MSTAR Practice Worksheet

Lesson 8-7: Equations and Inequalities Problem Solving

Grade 6 Mathematics · Standard 6.AT.8

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

A museum has some paintings. After adding 12, they have 45. Which equation models this?

Ap + 12 = 45
Bp − 12 = 45
C12p = 45
Dp / 12 = 45

Question 2Selected response · 1 point

A detective needs more than 8 hours to finish the investigation. She has already worked 3 hours. Which inequality represents the additional hours h she needs?

A3 + h > 8
B3 + h = 8
Ch > 3
D8 + h > 3

Question 3Selected response · 1 point

Which model is correct for: 'A number divided by 6 equals 7'?

An / 6 = 7
B6n = 7
Cn − 6 = 7
Dn + 6 = 7

Question 4Selected response · 1 point

A bus can carry at most 48 passengers. There are already 31 on board. Which inequality shows how many more can board?

A31 + p ≤ 48
B31 + p > 48
C31 + p = 48
Dp − 31 ≤ 48

Question 5Selected response · 1 point

A student solved 4n = 52 and got n = 13. Is the answer reasonable if n represents the number of notebooks in a box?

ANo — 13 is too many notebooks
BNo — the answer should be 48
CYes — 13 notebooks per box is reasonable
DYes — but only if n is a fraction

Question 6Selected response · 1 point

Room 2: The vault keypad clue reads, 'A number of stolen coins plus 6 equals 14.' Solve x + 6 = 14 to find the code x.

Ax = 2
Bx = 6
Cx = 8
Dx = 20

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

A school van can carry at most 14 passengers. There are already 9 passengers on board. Let p be the number of additional passengers who can get on. Which inequality models this situation?

Fill in the bubble next to the one best answer.

A9 + p ≤ 14
B9 + p ≥ 14
C9 + p < 14
Dp − 9 ≤ 14

Part B

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

Which reasoning justifies that model and gives the greatest number of additional passengers?

AThe van must end up completely full, so 9 + p = 14 and exactly 5 more passengers must get on.
BThe 9 passengers are taken away from p, so p − 9 ≤ 14 and at most 23 more passengers can get on.
CThe total cannot pass the limit of 14, so 9 + p ≤ 14 and at most 5 more passengers can get on.
DThe words 'at most' mean the total has to be more than 14, so 9 + p ≥ 14 and 5 or more passengers can get on.

Question 8Select all that apply

A club has already sold 46 tickets and must sell at least 120 tickets in all. Let t be the number of additional tickets the club sells. Select ALL statements that are true about this situation.

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

AThe inequality 46 + t ≥ 120 models the situation.
BThe club must sell at least 74 more tickets to reach its goal.
CSelling exactly 74 more tickets reaches the goal.
DThe inequality 46 + t ≤ 120 models the situation.
ESelling 70 more tickets reaches the goal.

Part C — Show Your Thinking

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

Question 9Written response · 2 points

Create two word problems about the same situation: one that requires an equation and one that requires an inequality. Solve both and explain why the models are different.

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