MSTAR Practice Worksheet

Lesson 6-10: Divide Mixed Numbers

Grade 6 Mathematics · Standard 6.NOS.1

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

What is 1 1/2 ÷ 3/4?

A1 1/8
B2
C3/4
D1/2

Question 2Selected response · 1 point

Convert 3 2/5 to an improper fraction.

A6/5
B15/5
C17/5
D32/5

Question 3Selected response · 1 point

What is 2 1/4 ÷ 3/4?

A1 1/2
B2 1/3
C3
D9/16

Question 4Selected response · 1 point

What is 3 1/2 ÷ 1/4?

A3 1/8
B7/8
C13/4
D14

Question 5Selected response · 1 point

A baker has 2 1/4 cups of butter. Each batch of cookies needs 3/4 cup of butter. How many batches can the baker make?

A1 1/2 batches
B2 batches
C3 batches
D6 batches

Question 6Selected response · 1 point

Agent Chen has walked 2 1/4 miles, which is 3/4 of her whole route. How long is the whole route? (2 1/4 ÷ 3/4 asks how much is in one whole route.)

A1 11/16 miles
B3 miles
C1/3 mile
D2 1/3 miles

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 value of 3 3/4 ÷ 1 1/2?

Fill in the bubble next to the one best answer.

A1 1/2
B2 1/2
C2
D5 5/8

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?

AConvert 3 3/4 by multiplying 3 × 4 and keeping the denominator, giving 12/4, then 12/4 × 2/3 = 2.
BIgnore the whole numbers and divide only the fraction parts: 3/4 ÷ 1/2 = 3/4 × 2/1 = 6/4 = 1 1/2.
CConvert to improper fractions, 15/4 and 3/2. Dividing by 3/2 gives the same result as multiplying by its reciprocal 2/3: 15/4 × 2/3 = 30/12 = 2 1/2. Check: 2 1/2 × 1 1/2 = 5/2 × 3/2 = 15/4 = 3 3/4.
DConvert to improper fractions and multiply straight across without flipping: 15/4 × 3/2 = 45/8 = 5 5/8.

Question 8Written response · 2 points

Type II Reasoning: Skipping the Conversion

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.

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

Part C — Show Your Thinking

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

Question 9Written response · 2 points

A detective has a rope that is 5 1/4 feet long. She needs to cut it into pieces that are each 3/4 foot for tying evidence tags. How many pieces can she cut? Write the equation, show each step (convert, the reciprocal shortcut, multiply, simplify), and verify your answer.

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