Unit 6 MSTAR-Style Practice Test · Form A

Numerical and Algebraic Expressions · 15 questions · English only, like the real test · No timer — take the time you need.

These are MSTAR-style questions written for this curriculum to rehearse the format. They are not official Maryland assessment items. MSTAR — Maryland's new state test, first given in spring 2027 — uses the same kinds of questions you see here: selected response, select-all, two-part evidence questions, and written responses.

How this works: Answer every question, then press Submit & Grade. Selected-response parts grade instantly with an explanation for each; written responses go to your teacher. Your answers save on this device.

On the real MSTAR: math runs as three 40-minute sessions, in English, on a computer. Here there is no clock — practice the thinking first; the pacing comes with rehearsal.

Written responses: how should the explain-the-error questions be scored?

Instant scoring checks whether your explanation states the value and uses the reasoning the question is about. It matches words and numbers, so a right answer worded differently can score low — your teacher can always re-score it from the answer key.

16.NOS.1Division Expressions with Fractions and Whole Numbers

Select all that apply

Select ALL statements that are true about the expression 4 ÷ 1/3.

The whole number 4 can be written as the fraction 4/1. Keep, change, flip rewrites the expression as 4/1 × 3/1. The reciprocal of 1/3 is 3/1. The quotient is 4/3. The quotient is 12. The quotient must be less than 4 because the expression uses division.

26.NOS.1Division Expressions with Fractions and Mixed Numbers

Explain the error

Marisol divided 5/6 ÷ 2/3. Her work was: 6/5 × 2/3 = 12/15 = 4/5. She wrote that the quotient is 4/5.

Explain Marisol's misconception and give the correct quotient.

✍️ Written response — 2 points.

36.AT.5Explore Numerical Expressions with Exponents

Part A

Which value is equal to the power 3⁴?

7 12 64 81

Part B

Which reasoning shows why your answer to Part A is correct?

Multiply the base by the exponent: 3 × 4 = 12. Add the base and the exponent: 3 + 4 = 7. The exponent 4 tells how many times to use the base 3 as a factor: 3 × 3 × 3 × 3 = 81. Use the exponent as the base and the base as the exponent: 4 × 4 × 4 = 64.

46.AT.6cWrite and Evaluate Numerical Expressions with Exponents

Part A

Evaluate the numerical expression 3 × 4² − 8.

16 24 40 136

Part B

Which reasoning shows why your answer to Part A is correct?

Multiply 3 × 4 first, then square the product: 12² = 144, and 144 − 8 = 136. Evaluate the power first: 4² = 16. Then multiply: 3 × 16 = 48. Then subtract: 48 − 8 = 40. Read 4² as 4 × 2 = 8, then multiply 3 × 8 = 24 and subtract: 24 − 8 = 16. Subtract first because 16 and 8 are next to each other: 16 − 8 = 8, then 3 × 8 = 24.

56.AT.6aWrite and Evaluate Algebraic Expressions

Select all that apply

Select ALL statements that are true about the algebraic expression 7n + 4.

The variable is n. The coefficient of the variable term is 7. The constant is 4. When n = 3, the expression has a value of 25. When n = 3, the expression has a value of 33. The term 7n means 7 plus n.

66.AT.7Identify Equivalent Algebraic Expressions

Explain the error

Priya claimed that 2x + x and 2x² are equivalent expressions. Her only check was x = 0. She wrote: 2(0) + 0 = 0 and 2(0)² = 0. Because both results were 0, she said the expressions are equivalent.

Explain Priya's misconception and give the correct simplified form of 2x + x.

✍️ Written response — 2 points.

76.NOS.4Find Factors and Multiples

Part A

What is the greatest common factor of 18 and 24?

2 3 6 72

Part B

Which reasoning shows why your answer to Part A is correct?

List the factors of each number, find the ones they share, which are 1, 2, 3, and 6, and take the largest shared factor, 6. Stop at the first prime that divides both numbers, which is 3. Find the smallest multiple that 18 and 24 share, which is 72, and use it as the greatest common factor. Both 18 and 24 are even numbers, so the greatest shared factor is 2.

86.AT.7Generate Equivalent Expressions

Part A

Which property of operations is shown by the equation (7 + 4) + 6 = 7 + (4 + 6)?

Commutative Property of Addition Identity Property of Addition Distributive Property Associative Property of Addition

Part B

Which reasoning shows why your answer to Part A is correct?

The addends appear in a different order on the two sides, which is the commutative property. Adding zero leaves a number unchanged, which is the identity property. A factor outside the parentheses is multiplied by each term inside, which is the distributive property. The addends appear in the same order on both sides, but the parentheses move. Changing the grouping without changing the sum is the associative property, and both sides equal 17.

96.NOS.1Divide Whole Numbers by Fractions

Select all that apply

Select ALL statements that are true about the expression 10 ÷ 2/5.

The reciprocal of the divisor 2/5 is 5/2. The expression can be rewritten as 10/1 × 5/2. The quotient is 25. The quotient is 4. The quotient is greater than 10 because the divisor is less than 1. The reciprocal of 2/5 is 2/5.

106.NOS.1Divide Mixed Numbers

Explain the error

Tyrone divided 2 1/2 ÷ 1/4. His work was: keep 2 1/2, change ÷ to ×, flip 1/4 to 4/1. Then he multiplied only the whole number, 2 × 4 = 8, and carried the 1/2 along, so he answered 8 1/2.

Explain Tyrone's misconception and give the correct quotient.

✍️ Written response — 2 points.

116.NOS.1Fraction Division Problem Solving

Part A

A ribbon is 4 1/2 feet long. Marta cuts the whole ribbon into pieces that are each 3/4 foot long. How many pieces does she get?

1/6 of a piece 3 3/8 pieces 5 1/4 pieces 6 pieces

Part B

Which reasoning shows why your answer to Part A is correct?

Divide the size of each piece by the total length: 3/4 ÷ 9/2 = 3/4 × 2/9 = 6/36 = 1/6. Add the total length and the size of each piece: 4 1/2 + 3/4 = 5 1/4. The total amount is the dividend and the size of each group is the divisor, so total ÷ size = number of groups: 9/2 ÷ 3/4 = 9/2 × 4/3 = 36/6 = 6. Multiply the total length by the size of each piece: 9/2 × 3/4 = 27/8 = 3 3/8.

126.NOS.4Least Common Multiple

Part A

What is the least common multiple of 6 and 8?

2 14 24 48

Part B

Which reasoning shows why your answer to Part A is correct?

Multiply the two numbers together, 6 × 8 = 48, because the product is always the least common multiple. Find the largest number that divides both 6 and 8, which is 2. Add the two numbers, 6 + 8 = 14. Skip count starting with the larger number: 8, 16, 24. Then skip count by 6: 6, 12, 18, 24. The first non-zero multiple in both lists is 24.

136.NOS.4Prime Factorization

Select all that apply

Select ALL statements that are true about the number 45.

45 is a composite number. The prime factorization of 45 is 3² × 5. The prime factorization of 45 is 5 × 9. 45 is a prime number. The only prime factors of 45 are 3 and 5. 1 is a prime factor of 45.

146.AT.7The Distributive Property

Explain the error

Elena was asked to factor 18m + 24 completely. She wrote 18m + 24 = 2(9m + 12) and said she was finished because 2 divides both terms.

Explain Elena's misconception and give the completely factored expression.

✍️ Written response — 2 points.

156.AT.7Simplify Algebraic Expressions

Part A

Simplify the expression 8x + 3 + 2x − 1.

6x + 2 10x + 2 10x + 4 12x

Part B

Which reasoning shows why your answer to Part A is correct?

8x and 2x share the same variable part, so add their coefficients to get 10x. The constants 3 and −1 combine separately to 2, giving 10x + 2. Combine every number in the expression into one coefficient: 8 + 3 + 2 − 1 = 12, giving 12x. Subtract the coefficients of the variable terms: 8 − 2 = 6, giving 6x + 2. Add the coefficients of the variable terms and then add both constants: 10x + 4.

Unit 6 MSTAR-Style Practice Test — Form A