A backpack has a regular price of $80. It is marked down 35%. What is the sale price?Answer: $52. Source: CMAS Grade 7 Mathematics Frameworks (Colorado Department of Education, 2020), Subclaim A: Major Content, evidence outcome 7.RP.A.3
A car travels 32 miles on each gallon of gas. Which equation gives the miles, m, it travels on g gallons?Answer: m = 32g. Source: CMAS Grade 7 Mathematics Frameworks (Colorado Department of Education, 2020), Subclaim A: Major Content, evidence outcome 7.RP.A.2.c
A music school charges a $45 enrollment fee and $32 for each lesson. Dana has paid $301 in all. How many lessons has she paid for?Answer: 8. Source: CMAS Grade 7 Mathematics Frameworks (Colorado Department of Education, 2020), Subclaim A: Major Content, evidence outcome 7.EE.B.4.a
A plumber charges $65 for a visit plus $48.50 for each hour of work. A job takes 2 1/2 hours. What is the bill?Answer: $186.25. Source: CMAS Grade 7 Mathematics Frameworks (Colorado Department of Education, 2020), Subclaim A: Major Content, evidence outcome 7.EE.B.3
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Major content, continued
A printer works at a steady rate and prints 96 pages in 8 minutes. What is the constant of proportionality, in pages per minute?Answer: 12. Source: CMAS Grade 7 Mathematics Frameworks (Colorado Department of Education, 2020), Subclaim A: Major Content, evidence outcome 7.RP.A.2.b
A savings account holds $800 and earns 3% simple interest each year. How much interest does it earn in 4 years?Answer: $96. Source: CMAS Grade 7 Mathematics Frameworks (Colorado Department of Education, 2020), Subclaim A: Major Content, evidence outcome 7.RP.A.3
A snail crawls 2/3 foot in 1/8 hour. At that rate, how far does it crawl in 1 hour?Answer: 5 1/3 feet. Source: CMAS Grade 7 Mathematics Frameworks (Colorado Department of Education, 2020), Subclaim A: Major Content, evidence outcome 7.RP.A.1
Four tables pair values of x and y. In which table is y ÷ x the same for every pair, so that y is proportional to x?Answer: x: 2, 5, 8 and y: 5, 12.5, 20. Source: CMAS Grade 7 Mathematics Frameworks (Colorado Department of Education, 2020), Subclaim A: Major Content, evidence outcome 7.RP.A.2.a
The graph of a proportional relationship shows gallons of paint, x, and square feet of wall covered, y. The graph passes through the point (1, 350). What does that point mean?Answer: One gallon of paint covers 350 square feet. Source: CMAS Grade 7 Mathematics Frameworks (Colorado Department of Education, 2020), Subclaim A: Major Content, evidence outcome 7.RP.A.2.d
Kai has $60. He buys a game for $24 and wants to buy snacks that cost $4.50 each. What is the greatest number of snacks he can buy?Answer: 8. Source: CMAS Grade 7 Mathematics Frameworks (Colorado Department of Education, 2020), Subclaim A: Major Content, evidence outcome 7.EE.B.4.b
On a number line, a point starts at −3.5 and moves 6 units in the positive direction. Where does it stop?Answer: 2.5. Source: CMAS Grade 7 Mathematics Frameworks (Colorado Department of Education, 2020), Subclaim A: Major Content, evidence outcome 7.NS.A.1.b
The perimeter of a rectangle can be written 2l + 2w or 2(l + w). What does the second form show?Answer: The perimeter is twice the sum of the length and the width. Source: CMAS Grade 7 Mathematics Frameworks (Colorado Department of Education, 2020), Subclaim A: Major Content, evidence outcome 7.EE.A.2
The population of a town grows from 2,500 to 2,800. What is the percent increase?Answer: 12%. Source: CMAS Grade 7 Mathematics Frameworks (Colorado Department of Education, 2020), Subclaim A: Major Content, evidence outcome 7.RP.A.3
The temperature at dawn is −6.5°F. By noon it has risen 4.25 degrees. What is the temperature at noon?Answer: −2.25°F. Source: CMAS Grade 7 Mathematics Frameworks (Colorado Department of Education, 2020), Subclaim A: Major Content, evidence outcome 7.NS.A.3
What is (−2.5)(4)(−0.6)?Answer: 6. Source: CMAS Grade 7 Mathematics Frameworks (Colorado Department of Education, 2020), Subclaim A: Major Content, evidence outcome 7.NS.A.2.c
What is −2/3 + 5/6 − 1/2?Answer: −1/3. Source: CMAS Grade 7 Mathematics Frameworks (Colorado Department of Education, 2020), Subclaim A: Major Content, evidence outcome 7.NS.A.1.d
What value of x makes −6(x − 1.5) = 21 true?Answer: −2. Source: CMAS Grade 7 Mathematics Frameworks (Colorado Department of Education, 2020), Subclaim A: Major Content, evidence outcome 7.EE.B.4.a
Which expression has the same value as −(15/4)?Answer: 15/(−4). Source: CMAS Grade 7 Mathematics Frameworks (Colorado Department of Education, 2020), Subclaim A: Major Content, evidence outcome 7.NS.A.2.b
Which expression is equivalent to (−4)(9 + (−5))?Answer: (−4)(9) + (−4)(−5). Source: CMAS Grade 7 Mathematics Frameworks (Colorado Department of Education, 2020), Subclaim A: Major Content, evidence outcome 7.NS.A.2.a
Which expression is equivalent to −7 − (−12)?Answer: −7 + 12. Source: CMAS Grade 7 Mathematics Frameworks (Colorado Department of Education, 2020), Subclaim A: Major Content, evidence outcome 7.NS.A.1.c
Which factored expression is equivalent to 28x − 21?Answer: 7(4x − 3). Source: CMAS Grade 7 Mathematics Frameworks (Colorado Department of Education, 2020), Subclaim A: Major Content, evidence outcome 7.EE.A.1
Which fraction becomes a repeating decimal?Answer: 7/15. Source: CMAS Grade 7 Mathematics Frameworks (Colorado Department of Education, 2020), Subclaim A: Major Content, evidence outcome 7.NS.A.2.d
Which situation shows two opposite quantities that combine to make 0?Answer: A hiker climbs 250 feet and then descends 250 feet. Source: CMAS Grade 7 Mathematics Frameworks (Colorado Department of Education, 2020), Subclaim A: Major Content, evidence outcome 7.NS.A.1.a
Supporting content 8
A coin is tossed, and a spinner with 4 equal sections colored red, blue, green and yellow is spun. What is the probability of heads together with red or blue?Answer: 1/4. Source: CMAS Grade 7 Mathematics Frameworks (Colorado Department of Education, 2020), Subclaim B: Supporting Content, evidence outcome 7.SP.C.8
A plane cuts a right rectangular pyramid straight down through its top vertex, perpendicular to the base. What shape is the cut face?Answer: A triangle. Source: CMAS Grade 7 Mathematics Frameworks (Colorado Department of Education, 2020), Subclaim B: Supporting Content, evidence outcome 7.G.A.3
A round pond has a diameter of 50 meters. What is its circumference? Use 3.14 for π.Answer: 157 meters. Source: CMAS Grade 7 Mathematics Frameworks (Colorado Department of Education, 2020), Subclaim B: Supporting Content, evidence outcome 7.G.B.4
A spinner lands on yellow 34 times in 80 spins. Based on these results, about how many times should it land on yellow in 200 spins?Answer: 85. Source: CMAS Grade 7 Mathematics Frameworks (Colorado Department of Education, 2020), Subclaim B: Supporting Content, evidence outcome 7.SP.C.6
A student has straws of several lengths. Which three straws cannot be joined end to end to make a triangle?Answer: 3 cm, 6 cm and 10 cm. Source: CMAS Grade 7 Mathematics Frameworks (Colorado Department of Education, 2020), Subclaim B: Supporting Content, evidence outcome 7.G.A.2
A town wants to learn which park its residents use most. Which sample is most likely to represent the whole town?Answer: Every 10th name on a list of all residents. Source: CMAS Grade 7 Mathematics Frameworks (Colorado Department of Education, 2020), Subclaim B: Supporting Content, evidence outcome 7.SP.A.1
On a map, 1 inch stands for 40 miles. Two towns are 3 1/2 inches apart on the map. How far apart are the towns?Answer: 140 miles. Source: CMAS Grade 7 Mathematics Frameworks (Colorado Department of Education, 2020), Subclaim B: Supporting Content, evidence outcome 7.G.A.1
Random samples of two classes time their walk to school. The mean is 14 minutes for one class and 20 minutes for the other, and the mean absolute deviation of each is 2 minutes. The difference between the means is how many times the mean absolute deviation?Answer: 3 times. Source: CMAS Grade 7 Mathematics Frameworks (Colorado Department of Education, 2020), Subclaim B: Supporting Content, evidence outcome 7.SP.B.3
Reasoning 10
A $50 item is marked up 20%, and then the new price is marked down 20%. Zoe says the final price is $50. What is the final price?Answer: $48, because the 20% markdown is taken from $60. Source: CMAS Grade 7 Mathematics Frameworks (Colorado Department of Education, 2020), Subclaim C: Expressing Mathematical Reasoning, content scope 7.RP.3
A graph is a straight line through (0, 2) and (1, 5). Ben says it shows a proportional relationship because it is straight. Is he right?Answer: No. The line does not pass through the origin. Source: CMAS Grade 7 Mathematics Frameworks (Colorado Department of Education, 2020), Subclaim C: Expressing Mathematical Reasoning, content scope 7.RP.A
Ana says: "If y is proportional to x, then doubling x always doubles y." Which reasoning supports her?Answer: y = kx, so when x becomes 2x, y becomes k(2x) = 2(kx). Source: CMAS Grade 7 Mathematics Frameworks (Colorado Department of Education, 2020), Subclaim C: Expressing Mathematical Reasoning, content scope 7.RP.2
Cal writes 1/3 = 0.3. What is the mistake?Answer: 1/3 is 0.333..., with the 3 repeating forever, and 0.3 is only 3/10. Source: CMAS Grade 7 Mathematics Frameworks (Colorado Department of Education, 2020), Subclaim C: Expressing Mathematical Reasoning, content scope 7.NS.2d
Li rewrites −3(2x − 5) as −6x − 15. What is the error?Answer: −3 times −5 is +15, so the expression is −6x + 15. Source: CMAS Grade 7 Mathematics Frameworks (Colorado Department of Education, 2020), Subclaim C: Expressing Mathematical Reasoning, content scope 7.EE.1
Mo says the distance between −4.5 and 2 on a number line is 2.5, because 4.5 − 2 = 2.5. Which statement is correct?Answer: The distance is 6.5, the absolute value of 2 − (−4.5). Source: CMAS Grade 7 Mathematics Frameworks (Colorado Department of Education, 2020), Subclaim C: Expressing Mathematical Reasoning, content scope 7.NS.A
Pat says 4 + 3x is equivalent to 7x. Which test shows that he is wrong?Answer: When x = 2, 4 + 3x is 10 and 7x is 14. Source: CMAS Grade 7 Mathematics Frameworks (Colorado Department of Education, 2020), Subclaim C: Expressing Mathematical Reasoning, content scope 6.EE.A
Which addition shows that 4 − (−9) = 13 is correct?Answer: 13 + (−9) = 4. Source: CMAS Grade 7 Mathematics Frameworks (Colorado Department of Education, 2020), Subclaim C: Expressing Mathematical Reasoning, content scope 7.NS.1
Which argument explains why (−1)(−1) = 1?Answer: (−1)(1) + (−1)(−1) must equal (−1)(0) = 0, and (−1)(1) = −1, so (−1)(−1) is 1. Source: CMAS Grade 7 Mathematics Frameworks (Colorado Department of Education, 2020), Subclaim C: Expressing Mathematical Reasoning, content scope 7.NS.2
Which steps form a correct argument that solves 5x − 8 = 27?Answer: Add 8 to both sides to get 5x = 35. Divide both sides by 5 to get x = 7. Source: CMAS Grade 7 Mathematics Frameworks (Colorado Department of Education, 2020), Subclaim C: Expressing Mathematical Reasoning, content scope 7.EE.4a
Modeling 9
A bike has a regular price of $240. It is on sale for 15% off, and a sales tax of 5% is added to the sale price. What is the total cost?Answer: $214.20. Source: CMAS Grade 7 Mathematics Frameworks (Colorado Department of Education, 2020), Subclaim D: Modeling and Application, content scope 7.RP.3
A garden bed is a right triangle with legs of 9 feet and 12 feet. Soil for the bed costs $2.50 for each square foot. What does the soil cost?Answer: $135. Source: CMAS Grade 7 Mathematics Frameworks (Colorado Department of Education, 2020), Subclaim D: Modeling and Application, content scope 6.G
A hiker starts on a canyon floor at an elevation of −120 feet. She climbs 45 feet each hour for 6 hours and then descends 80 feet. What is her elevation at the end?Answer: 70 feet. Source: CMAS Grade 7 Mathematics Frameworks (Colorado Department of Education, 2020), Subclaim D: Modeling and Application, content scope 7.NS.3, 7.EE.3
A phone plan costs $25 a month plus $0.08 for each text message. One month the bill is $34.60. How many text messages were sent?Answer: 120. Source: CMAS Grade 7 Mathematics Frameworks (Colorado Department of Education, 2020), Subclaim D: Modeling and Application, content scope 7.EE.4a
A pump fills 3/4 of a tank in 1/2 hour. At that rate, how long does it take to fill 2 tanks of that size?Answer: 1 hour 20 minutes. Source: CMAS Grade 7 Mathematics Frameworks (Colorado Department of Education, 2020), Subclaim D: Modeling and Application, content scope 7.RP.1
A salesperson earns $400 a week plus a 6% commission on sales. How much must she sell in a week to earn at least $700?Answer: At least $5,000. Source: CMAS Grade 7 Mathematics Frameworks (Colorado Department of Education, 2020), Subclaim D: Modeling and Application, content scope 7.RP.3, 7.EE.4b
A seedling is 3.2 centimeters tall 4 weeks after it sprouts. If it keeps growing at about the same rate, about how tall will it be 10 weeks after it sprouts?Answer: 8 centimeters. Source: CMAS Grade 7 Mathematics Frameworks (Colorado Department of Education, 2020), Subclaim D: Modeling and Application, content scope 7.RP.2
A student takes about 2,000 steps to walk to school, and each step is about 2.5 feet long. A mile is 5,280 feet. About how long is the walk?Answer: A little less than 1 mile. Source: CMAS Grade 7 Mathematics Frameworks (Colorado Department of Education, 2020), Subclaim D: Modeling and Application, content scope 7.EE.3; unit size: NIST Handbook 44 (2026), Appendix C
A van can carry at most 1,200 pounds. The driver weighs 180 pounds, and each box weighs 42.5 pounds. What is the greatest number of boxes the van can carry with the driver?Answer: 24. Source: CMAS Grade 7 Mathematics Frameworks (Colorado Department of Education, 2020), Subclaim D: Modeling and Application, content scope 7.EE.4b
How this list was compiled: Outline and standards: CMAS Grade 7 Mathematics Frameworks (Colorado Department of Education, 2020), https://ed.cde.state.co.us/fs/resource-manager/view/2c933bb9-6322-4bac-b130-3e577e2ccf53, and CMAS Grade 7 Mathematics Evidence Statements, https://ed.cde.state.co.us/fs/resource-manager/view/79b5c09e-a9e0-480d-9378-45dcea5a1fec, both linked from CMAS Test Design, https://ed.cde.state.co.us/assessment/cmas-testdesign. The framework lists the evidence outcomes of the Colorado Academic Standards that the test may ask, the score points of each reporting category and the split between calculator and non-calculator points; the evidence statements say which outcomes are calculator items. Calculator rule: Calculator Policy for Calculator Units and Sections of CMAS Mathematics Assessments, https://ed.cde.state.co.us/fs/resource-manager/view/a0c6675f-d4e5-4752-a9b2-3c9dc7e719a4. The length of a mile in one question: NIST Handbook 44 (2026), Appendix C, General Tables of Units of Measurement, https://www.nist.gov/document/2026-nist-handbook-44-appendix-c. All read 2026-10-13. Each question names the reporting category and the outcome it practices. Every numeric answer is arithmetic on the numbers in the question, worked a second time. Licence: Own work. Questions, answer choices and explanations were written for this site. Nothing is copied or reworded from a CMAS test, a released or sample item, a Colorado Practice Resource, an example in the standards or evidence statements, or another practice test.
How it works
Unofficial 7th grade math practice test for CMAS, the Colorado Measures of Academic Success: 50 questions of our own, built on the state's grade 7 framework. No question comes from the state. Not affiliated with the Colorado Department of Education.
Read the full guide
What 7th grade CMAS math covers
Colorado's framework for grade 7 has 50 to 51 score points, and this set has a question for each of 50. Major content is 23 of them: unit rates, proportional relationships, percent problems, adding and multiplying negative numbers, equivalent expressions, and two-step equations and inequalities. Supporting content is 8: random samples, probability, scale drawings, triangles, cross sections and circles. Ten reasoning questions ask for the argument behind an answer or the error in one. Nine modeling questions are real-world problems of several steps.
Colorado marks unit rates, multistep percent problems, geometry and statistics as calculator items. Signed-number arithmetic and solving equations are tested without one.
Questions and answers
Can 7th graders use a calculator on CMAS math?
On part of it. A five-function calculator, with square root and percent keys, is allowed on the calculator sections, which carry 76% of the points. The other 12 points are earned without a calculator.
What is a good CMAS math score in 7th grade?
For grade 7 math, Met Expectations is a scale score of 750 to 785 and Exceeded Expectations is 786 to 850, on a scale that starts at 650. Colorado treats those two levels as on track for college and career.
Which CMAS tests do 7th graders take?
Math, English language arts and social studies. Grade 7 is the grade that takes the CMAS social studies assessment. Science is given in grades 5, 8 and 11. Only math is practiced here.
Where are the official CMAS practice tests for 7th grade?
The Colorado Department of Education links its own CMAS Practice Resources from its CMAS page, and the box under the questions has the link. This page is unofficial and uses no state question.