MSTAR Practice Worksheet

Lesson 6-13: Prime Factorization

Grade 6 Mathematics · Standard 6.NOS.4

Name: Date:

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.

Part A — Skills Check

Warm up with the lesson's core skills — one best answer each.

Question 1Selected response · 1 point

Which of the following is a prime number?

Question 2Selected response · 1 point

What is the prime factorization of 30?

A2 × 3 × 5
B2 × 15
C3 × 10
D5 × 6

Question 3Selected response · 1 point

What is the prime factorization of 18?

A2 × 3 × 3
B2 × 9
C3 × 6
D6 × 3

Question 4Selected response · 1 point

Which of these numbers is composite?

Question 5Selected response · 1 point

Two students found different factor trees for 60. Student A started with 2 × 30. Student B started with 6 × 10. Which statement is true?

AOnly Student A gets the correct prime factorization
BOnly Student B gets the correct prime factorization
CThey will get different prime factorizations
DBoth get the same prime factorization: 2 × 2 × 3 × 5

Question 6Selected response · 1 point

The first lock panel shows 90. What is the prime factorization of 90?

A2 × 3 × 3 × 5
B2 × 45
C3 × 30
D9 × 10

Part B — Test-Format Questions

These match the state test's formats: two-part questions, select-all, and written responses.

Question 7Two-part question

Part A

What is the prime factorization of 72?

Fill in the bubble next to the one best answer.

A2³ × 3²
B2² × 3³
C2 × 3 × 12
D8 × 9

Part B

Answer Part A before Part B — Part B asks about your reasoning.

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

AThe tree gives two 2s and three 3s, so the prime factorization is 2² × 3³.
BEvery 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.
C72 splits into 2 × 3 × 12, and the branches can stop there.
D72 splits into 8 × 9, and those are the factors to report.

Question 8Select all that apply

Select ALL statements that are true about the number 45.

Mark the box next to EVERY answer that is true. More than one is correct.

A45 is a composite number.
BThe prime factorization of 45 is 3² × 5.
CThe prime factorization of 45 is 5 × 9.
D45 is a prime number.
EThe only prime factors of 45 are 3 and 5.
F1 is a prime factor of 45.

Part C — Show Your Thinking

Answer in writing, the way the state test's constructed responses work.

Question 9Written response · 2 points

Choose 24, 36, or 60. Show two factor trees with different first factor pairs. Finish both trees with prime factors, then explain how you checked that both products equal your chosen number.

Write your answer in complete sentences. Show or explain your mathematical thinking.