Problem Solving with Proportional Relationships

Problem Solving with Proportional Relationship

​Objective: The student will solve problems by writing and solving proportion.

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Math Standard:

MA.7.GR.1.5: Solve mathematical and real-world problems involving dimensions and areas of geometric figures, including scale drawings and scale factors.

Clarification 1: Instruction focuses on seeing the scale factor as a constant of proportionality between corresponding lengths in the scale drawing and the original object.

Clarification 2: Instruction includes the understanding that if the scaling factor is k, then the constant of proportionality between corresponding areas is k2 .

Clarification 3: Problem types include finding the scale factor given a set of dimensions as well as finding dimensions when given a scale factor.

Connecting Benchmark MA.7.AR.4.4 Suggested Material​

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Essential Question:​ Beatrice ran 8 miles in 3 hours. Write three different proportions to find how long it will take her to run 12 miles. How do you know each proportion will solve the problem?

• Scan the Problem.

• ​Underline the clues.

• Restate the question in your own words.

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​Understand the Problem

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Multiple Choice

The two rectangles are scale drawings. What is the measurement of x?

• 21
• 1.25
• 20
• 4

Multiple Choice

• 0.25
• 0.5
• 2
• 1/2

Multiple Choice

Which figure is scale copy of the original figure?

• A

• B

• C

• D

Multiple Choice

What is the scale factor from ΔDEF to ΔABC?

• 1/2
• 7/3
• 2
• 10/3

Multiple Choice

Scale is 1cm = 8km. Hatboro and Smithville are 24cm apart on the map, what is the actual distance between the 2 cities?

• 87 km
• 216 km 
• 33 km
• 192 km

Multiple Choice

Which equation matches the graph?

• y = 7x
• y = 42x
• y = 6x
• y = 2x

Multiple Select

Select all graphs that represent proportional relationships.

Multiple Choice

What is the equation y=kx for the table?

• y=1/3x
• y=3x
• y=5x
• y=1/5x

Multiple Choice

Find missing side

• 5
• 7
• 9
• 11

Multiple Choice

What is the scale factor from the small fry to the large fry?

• 1/3

• 48

• 4

• 3

Multiple Choice

Is Figure B a scaled copy of Figure A?

• Yes

• No