Sixth grade math for Colorado's CMAS: ratios and rates, negative numbers, expressions and equations, plus reasoning and modeling.
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Unofficial practice questions, not affiliated with the Colorado Department of Education. Bank checked October 13, 2026.
The real test: CMAS math, grade 6
Who takes it
Students enrolled in grade 6. CMAS math is given in grades 3 to 8.
Score points
50 to 51: major content 20, supporting content 11, reasoning 10 to 11, modeling 9.
Shares
Major content 39 to 40% of the points, supporting content 22%, reasoning 20 to 22%, modeling 18%.
Calculator
A five-function calculator, with square root and percent keys, on calculator sections, which carry 36 to 37 of the points. None on the other sections.
Reasoning and modeling
Reasoning tasks rest on the standards for constructing arguments and attending to precision; modeling tasks on modeling with mathematics. Both may draw on secur
Scores
Scale scores from 650 to 850 in five levels. In grade 6 math, Met Expectations is 750 to 787 and Exceeded Expectations is 788 to 850.
27 is 45% of what number?CMAS Grade 6 Mathematics Frameworks (Colorado Department of Education, 2020), Subclaim A: Major Content, evidence outcome 6.RP.A.3.c
A box holds 12 pencils and 20 pens. What is the ratio of pens to all the items in the box?CMAS Grade 6 Mathematics Frameworks (Colorado Department of Education, 2020), Subclaim A: Major Content, evidence outcome 6.RP.A.1
A diver is 35 feet below sea level. A bird is 20 feet above sea level. Sea level is 0. Which pair of numbers shows the two positions?CMAS Grade 6 Mathematics Frameworks (Colorado Department of Education, 2020), Subclaim A: Major Content, evidence outcome 6.NS.C.5
A dry lake bed has an elevation of −85 feet, which is below sea level. What does |−85| = 85 describe?CMAS Grade 6 Mathematics Frameworks (Colorado Department of Education, 2020), Subclaim A: Major Content, evidence outcome 6.NS.C.7.c
A recipe needs 2.5 pounds of apples. One pound is 16 ounces. How many ounces of apples does the recipe need?CMAS Grade 6 Mathematics Frameworks (Colorado Department of Education, 2020), Subclaim A: Major Content, evidence outcome 6.RP.A.3.d
Show all 40 questions (35 more)
Major content, continued
A shuttle bus may carry at most 40 riders. Which inequality shows the numbers of riders r that are allowed?CMAS Grade 6 Mathematics Frameworks (Colorado Department of Education, 2020), Subclaim A: Major Content, evidence outcome 6.EE.B.8
A table of equivalent ratios pairs 2 cups of flour with 3 cups of milk and 6 cups of flour with 9 cups of milk. How many cups of milk go with 10 cups of flour?CMAS Grade 6 Mathematics Frameworks (Colorado Department of Education, 2020), Subclaim A: Major Content, evidence outcome 6.RP.A.3.a
The point (−8, 3) is reflected across the x-axis. What are the coordinates of the new point?CMAS Grade 6 Mathematics Frameworks (Colorado Department of Education, 2020), Subclaim A: Major Content, evidence outcome 6.NS.C.6.b
Six oranges cost $4.50. What is the price for each orange?CMAS Grade 6 Mathematics Frameworks (Colorado Department of Education, 2020), Subclaim A: Major Content, evidence outcome 6.RP.A.2
What is 4/5 ÷ 3/10?CMAS Grade 6 Mathematics Frameworks (Colorado Department of Education, 2020), Subclaim A: Major Content, evidence outcome 6.NS.A.1
What is the distance between the points (4, −8) and (4, 3)?CMAS Grade 6 Mathematics Frameworks (Colorado Department of Education, 2020), Subclaim A: Major Content, evidence outcome 6.NS.C.8
What is the value of 6² − 3³ + 1?CMAS Grade 6 Mathematics Frameworks (Colorado Department of Education, 2020), Subclaim A: Major Content, evidence outcome 6.EE.A.1
What number is the opposite of the opposite of −23?CMAS Grade 6 Mathematics Frameworks (Colorado Department of Education, 2020), Subclaim A: Major Content, evidence outcome 6.NS.C.6.a
What value of x makes x + 3.8 = 12.5 true?CMAS Grade 6 Mathematics Frameworks (Colorado Department of Education, 2020), Subclaim A: Major Content, evidence outcome 6.EE.B.7
Which expression is equivalent to 24x + 18?CMAS Grade 6 Mathematics Frameworks (Colorado Department of Education, 2020), Subclaim A: Major Content, evidence outcome 6.EE.A.3
Which expression means "the quotient of a number n and 5, increased by 8"?CMAS Grade 6 Mathematics Frameworks (Colorado Department of Education, 2020), Subclaim A: Major Content, evidence outcome 6.EE.A.2.a
Supporting content 9
A data set is 4, 6, 7, 9, 10, 12, 15, 17. What is its interquartile range?CMAS Grade 6 Mathematics Frameworks (Colorado Department of Education, 2020), Subclaim B: Supporting Content, evidence outcome 6.SP.B.5.c
A trapezoid has parallel sides of 8 meters and 14 meters. The distance between them is 5 meters. What is its area?CMAS Grade 6 Mathematics Frameworks (Colorado Department of Education, 2020), Subclaim B: Supporting Content, evidence outcome 6.G.A.1
The net of a cube is made of 6 squares. Each square has sides of 5 centimeters. What is the surface area of the cube?CMAS Grade 6 Mathematics Frameworks (Colorado Department of Education, 2020), Subclaim B: Supporting Content, evidence outcome 6.G.A.4
Nine houses on a street sold for between $300,000 and $350,000. A tenth house sold for $2,000,000. Which measure best describes the price of a typical house on the street?CMAS Grade 6 Mathematics Frameworks (Colorado Department of Education, 2020), Subclaim B: Supporting Content, evidence outcome 6.SP.B.5.d
Seven students read 2, 9, 4, 4, 11, 6 and 3 books. What is the median number of books?CMAS Grade 6 Mathematics Frameworks (Colorado Department of Education, 2020), Subclaim B: Supporting Content, evidence outcome 6.SP.B.5.c
What is 4.06 × 3.5?CMAS Grade 6 Mathematics Frameworks (Colorado Department of Education, 2020), Subclaim B: Supporting Content, evidence outcome 6.NS.B.3
What is 7,616 ÷ 28?CMAS Grade 6 Mathematics Frameworks (Colorado Department of Education, 2020), Subclaim B: Supporting Content, evidence outcome 6.NS.B.2
Which expression writes 54 + 90 as a common factor times a sum of two whole numbers that have no common factor?CMAS Grade 6 Mathematics Frameworks (Colorado Department of Education, 2020), Subclaim B: Supporting Content, evidence outcome 6.NS.B.4
Which question is a statistical question, one whose answers are expected to vary?CMAS Grade 6 Mathematics Frameworks (Colorado Department of Education, 2020), Subclaim B: Supporting Content, evidence outcome 6.SP.A.1
Reasoning 8
A store sells 3 pens for $2.40. Lee says 5 pens cost $4.40, because 2 more pens cost 2 more dollars. Which is correct?CMAS Grade 6 Mathematics Frameworks (Colorado Department of Education, 2020), Subclaim C: Expressing Mathematical Reasoning, on the content of 6.RP.A
A student must solve 4x = 3. Which is a correct argument that ends with the solution?CMAS Grade 6 Mathematics Frameworks (Colorado Department of Education, 2020), Subclaim C: Expressing Mathematical Reasoning, on the content of 6.EE.B
A student says 0.4 × 0.2 = 0.8, because 4 × 2 = 8. What is wrong with this reasoning?CMAS Grade 6 Mathematics Frameworks (Colorado Department of Education, 2020), Subclaim C: Expressing Mathematical Reasoning, on the content of 5.NBT
Ari says 5(2x + 3) is equivalent to 10x + 3. What is his error?CMAS Grade 6 Mathematics Frameworks (Colorado Department of Education, 2020), Subclaim C: Expressing Mathematical Reasoning, on the content of 6.EE.3
Jo puts x = 0 into 2(x + 5) and gets 10. She puts x = 0 into 2x + 5 and gets 5. What can she conclude?CMAS Grade 6 Mathematics Frameworks (Colorado Department of Education, 2020), Subclaim C: Expressing Mathematical Reasoning, on the content of 6.EE.4
On a horizontal number line, point P is at −2.5. Point Q is to the left of P. Which could be the value of Q, and why?CMAS Grade 6 Mathematics Frameworks (Colorado Department of Education, 2020), Subclaim C: Expressing Mathematical Reasoning, on the content of 6.NS.7
Sam plots (3, −2) and (−3, −2). He says the points are 0 units apart because 3 and −3 are opposites. Which reasoning is correct?CMAS Grade 6 Mathematics Frameworks (Colorado Department of Education, 2020), Subclaim C: Expressing Mathematical Reasoning, on the content of 6.NS.8
Which multiplication equation shows that 2/3 ÷ 1/6 = 4 is correct?CMAS Grade 6 Mathematics Frameworks (Colorado Department of Education, 2020), Subclaim C: Expressing Mathematical Reasoning, on the content of 6.NS.1
Modeling 7
A cyclist rides at a constant speed, and the distance d, in miles, after t hours is d = 14t. How long does it take to ride 49 miles?CMAS Grade 6 Mathematics Frameworks (Colorado Department of Education, 2020), Subclaim D: Modeling and Application, on the content of 6.EE.C.9
A fish tank is 30 inches long, 12 inches wide and 15 inches tall. It is filled with water to 2/3 of its height. How many cubic inches of water are in the tank?CMAS Grade 6 Mathematics Frameworks (Colorado Department of Education, 2020), Subclaim D: Modeling and Application, on the content of 5.MD
A machine fills 45 bottles in 6 minutes. At that rate, how many bottles does it fill in 1 hour?CMAS Grade 6 Mathematics Frameworks (Colorado Department of Education, 2020), Subclaim D: Modeling and Application, on the content of 6.RP.A.3.b
A ribbon 5 1/4 yards long is cut into pieces that are each 7/8 yard long. How many pieces are there?CMAS Grade 6 Mathematics Frameworks (Colorado Department of Education, 2020), Subclaim D: Modeling and Application, on the content of 6.NS.A.1
A school has 28 classrooms with about 24 students in each. Each student gets 2 pencils. Which is the best estimate of the number of pencils needed?CMAS Grade 6 Mathematics Frameworks (Colorado Department of Education, 2020), Subclaim D: Modeling and Application, on the content of 6.RP.A
A team won 12 of its 16 games and lost the rest. What percent of its games did the team lose?CMAS Grade 6 Mathematics Frameworks (Colorado Department of Education, 2020), Subclaim D: Modeling and Application, on the content of 6.RP.A.3.c
Maya has $85. She buys 3 tickets that each cost the same amount and has $31 left. What is the price of one ticket?CMAS Grade 6 Mathematics Frameworks (Colorado Department of Education, 2020), Subclaim D: Modeling and Application, on the content of 6.EE.B.7
How this list was compiled: Outline and standards: CMAS Grade 6 Mathematics Frameworks (Colorado Department of Education, 2020), https://ed.cde.state.co.us/fs/resource-manager/view/1e9874d2-b848-420b-9950-c7b17d41a2f9, linked from the department's page CMAS Test Design, https://ed.cde.state.co.us/assessment/cmas-testdesign, read 2026-10-13. The framework lists the evidence outcomes of the Colorado Academic Standards that the grade 6 test may ask, the content scope of its reasoning and modeling tasks and the score points of each reporting category; each question names the outcome or content scope 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 item or practice resource of the department, or another practice test. No released item was read.
How it works
Unofficial practice for the sixth grade CMAS math test, the Colorado Measures of Academic Success: 40 questions written for this site from the state's framework. None is a released item. Not affiliated with the Colorado Department of Education.
Read the full guide
What 6th grade CMAS math covers
Colorado's framework splits the grade 6 score points among four reporting categories, and the 40 questions follow it. Major content has 16: ratios, unit rates and percents, dividing fractions, negative numbers and the coordinate plane, expressions, equations and inequalities. Supporting content has 9: long division, decimals, common factors, statistics, area and nets. Reasoning has 8, each asking which argument holds or where a worked answer goes wrong. Modeling has 7 multistep problems.
Reasoning and modeling reach back a grade
The framework lets these tasks use securely held grade 5 content, so one reasoning question here is on multiplying decimals and one modeling question is on volume.
About a quarter of the grade 6 score points are in sections with no calculator, so work some questions by hand.
Questions and answers
What is on the 6th grade CMAS math test?
50 to 51 score points in four reporting categories: major content 20 points, supporting content 11, expressing mathematical reasoning 10 to 11, and modeling and application 9. The framework lists the Colorado evidence outcomes that may be asked.
Can 6th graders use a calculator on CMAS math?
On calculator sections, yes: a five-function calculator, which has square root and percent keys. Those sections carry 36 to 37 of the score points. Graphing calculators and phone or tablet calculators are not allowed.
What is a good CMAS math score in 6th grade?
Scale scores run from 650 to 850. In grade 6 math, Met Expectations is 750 to 787 and Exceeded Expectations is 788 to 850. The state counts students at those two levels as on track for college and career.
Where are the official CMAS practice tests?
The Colorado Department of Education calls its CMAS Practice Resources the only state-sanctioned ones. They use released CMAS content and are linked from the box under the questions. This page is separate and unofficial.