Free Grade 6 MAP Math Practice Problems
Below are 14 free Grade 6 math practice problems with a complete answer key and worked explanations. They cover the five strands a sixth grader meets on an adaptive math test like MAP Growth: ratios and proportional reasoning, the number system, expressions and equations, geometry, and statistics. Every question is an original Helix Math question — work through them with your child, then check the answer key at the bottom.
How to use this set
Have your child try all 14 on paper or in their head first — no peeking at the answer key. The problems get harder as you go: the first few warm up a single skill, and the last few ask your child to combine steps or decide which method fits. Note not just what they miss, but where: a child who is solid on questions 1–8 but stalls on 11–14 isn't "behind in sixth grade math" — they have a couple of specific skills that haven't firmed up yet.
The 14 problems
1. Exponents. Which expression equals 4 × 4 × 4 × 4 × 4 × 4? A) 4⁶ B) 6⁴ C) 4 × 6 D) 24²
2. Greatest common factor. Find the greatest common factor (GCF) of 12 and 18.
3. Dividing fractions. What is the value of 1/2 ÷ 1/6?
4. Dividing fractions, in context. A string is 5 feet long. If you cut it into pieces that are each 1/4 foot long, how many pieces will you have?
5. Simplifying a ratio. Maya simplified the ratio 20 : 15. Which of these shows the correct simplified ratio? A) 10 : 5 B) 5 : 3 C) 2 : 1 D) 4 : 3
6. Unit rate. A bakery makes 24 cupcakes in 3 hours. At this constant rate, how many cupcakes does it make in 8 hours? A) 32 B) 64 C) 72 D) 192
7. Percent. What is 15% of 60?
8. One-step equation. Which value of x makes the equation x + 7 = 15 true? A) 8 B) 22 C) 15 D) 7
9. Equivalent expressions. Which expression is equivalent to 2(x + 4)? A) 2x + 4 B) 2x + 8 C) x + 8 D) 2x + 6
10. Inequalities (select all that apply). Which values from the set {5, 10, 15, 20} are solutions to the inequality x > 12?
11. Area of a triangle. Priya is making a triangular pennant for her school's sports team. The pennant has a base of 12 inches and a height of 18 inches. What is the area, in square inches, of the pennant?
12. Surface area of a prism. A triangular prism has two right-triangular faces and three rectangular faces. The right triangle has legs of 9 cm and 12 cm and a hypotenuse of 15 cm. The prism is 20 cm long. What is the total surface area of the prism? A) 828 cm² B) 936 cm² C) 720 cm² D) 756 cm²
13. Choosing a measure of center. Ms. Rodriguez's class recorded the number of hours students spent on homework last week: 5, 6, 4, 7, 5, 6, 5, 8, 25, 6. Which measure of center best represents the typical amount of homework time? A) Mean, because it uses all the data values B) Median, because the outlier of 25 hours makes the mean unrepresentative C) Mode, because it shows the most common value D) Mean, because it is always the best measure of center
14. Mean absolute deviation. What is the mean absolute deviation (MAD) of this data set: 5, 5, 10, 10, 15?
What the right answers don't show
Here's the part a worksheet can't tell you. Look at questions 3 and 4. They're the same skill — dividing by a fraction. Plenty of sixth graders nail "1/2 ÷ 1/6 = 3" because they've memorized keep–change–flip, then freeze on the string problem, because nothing in the words says "divide." That gap between knowing the procedure and knowing when to use it is what we call fluent but fragile — and a single right answer hides it completely.
Question 13 is the same story in reverse: a child can compute a mean and a median perfectly and still pick the wrong one, because the average can quietly hide what's really going on in a data set.
This is why one score — or one practice set — only takes you so far. It tells you roughly where your child is performing. It can't tell you which skills underneath are secure, which are shaky, and which are simply missing.
Is your sixth grader ready for fall MAP testing?
Most schools give MAP Growth in a fall window (often late August into September), and a sixth grader's fall score leans heavily on fifth-grade foundations — fractions, multiplication fluency, and early ratio reasoning — as much as on new sixth-grade material. If your child sailed through questions 1–10 here, those foundations are likely solid. If a few of those tripped them up, the summer is the cheapest, lowest-pressure time to firm them up before the school year layers new material on top.
A 14-question set like this is a useful spot-check. But it samples only a handful of skills at one difficulty level. A full diagnostic does something a worksheet can't: it adjusts to your child across many skills and difficulty levels, and comes back with a skill-by-skill map of what's secure, what's shaky, and what to work on first.
The free Helix diagnostic takes about 30 minutes and emails you a report showing exactly which Grade 6 skills are secure, shaky, or missing — so you know what to shore up before fall.
Start the free Helix diagnostic →Answer key and explanations
Try each problem first, then open the answer. A couple of these are worth talking through with your child even when they get them right.
1. Exponents — Answer: 4⁶
The base (4) is multiplied by itself 6 times, so it is written 4⁶. Don't mix up the base and the exponent: 6⁴ would mean 6 multiplied four times.
2. GCF of 12 and 18 — Answer: 6
Factors of 12: 1, 2, 3, 4, 6, 12. Factors of 18: 1, 2, 3, 6, 9, 18. The common factors are 1, 2, 3, and 6 — the greatest of these is 6.
3. 1/2 ÷ 1/6 — Answer: 3
To divide by a fraction, multiply by its reciprocal: 1/2 ÷ 1/6 = 1/2 × 6/1 = 6/2 = 3. (There are three 1/6-sized pieces in one half.)
4. 5 feet cut into 1/4-foot pieces — Answer: 20 pieces
This is a division problem even though it never says "divide": 5 ÷ 1/4 = 5 × 4 = 20 pieces. If your child got #3 but not #4, the gap is recognizing when to divide, not how.
5. Simplify 20 : 15 — Answer: 4 : 3
The GCF of 20 and 15 is 5. Divide both parts by 5: 20 ÷ 5 = 4 and 15 ÷ 5 = 3, giving 4 : 3. (Option A only divided the first number; the parts must be divided by the same factor.)
6. 24 cupcakes in 3 hours, rate for 8 hours — Answer: 64
First find the unit rate: 24 ÷ 3 = 8 cupcakes per hour. Then multiply by the target time: 8 × 8 = 64 cupcakes. (Answer D, 192, comes from doing 24 × 8 and skipping the rate.)
7. 15% of 60 — Answer: 9
15% = 0.15, so 0.15 × 60 = 9. (Or: 10% of 60 is 6, 5% is 3, and 6 + 3 = 9.)
8. x + 7 = 15 — Answer: 8
Subtract 7 from both sides: x = 15 − 7 = 8. Check: 8 + 7 = 15. ✓
9. 2(x + 4) — Answer: 2x + 8
Distribute the 2 to both terms: 2 · x + 2 · 4 = 2x + 8. (Option A forgets to multiply the 4; option C forgets the x.)
10. Solutions to x > 12 from {5, 10, 15, 20} — Answer: 15 and 20
"x > 12" means strictly greater than 12. Of the four values, only 15 and 20 are greater than 12. (5 and 10 are not.)
11. Triangle area, base 12, height 18 — Answer: 108 square inches
Area of a triangle = ½ × base × height = ½ × 12 × 18 = ½ × 216 = 108 square inches.
12. Triangular prism surface area — Answer: 828 cm²
Add the two triangular faces and the three rectangular faces. Two triangles: 2 × (½ × 9 × 12) = 2 × 54 = 108 cm². Three rectangles, each side of the triangle × the length: (9 × 20) + (12 × 20) + (15 × 20) = 180 + 240 + 300 = 720 cm². Total surface area = 108 + 720 = 828 cm². (Option C, 720, forgets the two triangular faces.)
13. Best measure of center — Answer: the median
The data set has an outlier (25 hours) far above the rest. The mean is pulled up to 7.7 hours, but the median is 6 hours, which better matches the typical student who spent 4–8 hours. When data has an outlier, the median is the more representative measure of center.
14. Mean absolute deviation of 5, 5, 10, 10, 15 — Answer: 3.2
Step 1 — mean: (5 + 5 + 10 + 10 + 15) ÷ 5 = 45 ÷ 5 = 9. Step 2 — absolute deviations from 9: |5−9| = 4, |5−9| = 4, |10−9| = 1, |10−9| = 1, |15−9| = 6. Step 3 — average the deviations: (4 + 4 + 1 + 1 + 6) ÷ 5 = 16 ÷ 5 = 3.2.
Where to go next
- See the whole skill map: the free Helix diagnostic shows which Grade 6 skills are secure, shaky, or missing.
- Other grades: Free Grade 5 practice problems and Free Grade 7 practice problems.
- Understand the score itself: What a MAP RIT score means by grade and what MAP scores don't tell you.
- The skill that decides sixth-grade math: fractions are the fault line.
- Is my child on grade level? The honest answer.
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