Smarter Balanced Math Practice Test

Pick a grade band and practice the three claim areas of the Smarter Balanced math blueprint, every answer worked out.

What is 63 ÷ 7?

Pick an answer, then press Check answer. Then you see Correct or Not quite, with the reason. Keys: A to D pick, Enter checks.

Print covers the next 25 questions. Share this set copies a link to the same questions in the same order.

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Unofficial practice questions, not affiliated with the Smarter Balanced Assessment Consortium. Bank checked October 7, 2026.

The real test: Smarter Balanced mathematics

Parts
A computer adaptive test and one performance task of 4 to 6 items.
Items by claim
Concepts and Procedures: 17 to 20 in grades 3 to 5, 16 to 20 in grades 6 to 8, 19 to 22 in grade 11. The other claims: 18 to 20 together.
Claim scores
Four claims, three scores: Problem Solving is reported together with Modeling and Data Analysis.
Calculator
None in grades 3 to 5. From grade 6, one section has an on-screen calculator: four-function in grade 6, scientific for grades 7 and 8, graphing in high school.
Time
Untimed. Estimates: 2 hours 30 minutes in grades 3 to 5, 3 hours in grades 6 to 8, 3 hours 30 minutes in grade 11.
Level 3 begins at
2436, 2485, 2528, 2552, 2567 and 2586 in grades 3 to 8, and 2628 in grade 11, on a scale from about 2000 to 3000.

Checked October 7, 2026 against the Smarter Balanced Assessment Consortium's mathematics blueprint, calculator rules, estimated testing times and score levels. Rules change, so confirm with the agency itself before your test.

The consortium's own practice and training tests

Next step Math and reading for your grade bandMore math by grade, grades 3 to 8

Grades 3 to 5: all 48 questions

Grade 3 16

  • 24 students are going on a trip. Each van holds 5 students. How many vans are needed so that every student gets a ride? Smarter Balanced Mathematics Summative Assessment Blueprint, grade 3, Claim 4 (Modeling and Data Analysis), target D: interpret results in the context of a situation
  • A baker has 54 rolls. Each tray holds 6 rolls. How many trays can the baker fill? Smarter Balanced Mathematics Summative Assessment Blueprint, grade 3, Claim 1 (Concepts and Procedures), target A: represent and solve problems involving multiplication and division
  • A class of 28 students sits at tables of 4. Which equation can be used to find t, the number of tables? Smarter Balanced Mathematics Summative Assessment Blueprint, grade 3, Claim 2 (Problem Solving), target D: identify important quantities in a practical situation and map their relationships
Show all 48 questions (45 more)

Grade 3, continued

  • A movie starts at 2:45 and ends at 4:10. How long is the movie? Smarter Balanced Mathematics Summative Assessment Blueprint, grade 3, Claim 1 (Concepts and Procedures), target G: solve problems involving measurement and estimation of intervals of time, liquid volumes, and masses of objects
  • A number line from 0 to 1 is cut into 8 equal parts. Which fraction names the point at the end of the third part? Smarter Balanced Mathematics Summative Assessment Blueprint, grade 3, Claim 1 (Concepts and Procedures), target F: develop understanding of fractions as numbers
  • A rectangle has a perimeter of 30 inches. Its length is 9 inches. What is its width? Smarter Balanced Mathematics Summative Assessment Blueprint, grade 3, Claim 1 (Concepts and Procedures), target J: geometric measurement: recognize perimeter as an attribute of plane figures and distinguish between linear and area measures
  • A rectangle is split into 6 equal squares. Two of the squares are shaded. What fraction of the rectangle is shaded? Smarter Balanced Mathematics Summative Assessment Blueprint, grade 3, Claim 3 (Communicating Reasoning), target F: base arguments on concrete referents such as objects, drawings, diagrams, and actions
  • A rug is 7 feet long and 4 feet wide. What is the area of the rug? Smarter Balanced Mathematics Summative Assessment Blueprint, grade 3, Claim 1 (Concepts and Procedures), target I: geometric measurement: understand concepts of area and relate area to multiplication and to addition
  • Ana knows that 6 × 8 = 48. How can she use that fact to find 12 × 8? Smarter Balanced Mathematics Summative Assessment Blueprint, grade 3, Claim 3 (Communicating Reasoning), target B: construct, autonomously, chains of reasoning that will justify or refute propositions or conjectures
  • Ben says 1/4 is greater than 1/3 because 4 is greater than 3. What is wrong with his thinking? Smarter Balanced Mathematics Summative Assessment Blueprint, grade 3, Claim 3 (Communicating Reasoning), target E: distinguish correct logic or reasoning from that which is flawed
  • In a picture graph, one star stands for 5 books. Leo has 6 stars and Ava has 4 stars. How many more books did Leo read than Ava? Smarter Balanced Mathematics Summative Assessment Blueprint, grade 3, Claim 4 (Modeling and Data Analysis), target F: identify important quantities in a practical situation and map their relationships
  • Mia buys 4 packs of stickers with 8 stickers in each pack. She gives 5 stickers to her brother. How many stickers does she have left? Smarter Balanced Mathematics Summative Assessment Blueprint, grade 3, Claim 2 (Problem Solving), target A: apply mathematics to solve well-posed problems arising in everyday life, society, and the workplace
  • Tia says the product of two odd numbers is always even. Which example shows that Tia is wrong? Smarter Balanced Mathematics Summative Assessment Blueprint, grade 3, Claim 3 (Communicating Reasoning), target A: test propositions or conjectures with specific examples
  • What is 63 ÷ 7? Smarter Balanced Mathematics Summative Assessment Blueprint, grade 3, Claim 1 (Concepts and Procedures), target C: multiply and divide within 100
  • What is 468 rounded to the nearest ten? Smarter Balanced Mathematics Summative Assessment Blueprint, grade 3, Claim 1 (Concepts and Procedures), target E: use place value understanding and properties of operations to perform multi-digit arithmetic
  • Which expression is equal to 7 × 6? Smarter Balanced Mathematics Summative Assessment Blueprint, grade 3, Claim 1 (Concepts and Procedures), target B: understand properties of multiplication and the relationship between multiplication and division

Grade 4 16

  • A bar graph shows books read: Room A 45, Room B 60, Room C 35, Room D 60. How many more books did Rooms B and D read together than Rooms A and C together? Smarter Balanced Mathematics Summative Assessment Blueprint, grade 4, Claim 4 (Modeling and Data Analysis), target F: identify important quantities in a practical situation and map their relationships
  • A ribbon 50 inches long is cut into pieces that are each 8 inches long. How many full pieces are cut, and how much ribbon is left? Smarter Balanced Mathematics Summative Assessment Blueprint, grade 4, Claim 2 (Problem Solving), target C: interpret results in the context of a situation
  • A school orders 6 boxes of markers. Each box holds 144 markers. How many markers is that in all? Smarter Balanced Mathematics Summative Assessment Blueprint, grade 4, Claim 1 (Concepts and Procedures), target A: use the four operations with whole numbers to solve problems
  • A square has sides of 4 units. A rectangle is 6 units long and 2 units wide. Both have a perimeter of 16 units. Which statement is true? Smarter Balanced Mathematics Summative Assessment Blueprint, grade 4, Claim 3 (Communicating Reasoning), target D: use the technique of breaking an argument into cases
  • A theater has 18 rows with 24 seats in each row. 395 tickets are sold. How many seats are empty? Smarter Balanced Mathematics Summative Assessment Blueprint, grade 4, Claim 2 (Problem Solving), target A: apply mathematics to solve well-posed problems arising in everyday life, society, and the workplace
  • An angle turns through 1/4 of a full circle. What is its measure? Smarter Balanced Mathematics Summative Assessment Blueprint, grade 4, Claim 1 (Concepts and Procedures), target K: geometric measurement: understand concepts of angle and measure angles
  • Four friends each ate part of a sandwich of the same size. Who ate less than half of a sandwich? Smarter Balanced Mathematics Summative Assessment Blueprint, grade 4, Claim 1 (Concepts and Procedures), target F: extend understanding of fraction equivalence and ordering
  • Lee says every multiple of 4 is also a multiple of 8. Which number shows that Lee is wrong? Smarter Balanced Mathematics Summative Assessment Blueprint, grade 4, Claim 3 (Communicating Reasoning), target A: test propositions or conjectures with specific examples
  • Omar says 3/6 and 4/8 are equal. Which reason supports him? Smarter Balanced Mathematics Summative Assessment Blueprint, grade 4, Claim 3 (Communicating Reasoning), target B: construct, autonomously, chains of reasoning that will justify or refute propositions or conjectures
  • One batch of granola uses 3/4 cup of oats. How many batches use exactly 3 cups of oats? Smarter Balanced Mathematics Summative Assessment Blueprint, grade 4, Claim 4 (Modeling and Data Analysis), target A: apply mathematics to solve problems arising in everyday life, society, and the workplace
  • Rosa says 0.5 is less than 0.45 because 5 is less than 45. What is her mistake? Smarter Balanced Mathematics Summative Assessment Blueprint, grade 4, Claim 3 (Communicating Reasoning), target E: distinguish correct logic or reasoning from that which is flawed
  • What is 7/10 − 4/10? Smarter Balanced Mathematics Summative Assessment Blueprint, grade 4, Claim 1 (Concepts and Procedures), target G: build fractions from unit fractions by applying and extending previous understandings of operations on whole numbers
  • What is 3,005 − 1,278? Smarter Balanced Mathematics Summative Assessment Blueprint, grade 4, Claim 1 (Concepts and Procedures), target E: use place value understanding and properties of operations to perform multi-digit arithmetic
  • What is the value of the digit 7 in 472,916? Smarter Balanced Mathematics Summative Assessment Blueprint, grade 4, Claim 1 (Concepts and Procedures), target D: generalize place value understanding for multi-digit whole numbers
  • Which fraction names the same amount as 3/7? Smarter Balanced Mathematics Summative Assessment Blueprint, grade 4, Claim 1 (Concepts and Procedures), target F: extend understanding of fraction equivalence and ordering
  • Which number is both a multiple of 6 and a factor of 36? Smarter Balanced Mathematics Summative Assessment Blueprint, grade 4, Claim 1 (Concepts and Procedures), target B: gain familiarity with factors and multiples

Grade 5 16

  • A 3-pound bag of rice is shared equally among 4 families. How much rice does each family get? Smarter Balanced Mathematics Summative Assessment Blueprint, grade 5, Claim 1 (Concepts and Procedures), target F: apply and extend previous understandings of multiplication and division to multiply and divide fractions
  • A fish tank is 20 inches long, 10 inches wide and 12 inches tall. Water fills it to 2 inches below the top. How many cubic inches of water are in the tank? Smarter Balanced Mathematics Summative Assessment Blueprint, grade 5, Claim 4 (Modeling and Data Analysis), target D: interpret results in the context of a situation
  • A line plot shows six ribbon lengths in feet: 1/2, 1/2, 3/4, 3/4, 3/4 and 1 1/4. What is the total length of the ribbons? Smarter Balanced Mathematics Summative Assessment Blueprint, grade 5, Claim 4 (Modeling and Data Analysis), target F: identify important quantities in a practical situation and map their relationships
  • A storage bin is 8 inches long, 3 inches wide and 7 inches tall. What is its volume? Smarter Balanced Mathematics Summative Assessment Blueprint, grade 5, Claim 1 (Concepts and Procedures), target I: geometric measurement: understand concepts of volume and relate volume to multiplication and to addition
  • Eli says multiplying a number by a fraction always makes it smaller. Which example shows that he is wrong? Smarter Balanced Mathematics Summative Assessment Blueprint, grade 5, Claim 3 (Communicating Reasoning), target A: test propositions or conjectures with specific examples
  • Every square has four right angles and four equal sides. A rectangle is any four-sided shape with four right angles. Which statement must be true? Smarter Balanced Mathematics Summative Assessment Blueprint, grade 5, Claim 3 (Communicating Reasoning), target B: construct, autonomously, chains of reasoning that will justify or refute propositions or conjectures
  • Juice costs $2.75 a bottle. Which expression gives the change from $20 after buying 6 bottles? Smarter Balanced Mathematics Summative Assessment Blueprint, grade 5, Claim 2 (Problem Solving), target D: identify important quantities in a practical situation and map their relationships
  • Nora runs 1 3/4 miles on Monday and 2 1/2 miles on Wednesday. How many miles does she run in all? Smarter Balanced Mathematics Summative Assessment Blueprint, grade 5, Claim 2 (Problem Solving), target A: apply mathematics to solve well-posed problems arising in everyday life, society, and the workplace
  • On a grid of 100 small squares, a student shades 3 of the 10 columns, then marks 2 of the 10 rows inside those columns. What does the marked part show? Smarter Balanced Mathematics Summative Assessment Blueprint, grade 5, Claim 3 (Communicating Reasoning), target F: base arguments on concrete referents such as objects, drawings, diagrams, and actions
  • Pat adds 1/2 + 1/3 and gets 2/5. What did Pat do wrong? Smarter Balanced Mathematics Summative Assessment Blueprint, grade 5, Claim 3 (Communicating Reasoning), target E: distinguish correct logic or reasoning from that which is flawed
  • Point P is at (3, 5) on a coordinate grid. Point Q is 4 units to the right of P and 2 units down. What are the coordinates of Q? Smarter Balanced Mathematics Summative Assessment Blueprint, grade 5, Claim 1 (Concepts and Procedures), target J: graph points on the coordinate plane to solve real-world and mathematical problems
  • What is 3.847 rounded to the nearest hundredth? Smarter Balanced Mathematics Summative Assessment Blueprint, grade 5, Claim 1 (Concepts and Procedures), target C: understand the place value system
  • What is 3/5 + 1/4? Smarter Balanced Mathematics Summative Assessment Blueprint, grade 5, Claim 1 (Concepts and Procedures), target E: use equivalent fractions as a strategy to add and subtract fractions
  • What is 4.6 × 0.3? Smarter Balanced Mathematics Summative Assessment Blueprint, grade 5, Claim 1 (Concepts and Procedures), target D: perform operations with multi-digit whole numbers and with decimals to hundredths
  • What is 5/6 × 3/4? Smarter Balanced Mathematics Summative Assessment Blueprint, grade 5, Claim 1 (Concepts and Procedures), target F: apply and extend previous understandings of multiplication and division to multiply and divide fractions
  • What is the value of 4 × (9 − 3) + 5? Smarter Balanced Mathematics Summative Assessment Blueprint, grade 5, Claim 1 (Concepts and Procedures), target A: write and interpret numerical expressions

How this list was compiled: Outline: the Mathematics Summative Assessment Blueprint of the Smarter Balanced Assessment Consortium (as of the 2018-19 test administration), https://portal.smarterbalanced.org/library/en/mathematics-summative-assessment-blueprint.pdf, linked from https://contentexplorer.smarterbalanced.org/test-development, read 2026-10-07. Each question names the grade, the claim and the assessment target of that blueprint it practices. Every answer that is a number was worked out a second time from the numbers in the question. Licence: Own work. Questions, answer choices and explanations were written for this site. Nothing is copied or reworded from a Smarter Balanced test, a practice or training test, a sample item, an interim assessment or another practice test.

Grades 6 to 8: all 48 questions

Grade 6 16

  • A backpack costs $36. It is on sale for 25% off. What is the sale price? Smarter Balanced Mathematics Summative Assessment Blueprint, grade 6, Claim 2 (Problem Solving), target A: apply mathematics to solve well-posed problems arising in everyday life, society, and the workplace
  • A car travels 150 miles on 5 gallons of gas. At that rate, how far can it travel on 12 gallons? Smarter Balanced Mathematics Summative Assessment Blueprint, grade 6, Claim 4 (Modeling and Data Analysis), target D: interpret results in the context of a situation
  • A scoop holds 1/12 cup. How many scoops fill a jar that holds 5/6 cup? Smarter Balanced Mathematics Summative Assessment Blueprint, grade 6, Claim 1 (Concepts and Procedures), target B: apply and extend previous understandings of multiplication and division to divide fractions by fractions
Show all 48 questions (45 more)

Grade 6, continued

  • A store sells 5 pounds of apples for $8.00. What is the price per pound? Smarter Balanced Mathematics Summative Assessment Blueprint, grade 6, Claim 1 (Concepts and Procedures), target A: understand ratio concepts and use ratio reasoning to solve problems
  • A trail mix uses 2 cups of raisins for every 5 cups of nuts. How many cups of raisins go with 20 cups of nuts? Smarter Balanced Mathematics Summative Assessment Blueprint, grade 6, Claim 1 (Concepts and Procedures), target A: understand ratio concepts and use ratio reasoning to solve problems
  • A triangular sail has a base of 14 feet and a height of 9 feet. What is its area? Smarter Balanced Mathematics Summative Assessment Blueprint, grade 6, Claim 1 (Concepts and Procedures), target H: solve real-world and mathematical problems involving area, surface area, and volume
  • The ages of five cousins are 4, 7, 7, 10 and 12. What is the mean age? Smarter Balanced Mathematics Summative Assessment Blueprint, grade 6, Claim 1 (Concepts and Procedures), target J: summarize and describe distributions
  • Dee says that x² is always greater than x. Which value of x shows that she is wrong? Smarter Balanced Mathematics Summative Assessment Blueprint, grade 6, Claim 3 (Communicating Reasoning), target A: test propositions or conjectures with specific examples
  • For which numbers x is the statement |x| = x true? Smarter Balanced Mathematics Summative Assessment Blueprint, grade 6, Claim 3 (Communicating Reasoning), target G: determine conditions under which an argument does and does not apply
  • The high temperatures for one week were 61, 63, 62, 64, 62, 63 and 94 degrees. Which measure best describes a typical day that week? Smarter Balanced Mathematics Summative Assessment Blueprint, grade 6, Claim 4 (Modeling and Data Analysis), target E: analyze the adequacy of and make improvements to an existing model or develop a mathematical model of a real phenomenon
  • The ratio of red marbles to blue marbles in a bag is 2 to 3. Which statement must be true? Smarter Balanced Mathematics Summative Assessment Blueprint, grade 6, Claim 3 (Communicating Reasoning), target B: construct, autonomously, chains of reasoning that will justify or refute propositions or conjectures
  • Sam solves 3x = 12 and writes x = 9, because 12 − 3 = 9. What is his error? Smarter Balanced Mathematics Summative Assessment Blueprint, grade 6, Claim 3 (Communicating Reasoning), target E: distinguish correct logic or reasoning from that which is flawed
  • Tickets cost $9 each, and there is a one-time $4 service fee. Which equation gives the total cost c for t tickets? Smarter Balanced Mathematics Summative Assessment Blueprint, grade 6, Claim 2 (Problem Solving), target D: identify important quantities in a practical situation and map their relationships
  • What value of x makes 5x = 65 true? Smarter Balanced Mathematics Summative Assessment Blueprint, grade 6, Claim 1 (Concepts and Procedures), target F: reason about and solve one-variable equations and inequalities
  • Which expression is equivalent to 6(2x + 7)? Smarter Balanced Mathematics Summative Assessment Blueprint, grade 6, Claim 1 (Concepts and Procedures), target E: apply and extend previous understandings of arithmetic to algebraic expressions
  • Which list shows the numbers in order from least to greatest? Smarter Balanced Mathematics Summative Assessment Blueprint, grade 6, Claim 1 (Concepts and Procedures), target D: apply and extend previous understandings of numbers to the system of rational numbers

Grade 7 16

  • A bag holds 4 red, 5 blue and 3 green tiles. One tile is picked without looking. What is the probability that it is blue? Smarter Balanced Mathematics Summative Assessment Blueprint, grade 7, Claim 1 (Concepts and Procedures), target I: investigate chance processes and develop, use, and evaluate probability models
  • A circle has a radius of 5 inches. Which is closest to its area? Use 3.14 for π. Smarter Balanced Mathematics Summative Assessment Blueprint, grade 7, Claim 1 (Concepts and Procedures), target F: solve real-life and mathematical problems involving angle measure, area, surface area, and volume
  • A map has a scale of 1 inch to 25 miles. Two towns are 3.5 inches apart on the map. How far apart are the towns? Smarter Balanced Mathematics Summative Assessment Blueprint, grade 7, Claim 2 (Problem Solving), target A: apply mathematics to solve well-posed problems arising in everyday life, society, and the workplace
  • A phone plan costs $30 a month plus $0.10 for each text. Ray's bill is $42.50. How many texts did he send? Smarter Balanced Mathematics Summative Assessment Blueprint, grade 7, Claim 2 (Problem Solving), target C: interpret results in the context of a situation
  • A printer prints 45 pages in 3 minutes at a constant rate. What is its unit rate? Smarter Balanced Mathematics Summative Assessment Blueprint, grade 7, Claim 1 (Concepts and Procedures), target A: analyze proportional relationships and use them to solve real-world and mathematical problems
  • A shirt costs $24 before a 6% sales tax. What is the total cost? Smarter Balanced Mathematics Summative Assessment Blueprint, grade 7, Claim 1 (Concepts and Procedures), target D: solve real-life and mathematical problems using numerical and algebraic expressions and equations
  • A store raises a $50 price by 20%. Later it lowers the new price by 20%. What is the final price? Smarter Balanced Mathematics Summative Assessment Blueprint, grade 7, Claim 4 (Modeling and Data Analysis), target A: apply mathematics to solve problems arising in everyday life, society, and the workplace
  • Ana says subtracting a number always makes the result smaller. Which example shows that she is wrong? Smarter Balanced Mathematics Summative Assessment Blueprint, grade 7, Claim 3 (Communicating Reasoning), target A: test propositions or conjectures with specific examples
  • For which numbers n is the statement "the opposite of n is less than n" true? Smarter Balanced Mathematics Summative Assessment Blueprint, grade 7, Claim 3 (Communicating Reasoning), target G: determine conditions under which an argument does and does not apply
  • In a proportional relationship, y = 7 when x = 2 and y = 21 when x = 6. What is y when x = 10? Smarter Balanced Mathematics Summative Assessment Blueprint, grade 7, Claim 1 (Concepts and Procedures), target A: analyze proportional relationships and use them to solve real-world and mathematical problems
  • In a proportional relationship, y = 10 when x = 4. Which reasoning correctly finds y when x = 6? Smarter Balanced Mathematics Summative Assessment Blueprint, grade 7, Claim 3 (Communicating Reasoning), target B: construct, autonomously, chains of reasoning that will justify or refute propositions or conjectures
  • Lin says that raising a price by 10% and then lowering it by 10% brings it back to where it started. What is the flaw? Smarter Balanced Mathematics Summative Assessment Blueprint, grade 7, Claim 3 (Communicating Reasoning), target E: distinguish correct logic or reasoning from that which is flawed
  • Solve 3x + 7 = 31. Smarter Balanced Mathematics Summative Assessment Blueprint, grade 7, Claim 1 (Concepts and Procedures), target D: solve real-life and mathematical problems using numerical and algebraic expressions and equations
  • To estimate how many students at her school walk to school, Jo surveys 40 members of the walking club. Why may her estimate be poor? Smarter Balanced Mathematics Summative Assessment Blueprint, grade 7, Claim 4 (Modeling and Data Analysis), target E: analyze the adequacy of and make improvements to an existing model or develop a mathematical model of a real phenomenon
  • What is −6 − (−10)? Smarter Balanced Mathematics Summative Assessment Blueprint, grade 7, Claim 1 (Concepts and Procedures), target B: apply and extend previous understandings of operations with fractions to add, subtract, multiply, and divide rational numbers
  • Which expression is equivalent to 7x − 3(x − 5)? Smarter Balanced Mathematics Summative Assessment Blueprint, grade 7, Claim 1 (Concepts and Procedures), target C: use properties of operations to generate equivalent expressions

Grade 8 16

  • A cylinder has a radius of 3 centimeters and a height of 10 centimeters. Which is closest to its volume? Use 3.14 for π. Smarter Balanced Mathematics Summative Assessment Blueprint, grade 8, Claim 1 (Concepts and Procedures), target I: solve real-world and mathematical problems involving volume of cylinders, cones, and spheres
  • A line of best fit for a plant is h = 2.5w + 4, where h is its height in centimeters and w is the number of weeks. What does 2.5 mean? Smarter Balanced Mathematics Summative Assessment Blueprint, grade 8, Claim 4 (Modeling and Data Analysis), target D: interpret results in the context of a situation
  • A line passes through the points (0, 2) and (4, 10). What is its slope? Smarter Balanced Mathematics Summative Assessment Blueprint, grade 8, Claim 1 (Concepts and Procedures), target C: understand the connections between proportional relationships, lines, and linear equations
  • A right triangle has legs of length 9 and 12. How long is the hypotenuse? Smarter Balanced Mathematics Summative Assessment Blueprint, grade 8, Claim 1 (Concepts and Procedures), target H: understand and apply the Pythagorean Theorem
  • A tank holds 300 gallons and drains at 12 gallons a minute. Which function gives the gallons g left after m minutes? Smarter Balanced Mathematics Summative Assessment Blueprint, grade 8, Claim 2 (Problem Solving), target D: identify important quantities in a practical situation and map their relationships
  • A triangle has side lengths 5, 12 and c, where c is the longest side. For which value of c is it a right triangle? Smarter Balanced Mathematics Summative Assessment Blueprint, grade 8, Claim 3 (Communicating Reasoning), target G: determine conditions under which an argument does and does not apply
  • Ivy simplifies 3² × 3⁴ and writes 3⁸. What is her error? Smarter Balanced Mathematics Summative Assessment Blueprint, grade 8, Claim 3 (Communicating Reasoning), target E: distinguish correct logic or reasoning from that which is flawed
  • Max says the square root of a number is always smaller than the number. Which number shows that he is wrong? Smarter Balanced Mathematics Summative Assessment Blueprint, grade 8, Claim 3 (Communicating Reasoning), target A: test propositions or conjectures with specific examples
  • Of 40 students, 15 play both a sport and an instrument, 10 play only a sport, 5 play only an instrument and 10 play neither. What fraction of the students who play a sport also play an instrument? Smarter Balanced Mathematics Summative Assessment Blueprint, grade 8, Claim 4 (Modeling and Data Analysis), target F: identify important quantities in a practical situation and map their relationships
  • One gym charges a $25 sign-up fee and $15 a month. Another charges no fee and $20 a month. After how many months is the total cost the same? Smarter Balanced Mathematics Summative Assessment Blueprint, grade 8, Claim 2 (Problem Solving), target A: apply mathematics to solve well-posed problems arising in everyday life, society, and the workplace
  • Solve 4(x − 3) = 2x + 6. Smarter Balanced Mathematics Summative Assessment Blueprint, grade 8, Claim 1 (Concepts and Procedures), target D: analyze and solve linear equations and pairs of simultaneous linear equations
  • Triangle ABC is reflected across the y-axis. Point A is at (−3, 4). Where is the image of A? Smarter Balanced Mathematics Summative Assessment Blueprint, grade 8, Claim 1 (Concepts and Procedures), target G: understand congruence and similarity using physical models, transparencies, or geometry software
  • Two lines have the equations y = 3x + 2 and y = 3x − 5. Why does this system have no solution? Smarter Balanced Mathematics Summative Assessment Blueprint, grade 8, Claim 3 (Communicating Reasoning), target B: construct, autonomously, chains of reasoning that will justify or refute propositions or conjectures
  • What is the solution of the system y = 2x + 1 and y = −x + 7? Smarter Balanced Mathematics Summative Assessment Blueprint, grade 8, Claim 1 (Concepts and Procedures), target D: analyze and solve linear equations and pairs of simultaneous linear equations
  • What is the value of 5⁻²? Smarter Balanced Mathematics Summative Assessment Blueprint, grade 8, Claim 1 (Concepts and Procedures), target B: work with radicals and integer exponents
  • Which set of (x, y) pairs is NOT a function? Smarter Balanced Mathematics Summative Assessment Blueprint, grade 8, Claim 1 (Concepts and Procedures), target E: define, evaluate, and compare functions

How this list was compiled: Outline: the Mathematics Summative Assessment Blueprint of the Smarter Balanced Assessment Consortium (as of the 2018-19 test administration), https://portal.smarterbalanced.org/library/en/mathematics-summative-assessment-blueprint.pdf, linked from https://contentexplorer.smarterbalanced.org/test-development, read 2026-10-07. Each question names the grade, the claim and the assessment target of that blueprint it practices. Every answer that is a number was worked out a second time from the numbers in the question. Licence: Own work. Questions, answer choices and explanations were written for this site. Nothing is copied or reworded from a Smarter Balanced test, a practice or training test, a sample item, an interim assessment or another practice test.

High school: all 48 questions

Algebra 17

  • A plumber charges $60 for a visit plus $45 an hour. Which inequality gives the hours h that keep the bill at or under $240? Smarter Balanced Mathematics Summative Assessment Blueprint, grade 11, Claim 1 (Concepts and Procedures), target G: create equations that describe numbers or relationships
  • A rectangle's perimeter is 56. Its length is 4 more than twice its width. What is the width? Smarter Balanced Mathematics Summative Assessment Blueprint, grade 11, Claim 2 (Problem Solving), target D: identify important quantities in a practical situation and map their relationships
  • A student claims that (a + b)² = a² + b² for all numbers. Which pair shows that the claim is false? Smarter Balanced Mathematics Summative Assessment Blueprint, grade 11, Claim 3 (Communicating Reasoning), target A: test propositions or conjectures with specific examples
Show all 48 questions (45 more)

Algebra, continued

  • A student predicts that a 150-mile trip will take 2.5 hours because the speed limit is 60 miles per hour. What is the student assuming? Smarter Balanced Mathematics Summative Assessment Blueprint, grade 11, Claim 4 (Modeling and Data Analysis), target C: state logical assumptions being used
  • A student solves x² = 5x by dividing both sides by x and gets x = 5. What is the flaw? Smarter Balanced Mathematics Summative Assessment Blueprint, grade 11, Claim 3 (Communicating Reasoning), target E: distinguish correct logic or reasoning from that which is flawed
  • A student writes: "x ÷ x = 1 for every number x." For which value of x is the statement false? Smarter Balanced Mathematics Summative Assessment Blueprint, grade 11, Claim 3 (Communicating Reasoning), target C: state logical assumptions being used
  • A theater sold 300 tickets for $2,100 in all. Adult tickets cost $9 and student tickets cost $5. How many adult tickets were sold? Smarter Balanced Mathematics Summative Assessment Blueprint, grade 11, Claim 2 (Problem Solving), target A: apply mathematics to solve well-posed problems arising in everyday life, society, and the workplace
  • At which points do the graphs of y = x² and y = x + 2 intersect? Smarter Balanced Mathematics Summative Assessment Blueprint, grade 11, Claim 1 (Concepts and Procedures), target J: represent and solve equations and inequalities graphically
  • The expression 500(1.04)^t gives the value in dollars of an account after t years. What does 1.04 show? Smarter Balanced Mathematics Summative Assessment Blueprint, grade 11, Claim 1 (Concepts and Procedures), target D: interpret the structure of expressions
  • The length of a rectangle is 3 more than its width w. Its area is 40. Which equation can be solved to find w? Smarter Balanced Mathematics Summative Assessment Blueprint, grade 11, Claim 1 (Concepts and Procedures), target G: create equations that describe numbers or relationships
  • Solve −3x + 5 > 17. Smarter Balanced Mathematics Summative Assessment Blueprint, grade 11, Claim 1 (Concepts and Procedures), target I: solve equations and inequalities in one variable
  • Squaring both sides of √(x + 3) = x − 3 leads to x = 1 and x = 6. Which values solve the original equation? Smarter Balanced Mathematics Summative Assessment Blueprint, grade 11, Claim 1 (Concepts and Procedures), target H: understand solving equations as a process of reasoning and explain the reasoning
  • What are the solutions of x² − 4x − 12 = 0? Smarter Balanced Mathematics Summative Assessment Blueprint, grade 11, Claim 1 (Concepts and Procedures), target I: solve equations and inequalities in one variable
  • What is (3x² − 2x + 4) − (x² + 5x − 1)? Smarter Balanced Mathematics Summative Assessment Blueprint, grade 11, Claim 1 (Concepts and Procedures), target F: perform arithmetic operations on polynomials
  • Which expression is equivalent to x² − 49? Smarter Balanced Mathematics Summative Assessment Blueprint, grade 11, Claim 1 (Concepts and Procedures), target D: interpret the structure of expressions
  • Which is the factored form of x² + 5x + 6? Smarter Balanced Mathematics Summative Assessment Blueprint, grade 11, Claim 1 (Concepts and Procedures), target E: write expressions in equivalent forms to solve problems
  • Which is the vertex form of y = x² − 6x + 5? Smarter Balanced Mathematics Summative Assessment Blueprint, grade 11, Claim 1 (Concepts and Procedures), target E: write expressions in equivalent forms to solve problems

Functions 14

  • $1,000 is invested at 5% interest, compounded once a year. What is the value after 2 years? Smarter Balanced Mathematics Summative Assessment Blueprint, grade 11, Claim 2 (Problem Solving), target A: apply mathematics to solve well-posed problems arising in everyday life, society, and the workplace
  • A company's profit in dollars is P(x) = −2x² + 80x − 300, where x is the price of its product in dollars. Which price gives the greatest profit? Smarter Balanced Mathematics Summative Assessment Blueprint, grade 11, Claim 4 (Modeling and Data Analysis), target B: construct, autonomously, chains of reasoning to justify mathematical models used, interpretations made, and solutions proposed for a complex problem
  • A culture starts with 200 bacteria and doubles every hour. Which function gives the number of bacteria after t hours? Smarter Balanced Mathematics Summative Assessment Blueprint, grade 11, Claim 1 (Concepts and Procedures), target N: build a function that models a relationship between two quantities
  • A function f is made of the pairs (1, 4), (2, 7) and (3, 10). What is the domain of f? Smarter Balanced Mathematics Summative Assessment Blueprint, grade 11, Claim 1 (Concepts and Procedures), target K: understand the concept of a function and use function notation
  • A student says any function with f(1) = 1 and f(2) = 4 must be f(x) = x². Which function shows that this is false? Smarter Balanced Mathematics Summative Assessment Blueprint, grade 11, Claim 3 (Communicating Reasoning), target A: test propositions or conjectures with specific examples
  • A taxi charges $3.50 plus $2.25 per mile. A ride costs $21.50. How many miles was the ride? Smarter Balanced Mathematics Summative Assessment Blueprint, grade 11, Claim 2 (Problem Solving), target A: apply mathematics to solve well-posed problems arising in everyday life, society, and the workplace
  • A town's population was 8,000 and has grown by about 200 people every year. A student models it as P = 8,000(1.2)^t. Which change fixes the model? Smarter Balanced Mathematics Summative Assessment Blueprint, grade 11, Claim 4 (Modeling and Data Analysis), target E: analyze the adequacy of and make improvements to an existing model or develop a mathematical model of a real phenomenon
  • The cost in dollars of printing n shirts is C(n) = 12n + 30. What does the 30 stand for? Smarter Balanced Mathematics Summative Assessment Blueprint, grade 11, Claim 1 (Concepts and Procedures), target L: interpret functions that arise in applications in terms of a context
  • f is a linear function with f(2) = 7 and f(5) = 16. Which reasoning correctly finds f(0)? Smarter Balanced Mathematics Summative Assessment Blueprint, grade 11, Claim 3 (Communicating Reasoning), target B: construct, autonomously, chains of reasoning that will justify or refute propositions or conjectures
  • For which values of b does y = b^x rise as x rises? Smarter Balanced Mathematics Summative Assessment Blueprint, grade 11, Claim 3 (Communicating Reasoning), target G: determine conditions under which an argument does and does not apply
  • The height of a ball in feet is h(t) = −16t² + 32t + 5, where t is seconds after it is thrown. What is the ball's greatest height? Smarter Balanced Mathematics Summative Assessment Blueprint, grade 11, Claim 1 (Concepts and Procedures), target L: interpret functions that arise in applications in terms of a context
  • If g(x) = 4x² − x − 6, what is g(−2)? Smarter Balanced Mathematics Summative Assessment Blueprint, grade 11, Claim 1 (Concepts and Procedures), target K: understand the concept of a function and use function notation
  • What is the average rate of change of f(x) = x² + 1 from x = 2 to x = 5? Smarter Balanced Mathematics Summative Assessment Blueprint, grade 11, Claim 1 (Concepts and Procedures), target M: analyze functions using different representations
  • Which function has zeros at x = −1 and x = 3? Smarter Balanced Mathematics Summative Assessment Blueprint, grade 11, Claim 1 (Concepts and Procedures), target M: analyze functions using different representations

Geometry and trigonometry 7

  • A ladder leans against a wall and makes a 60° angle with the ground. Its foot is 5 feet from the wall. How long is the ladder? Smarter Balanced Mathematics Summative Assessment Blueprint, grade 11, Claim 1 (Concepts and Procedures), target O: define trigonometric ratios and solve problems involving right triangles
  • A school's rule says a ramp's slope can be at most 1/12. A ramp must rise 2 feet. What is the shortest horizontal run the rule allows? Smarter Balanced Mathematics Summative Assessment Blueprint, grade 11, Claim 2 (Problem Solving), target C: interpret results in the context of a situation
  • A student says sin 30° + sin 60° = sin 90°, because 30 + 60 = 90. Is that right? Smarter Balanced Mathematics Summative Assessment Blueprint, grade 11, Claim 3 (Communicating Reasoning), target E: distinguish correct logic or reasoning from that which is flawed
  • A tank shaped like a cylinder has a radius of 2 meters and a height of 5 meters. About how many liters does it hold? (1 cubic meter = 1,000 liters. Use 3.14 for π.) Smarter Balanced Mathematics Summative Assessment Blueprint, grade 11, Claim 4 (Modeling and Data Analysis), target A: apply mathematics to solve problems arising in everyday life, society, and the workplace
  • A triangle has sides of length 7, 24 and 25. Which reasoning shows that it is a right triangle? Smarter Balanced Mathematics Summative Assessment Blueprint, grade 11, Claim 3 (Communicating Reasoning), target B: construct, autonomously, chains of reasoning that will justify or refute propositions or conjectures
  • In a right triangle, the leg opposite angle A has length 5 and the hypotenuse has length 13. What is sin A? Smarter Balanced Mathematics Summative Assessment Blueprint, grade 11, Claim 1 (Concepts and Procedures), target O: define trigonometric ratios and solve problems involving right triangles
  • Two triangles have the same three angle measures. What can be concluded? Smarter Balanced Mathematics Summative Assessment Blueprint, grade 11, Claim 3 (Communicating Reasoning), target F: base arguments on concrete referents such as objects, drawings, diagrams, and actions

Statistics, number and quantity 10

  • A car travels at 60 miles per hour. How many feet per second is that? (1 mile = 5,280 feet) Smarter Balanced Mathematics Summative Assessment Blueprint, grade 11, Claim 1 (Concepts and Procedures), target C: reason quantitatively and use units to solve problems
  • A line of best fit for a used car's value in dollars is v = 18,000 − 1,500t, with t in years. What does the model give for t = 12? Smarter Balanced Mathematics Summative Assessment Blueprint, grade 11, Claim 4 (Modeling and Data Analysis), target D: interpret results in the context of a situation
  • A survey finds that students who own more books tend to have higher grades. A student concludes that buying books raises grades. What is the flaw? Smarter Balanced Mathematics Summative Assessment Blueprint, grade 11, Claim 3 (Communicating Reasoning), target E: distinguish correct logic or reasoning from that which is flawed
  • Five test scores are 70, 72, 74, 76 and 78. A sixth score of 20 is added. Which statement is true? Smarter Balanced Mathematics Summative Assessment Blueprint, grade 11, Claim 1 (Concepts and Procedures), target P: summarize, represent, and interpret data on a single count or measurement variable
  • For which values of x is √(x²) = x true? Smarter Balanced Mathematics Summative Assessment Blueprint, grade 11, Claim 3 (Communicating Reasoning), target G: determine conditions under which an argument does and does not apply
  • Is the product of two consecutive whole numbers always even? Which argument is complete? Smarter Balanced Mathematics Summative Assessment Blueprint, grade 11, Claim 3 (Communicating Reasoning), target D: use the technique of breaking an argument into cases
  • Of 200 students surveyed, 120 have a job. Of those with a job, 45 play a sport. Of those without a job, 50 play a sport. What percent of all the students play a sport? Smarter Balanced Mathematics Summative Assessment Blueprint, grade 11, Claim 4 (Modeling and Data Analysis), target F: identify important quantities in a practical situation and map their relationships
  • What are the median and the range of the data set 3, 5, 5, 6, 8, 9, 13? Smarter Balanced Mathematics Summative Assessment Blueprint, grade 11, Claim 1 (Concepts and Procedures), target P: summarize, represent, and interpret data on a single count or measurement variable
  • Which display best shows how the heights of 200 students are spread out? Smarter Balanced Mathematics Summative Assessment Blueprint, grade 11, Claim 2 (Problem Solving), target B: select and use appropriate tools strategically
  • Which is equal to 27^(2/3)? Smarter Balanced Mathematics Summative Assessment Blueprint, grade 11, Claim 1 (Concepts and Procedures), target A: extend the properties of exponents to rational exponents

How this list was compiled: Outline: the Mathematics Summative Assessment Blueprint of the Smarter Balanced Assessment Consortium (as of the 2018-19 test administration), https://portal.smarterbalanced.org/library/en/mathematics-summative-assessment-blueprint.pdf, linked from https://contentexplorer.smarterbalanced.org/test-development, read 2026-10-07. Each question names the grade, the claim and the assessment target of that blueprint it practices. Every answer that is a number was worked out a second time from the numbers in the question. Licence: Own work. Questions, answer choices and explanations were written for this site. Nothing is copied or reworded from a Smarter Balanced test, a practice or training test, a sample item, an interim assessment or another practice test.

How it works

Unofficial practice for the mathematics part of the Smarter Balanced tests, grades 3 to 8 and high school. Every question was written for this page, and none comes from a real test. Not affiliated with, endorsed by or sponsored by the Smarter Balanced Assessment Consortium.

Read the full guide

What the math test measures

The blueprint sorts every question into claims. Concepts and Procedures is about half of the test. Problem Solving with Modeling and Data Analysis, and Communicating Reasoning, share the rest. Each band here keeps those shares, 24 questions, 12 and 12, and names the claim and target under each answer.

How the answers are checked

Every answer that is a number was worked out a second time from the numbers in the question. Wrong choices are common slips, such as giving the perimeter when the question asks for the area.

  • In grades 3 to 5, practice with no calculator, as on the real test.
  • A reasoning question asks which argument holds. Say why in your own words before you read the choices.

Questions and answers

Can you use a calculator on the Smarter Balanced math test?

Not in grades 3 to 5. From grade 6 the test has one section with an on-screen calculator and one without: four-function in grade 6, scientific in grades 7 and 8, and scientific, regression and graphing in high school.

How many questions are on the Smarter Balanced math test?

The blueprint gives ranges, because the test adapts. In grades 3 to 5 it lists 17 to 20 items on concepts and procedures and 18 to 20 across the other claims. Those counts include a performance task of 4 to 6 items.

How long is the Smarter Balanced math test?

It is untimed. The consortium estimates 2 hours 30 minutes in grades 3 to 5, 3 hours in grades 6 to 8 and 3 hours 30 minutes in grade 11, counting the computer adaptive part and the performance task.

Where is the official Smarter Balanced math practice test?

On the consortium's site, under Practice Tests and Sample Questions. It runs in the real testing software, each member state has its own copy, and no login is needed. The box under the questions links there. This page is separate, unofficial practice.

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