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Grade 6 Math · Unit 7

Expressions, equations, and inequalities

Use this low-stakes check after studying the unit. It has 10 fresh questions and one written reasoning prompt. No timer, grade, or gate blocks your next lesson.

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1. Write an algebraic expression for the phrase: a number plus 8.

Writing Algebraic Expressions 6.EE.A.2 · 6.EE.B.6 Review lesson

2. If a = 5 and b = 2, what is the value of 3a + 4b?

Evaluating Algebraic Expressions 6.EE.A.2 Review lesson

3. Calculate: 5^3

Order of Operations 6.EE.A.1 · 6.EE.A.2.c Review lesson

4. Which of the following expressions is equivalent to 5(x + 6)?

The Distributive Property 6.EE.A.4 Review lesson

5. Simplify: 2x + 3x

Combining Like Terms 6.EE.A.3 Review lesson

6. A school is selling tickets for a play. They have already sold 45 tickets and need to sell a total of 120 tickets. Which equation can be used to find how many more tickets t they need to sell?

Writing Equations from Word Problems 6.EE.B.7 · 6.EE.C.9 Review lesson

7. Solve for n: n + 8 = 15

Solving One-Step Addition and Subtraction Equations 6.EE.B.5 · 6.EE.B.7 Review lesson

8. Solve: (x)/4 = 6

Solving One-Step Multiplication and Division Equations 6.EE.B.7 Review lesson

9. Which number-line description represents n > −2?

Writing and Graphing Inequalities 6.EE.B.8 Review lesson

10. Solve for x: 3x ≥ 18

Solving One-Step Inequalities 6.EE.B.8 Review lesson

Explain your reasoning · Write and solve an inequality

A bike rental costs $8 to start plus $3 per hour. A student has at most $20. Write and solve an inequality to find how many whole hours the student can rent the bike. Check the boundary value.

Open a sample approach and scoring guide

One possible approach: 8 + 3h ≤ 20; subtract 8 to get 3h ≤ 12; divide by 3 to get h ≤ 4. The student can rent for at most 4 whole hours. At 4 hours the cost is $20.

2-point guide: 1 point for a correct inequality and solving steps; 1 point for h ≤ 4 and checking that 4 hours costs $20.

Try the problem before opening the example. A tutor or teacher can use the guide to discuss your representation and reasoning.

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