Unit 6 MSTAR-Style Practice Test · Form B

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

Part A

What is the value of 6 ÷ 1/5?

1/30 6/5 11 30

Part B

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

Keep 1/5, change ÷ to ×, and flip 6/1 to 1/6: 1/5 × 1/6 = 1/30. Write 6 as 6/1. Keep 6/1, change ÷ to ×, flip 1/5 to 5/1, then multiply across: 6/1 × 5/1 = 30. Write 6 as 6/1 and multiply straight across without flipping: 6/1 × 1/5 = 6/5. Add the whole number and the denominator of the fraction: 6 + 5 = 11.

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

Part A

What is the value of 2 1/4 ÷ 3/8?

1/6 2 2/3 6 27/32

Part B

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

Divide only the fraction parts, 1/4 ÷ 3/8 = 2/3, then put the whole number 2 back in front to get 2 2/3. Change 2 1/4 to 9/4. Keep 9/4, change ÷ to ×, flip 3/8 to 8/3: 9/4 × 8/3 = 72/12 = 6. Change 2 1/4 to 9/4, then multiply straight across without flipping: 9/4 × 3/8 = 27/32. Change 2 1/4 to 9/4, then flip the first fraction instead of the second: 4/9 × 3/8 = 1/6.

36.AT.5Explore Numerical Expressions with Exponents

Select all that apply

Select ALL statements that are true about the power 2⁵.

The base is 2. The exponent is 5. It means 2 × 2 × 2 × 2 × 2. Its value is 10. Its value is 32. It means 5 × 5.

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

Explain the error

Devon evaluated 20 − 2 × 3². His work was: 3² = 9, then 20 − 2 = 18, then 18 × 9 = 162. He wrote that the value of the expression is 162.

Explain Devon's misconception and give the correct value of the expression.

✍️ Written response — 2 points.

56.AT.6aWrite and Evaluate Algebraic Expressions

Part A

A concert ticket costs 8 dollars. The website also charges one 5 dollar service fee for the whole order. Let t represent the number of tickets bought in one order. Which expression gives the total cost in dollars?

8t + 5 8 + 5t 8(t + 5) 13t

Part B

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

The 5 dollar fee is paid for each ticket, so 5 is the coefficient: 8 + 5t. The 8 is the coefficient because it is paid for each ticket, and the 5 is a constant because it is paid one time. This gives 8t + 5, so an order of 6 tickets costs 8 × 6 + 5 = 53 dollars. Add the fee to the number of tickets first, then multiply by the ticket price: 8(t + 5). Combine 8 and 5 into a single coefficient because both are numbers: 13t.

66.AT.7Identify Equivalent Algebraic Expressions

Part A

Which expression is equivalent to 4(x + 3)?

4x + 12 4x + 3 7x x + 12

Part B

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

Multiply 4 by each term inside the parentheses: 4 · x + 4 · 3 = 4x + 12. Testing x = 2 gives 4(2 + 3) = 20 and 4(2) + 12 = 20, so the two expressions match. Multiply only the first term inside the parentheses and copy the second term: 4x + 3. Add 4 and 3 because both are numbers, then attach the variable: 7x. Multiply only the second term inside the parentheses and copy the first term: x + 12.

76.NOS.4Find Factors and Multiples

Select all that apply

Select ALL statements that are true about the numbers 12 and 20.

6 is a factor of 12. The greatest common factor of 12 and 20 is 4. The least common multiple of 12 and 20 is 60. The greatest common factor of 12 and 20 is 60. 40 is a multiple of 20. 5 is a factor of 12.

86.AT.7Generate Equivalent Expressions

Explain the error

Jamal wrote (20 − 8) − 5 = 20 − (8 − 5). He said the associative property lets him move the parentheses anywhere, so both sides must have the same value of 7.

Explain Jamal's misconception and give the correct value of each side.

✍️ Written response — 2 points.

96.NOS.1Divide Whole Numbers by Fractions

Part A

What is the value of 6 ÷ 3/4?

2 2/9 4 1/2 8

Part B

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

Flip the whole number instead of the divisor: 1/6 × 4/3 = 4/18 = 2/9. Write 6 as 6/1 and multiply by the reciprocal of the divisor: 6/1 × 4/3. Cross-cancel the common factor 3 to get 2/1 × 4/1 = 8. Multiply straight across without using the reciprocal: 6/1 × 3/4 = 18/4 = 4 1/2. Divide 6 by the numerator of the divisor and ignore the denominator: 6 ÷ 3 = 2.

106.NOS.1Divide Mixed Numbers

Part A

What is the value of 3 3/4 ÷ 1 1/2?

1 1/2 2 1/2 2 5 5/8

Part B

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

Convert 3 3/4 by multiplying 3 × 4 and keeping the denominator, giving 12/4, then 12/4 × 2/3 = 2. Ignore the whole numbers and divide only the fraction parts: 3/4 ÷ 1/2 = 3/4 × 2/1 = 6/4 = 1 1/2. Convert to improper fractions, 15/4 and 3/2, then keep, change, flip: 15/4 × 2/3 = 30/12 = 5/2 = 2 1/2. Convert to improper fractions and multiply straight across without flipping: 15/4 × 3/2 = 45/8 = 5 5/8.

116.NOS.1Fraction Division Problem Solving

Select all that apply

A jug holds 3/4 gallon of juice. Each cup holds 1/8 gallon. Select ALL statements that correctly describe this situation.

The dividend is 3/4 gallon, the total amount of juice in the jug. The divisor is 1/8 gallon, the size of one group. The equation that models the situation is 3/4 ÷ 1/8. The jug fills 6 cups. The answer is 3/32 gallon. The answer must be less than 1 because both numbers in the problem are less than 1.

126.NOS.4Least Common Multiple

Explain the error

Sofia found the least common multiple of 4 and 10 by multiplying the two numbers: 4 × 10 = 40. She wrote that the least common multiple of 4 and 10 is 40.

Explain Sofia's misconception and give the correct least common multiple.

✍️ Written response — 2 points.

136.NOS.4Prime Factorization

Part A

What is the prime factorization of 72?

2³ × 3² 2² × 3³ 2 × 3 × 12 8 × 9

Part B

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

The tree gives two 2s and three 3s, so the prime factorization is 2² × 3³. Every branch of the factor tree for 72 ends in a prime: 2, 2, 2, 3, 3. Grouping the repeated primes with exponents gives 2³ × 3², and 2³ × 3² = 8 × 9 = 72. 72 splits into 2 × 3 × 12, and the branches can stop there. 72 splits into 8 × 9, and those are the factors to report.

146.AT.7The Distributive Property

Part A

Which expression is equivalent to 6(2x + 5)?

2x + 30 12x + 30 12x + 5 12x + 11

Part B

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

Multiply the outside factor by the second term only and copy the first term: 2x + 30. Multiply the outside factor by every term inside the parentheses: 6 · 2x = 12x and 6 · 5 = 30, giving 12x + 30. Multiply 6 by 2x, then add 6 and 5 instead of multiplying them: 12x + 11. Multiply the outside factor by the first term only and copy the second term: 12x + 5.

156.AT.7Simplify Algebraic Expressions

Select all that apply

Select ALL statements that are true about the expression 5y + 7 + 3y + y.

5y, 3y, and y are like terms. The coefficient of the term y is 1. The simplified expression is 9y + 7. The simplified expression is 16y. 7 is a constant and cannot be combined with the y terms. The simplified expression is 8y + 7.

Unit 6 MSTAR-Style Practice Test — Form B