← All Grade 6 unit checks · Course lessons

Grade 6 Math · Unit 1

Ratios, rates, and proportional relationships

Use this low-stakes check after studying the unit. It has 8 fresh questions and one written reasoning prompt. No timer, grade, or gate blocks your next lesson.

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1. A paint mix uses 2 cups of blue for every 5 cups of white. If the same mix uses 6 cups of blue, how many cups of white are needed?

Understanding Ratios 6.RP.A.1 Review lesson

2. Which colon notation matches the ratio “6 to 11”?

Writing Ratios in Different Forms 6.RP.A.2 Review lesson

3. A paint mixture uses blue paint and white paint in the ratio 5:2. If you want to double the recipe, what is the new ratio?

Equivalent Ratios 6.RP.A.3 Review lesson

4. A ratio table pairs 3 notebooks with 6 dollars and 6 notebooks with 12 dollars. At the same rate, what is the cost of 9 notebooks?

Ratio Tables 6.RP.A.3 Review lesson

5. A store sells apples for 1.20 per pound. If you buy 3.5 pounds of apples, how much will you pay?

Unit Rates 6.RP.A.2 Review lesson

6. Store A sells 8 apples for 4. Store B sells 6 apples for 3. Which store has the cheaper price per apple?

Comparing Unit Rates 6.RP.A.2 Review lesson

7. The ratio of boys to girls in a class is 3:2. There are 12 boys. How many girls are in the class?

Solving Ratio Problems 6.RP.A.3 · 6.RP.A.3.d Review lesson

8. If 5 pencils cost $2, how much do 15 pencils cost at the same price per pencil?

Proportions and Cross Multiplication 6.RP.A.3 Review lesson

Explain your reasoning · Equivalent ratios

A bead pattern uses 3 blue beads for every 5 white beads. If it uses 20 white beads, how many blue beads are needed? Show a ratio table or double number line and explain why the ratio stays equivalent.

Open a sample approach and scoring guide

One possible approach: 12 blue beads. Scale 5 white beads to 20 by multiplying by 4; multiply 3 blue beads by 4 as well. A table or double number line should show 3:5 and 12:20.

2-point guide: 1 point for a correct representation or scale factor of 4; 1 point for 12 blue beads with an explanation that both quantities scale by the same factor.

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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