x + 7 = 12.
6.EE · EquationsEQUATION
48. Solve 4x = 20.
6.EE · EquationsEQUATION
49. Solve x − 3 = 9.
6.EE · EquationsEQUATION
50. Solve x ÷ 2 = 6.
6.EE · EquationsEQUATION
51. Which value makes x + 4 = 10 true?
6.EE · EquationsEQUATION
52. The inequality x > 5 means x is —
6.EE · EquationsEQUATION
53. Which number is a solution to x < 3?
6.EE · EquationsEQUATION
54. Solve 3x = 18.

🟡 Part H — The coordinate plane

An ordered pair (x, y) gives a point: x is across, y is up/down. The axes cross at the origin (0,0) and form four quadrants.

6.NS · Coordinate planeGEOMETRY
55. In the point (4, 2), the x-coordinate is —
6.NS · Coordinate planeGEOMETRY
56. The point (0, 0) is called the —
6.NS · Coordinate planeGEOMETRY
57. Point (−3, 2) lies in which quadrant?
6.NS · Coordinate planeGEOMETRY
58. To plot (5, 3), you move —
6.NS · Coordinate planeGEOMETRY
59. The points (2, 1) and (2, 5) are —
6.NS · Coordinate planeGEOMETRY
60. Which point lies ON the x-axis?

🟣 Part I — Area, surface area & volume

Rectangle area = l × w; triangle = ½ × b × h; parallelogram = b × h. Volume of a box = l × w × h.

6.G · GeometryGEOMETRY
61. The area of a rectangle 8 by 5 is —
6.G · GeometryGEOMETRY
62. The area of a triangle with base 10 and height 6 is —
6.G · GeometryGEOMETRY
63. The volume of a box 2 × 3 × 4 is —
6.G · GeometryGEOMETRY
64. The area of a parallelogram with base 7 and height 4 is —
6.G · GeometryGEOMETRY
65. A cube has how many faces?
6.G · GeometryGEOMETRY
66. The volume of a cube with side 3 is —
6.G · GeometryGEOMETRY
67. The area of a square with side 9 is —
6.G · GeometryGEOMETRY
68. A net made of 6 equal squares folds into a —

⚪ Part J — Statistics

Mean = add and divide by how many. Median = the middle of ordered data. Mode = most frequent. Range = greatest − least.

6.SP · StatisticsSTATISTICS
69. Find the mean of 4, 6, and 8.
6.SP · StatisticsSTATISTICS
70. Find the median of 3, 5, 7, 9, 12.
6.SP · StatisticsSTATISTICS
71. Find the mode of 2, 3, 3, 5, 7.
6.SP · StatisticsSTATISTICS
72. Find the range of 10, 4, 7, 2.
6.SP · StatisticsSTATISTICS
73. The mean of 5 numbers is 10. Their total sum is —
6.SP · StatisticsSTATISTICS
74. Which measure is the MIDDLE value of ordered data?
6.SP · StatisticsSTATISTICS
75. In the set 1, 2, 2, 2, 9, which is most affected by the outlier 9?
6.SP · StatisticsSTATISTICS
76. Find the mean of 12, 14, 16, and 18.

🧮 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.

6.NS · ComputationCOMPUTATION
77. 3,475 + 2,896 = ?
6.NS · ComputationCOMPUTATION
78. 8,002 − 3,564 = ?
6.NS · ComputationCOMPUTATION
79. 47 × 23 = ?
6.NS · ComputationCOMPUTATION
80. 1,176 ÷ 8 = ?
6.NS · ComputationCOMPUTATION
81. 25% of 160 = ?
6.NS · ComputationCOMPUTATION
82. −7 + 12 = ?
6.NS · ComputationCOMPUTATION
83. 3/4 + 1/8 = ?
6.NS · ComputationCOMPUTATION
84. 6.5 × 4 = ?
6.NS · ComputationCOMPUTATION
85. 144 ÷ 6 = ?
6.NS · ComputationCOMPUTATION
86. 0.9 − 0.45 = ?
🏆 Challenge score: 0 / 18
🏆 Challenge round. Multi-step problems for sharp Grade 6 thinkers.
Grade 6 MathCHALLENGE
87. A $25 shirt is 20% off. The SALE price is —
Grade 6 MathCHALLENGE
88. A car goes 240 miles on 8 gallons. Its mileage is —
Grade 6 MathCHALLENGE
89. If 3 notebooks cost $6, then 7 notebooks cost —
Grade 6 MathCHALLENGE
90. The ratio of red to blue marbles is 2:5. If there are 14 red, the number of blue is —
Grade 6 MathCHALLENGE
91. Evaluate 2(x + 3) − 4 when x = 5.
Grade 6 MathCHALLENGE
92. Solve 2x + 3 = 11.
Grade 6 MathCHALLENGE
93. A rectangle has area 48 and width 6. Its length is —
Grade 6 MathCHALLENGE
94. The mean of 4 tests is 85. The total points scored is —
Grade 6 MathCHALLENGE
95. The temperature rises from −3°C to 4°C. The change is —
Grade 6 MathCHALLENGE
96. What is 15% of 60?
Grade 6 MathCHALLENGE
97. A box measures 5 × 4 × 3. Its volume is —
Grade 6 MathCHALLENGE
98. Order from least to greatest: −2, 1/2, 0, −1.5
6.SPCHALLENGE
99. A dot plot shows the number of books read by students last month: 2 students read 1 book, 4 students read 2 books, 3 students read 3 books, and 1 student read 5 books. How many students are shown in the dot plot?
6.SPCHALLENGE
100. Five houses on a street sold for $200,000, $210,000, $205,000, $215,000, and $900,000. Which measure better describes a typical home price, and why?
6.SPCHALLENGE
101. A bag holds 3 red marbles, 5 blue marbles, and 4 green marbles. If one marble is drawn at random, what is the probability it is blue?
6.RPCHALLENGE
102. A recipe uses 2 cups of flour for every 3 cups of sugar. If a baker uses 8 cups of flour, how many cups of sugar are needed?
6.RPCHALLENGE
103. A jacket costs $80. It is on sale for 25% off, and then a $5 coupon is taken off the sale price. What is the final price?
6.SPCHALLENGE
104. A table lists weekend sales: Friday 12, Saturday 20, Sunday 16. How many more items were sold on Saturday than on Friday and Sunday combined?
✍️ Write it. Explain your thinking. Fred checks length, key words, and mechanics.
✍️ EXPLAIN #1 · SCORED
🦉 Fred asks: A store sells 3 apples for $2. Explain how you would find the cost of 9 apples.
Sentence starter: To find the cost of 9 apples, I would __________ because __________ .

✍️ EXPLAIN #2 · SCORED
🦉 Fred asks: Explain what it means for a number to have a negative value, using a real example.
Sentence starter: A negative number means __________, for example __________ .

✍️ EXPLAIN #3 · SCORED
🦉 Fred asks: Write and solve a simple equation for: 'A number plus 6 equals 15.' Show your steps.
Sentence starter: The equation is __________ and the answer is __________ because __________ .

✍️ EXPLAIN #4 · CHALLENGE · SCORED
🦉 Fred asks: The mean of 4 test scores is 90. Explain how to find the total of all four scores.
Sentence starter: To find the total, I would __________ because the mean is __________ .

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