7th Grade Math

GLE 0706.1.2 Apply and adapt a variety of appropriate strategies to problem solving, including estimation,

and reasonableness of the solution. Also addresses GLE 0706.2.3, GLE 0706.2.4, SPI 0706.2.7.

282 Proportions and Similarity

Problem-Solving Investigation

Multi-Part

Lesson 2

Draw a Diagram

GRACE: I am making trail mix for my sister’s

birthday party. On Saturday, I bought sunflower

seeds and peanuts in a ratio of 3:4. On Sunday,

I bought sunflower seeds and peanuts in a ratio

of 2:3. I bought 18 ounces of sunflower seeds and

peanuts altogether. How many ounces of peanuts did

I buy?

YOUR MISSION: Draw a diagram to determine how

many ounces of peanuts Grace bought.

Main Idea Solve problems by drawing a diagram.

Scale Drawings and Models

PART A BC

Understand You know that she bought two mixtures of sunflower seeds and peanuts, one in the

ratio of 3 : 4 and the other in the ratio of 2 : 3. She bought 18 ounces of mixture.

Plan Draw a diagram to represent the two mixtures.

Solve Start with a bar diagram representing the mixtures.

3 : 4 ratio of sunflower seeds to peanuts 2 : 3 ratio of sunflower seeds to peanuts

peanuts peanuts peanuts peanuts

sunflower

seeds

sunflower

seeds

sunflower

seeds

peanuts peanuts peanuts

sunflower

seeds

sunflower

seeds

There is a total of 12 parts. Each part represents 18 ÷ 12 or 1.5 ounces. So, she

bought 7 · 1.5 or 10.5 ounces of peanuts.

Check For each mixture, there are more peanuts than sunflower seeds. So, more than

half of the total should be peanuts. The answer is reasonable. 

1. E WRITE MATH How can drawing a diagram be useful when solving a
   real-world problem?

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Multi-Part

Lesson 2

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