Lesson 18 | Percent and Scaling | 7th Grade Mathematics

Objective

Draw scale drawings at different scales.

Common Core Standards

Core Standards

The core standards covered in this lesson

7.G.A.1 — Solve problems involving scale drawings of geometric figures, including computing actual lengths and areas from a scale drawing and reproducing a scale drawing at a different scale.

Geometry

7.G.A.1 — Solve problems involving scale drawings of geometric figures, including computing actual lengths and areas from a scale drawing and reproducing a scale drawing at a different scale.

7.RP.A.3 — Use proportional relationships to solve multistep ratio and percent problems. Examples: simple interest, tax, markups and markdowns, gratuities and commissions, fees, percent increase and decrease, percent error.

Ratios and Proportional Relationships

7.RP.A.3 — Use proportional relationships to solve multistep ratio and percent problems. Examples: simple interest, tax, markups and markdowns, gratuities and commissions, fees, percent increase and decrease, percent error.

Foundational Standards

The foundational standards covered in this lesson

7.RP.A.2

Ratios and Proportional Relationships

7.RP.A.2 — Recognize and represent proportional relationships between quantities.

Criteria for Success

The essential concepts students need to demonstrate or understand to achieve the lesson objective

Understand what happens to an image as the scale increases or decreases.
Understand that the actual measurements of a figure do not change, even as the scale and image of the scale drawing increase or decrease.
Redraw a scale drawing using a different scale.

Tips for Teachers

Suggestions for teachers to help them teach this lesson

Lesson Materials

Ruler (1 per student)

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Anchor Problems

Problems designed to teach key points of the lesson and guiding questions to help draw out student understanding

Problem 1

The same image of a cat is shown at three different zoom levels on a computer.

What do you notice about what happens to the scale as you zoom in and out on the image?

Guiding Questions

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Problem 2

Your computer shows you a map of Washington Park in Eugene, Oregon. The scale in the bottom right corner of the map tells us that the length of the bar represents 200 feet on the map.

Clicking a resizing button on the computer screen will result in an image of Washington Park, where the exact same-sized bar now represents 150 feet.

a. Do you think the size of Washington Park under the 150 ft. scale will appear smaller or larger than it was under the 200 ft. scale?

b. Draw an accurate picture/map of Washington Park under this new 150 ft. scale. Use the handout.

c. Was your guess in part (a) correct? Can you explain why the size of the map changed as it did?

Guiding Questions

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References

Illustrative Mathematics Rescaling Washington Park

Rescaling Washington Park, accessed on Dec. 27, 2017, 4:03 p.m., is licensed by Illustrative Mathematics under either the CC BY 4.0 or CC BY-NC-SA 4.0. For further information, contact Illustrative Mathematics.

Problem Set

A set of suggested resources or problem types that teachers can turn into a problem set

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Target Task

A task that represents the peak thinking of the lesson - mastery will indicate whether or not objective was achieved

A toddler indoor basketball hoop is advertised in a magazine. The image of the basketball hoop uses a scale of 1 inch to $${{1\over2}}$$ foot.

Draw another scale image of the basketball hoop using a scale of 1 inch to 2 feet. Label the dimensions of your image.

Student Response

An example response to the Target Task at the level of detail expected of the students.

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Additional Practice

The following resources include problems and activities aligned to the objective of the lesson that can be used for additional practice or to create your own problem set.

EngageNY Mathematics Grade 7 Mathematics > Module 1 > Topic D > Lesson 22 — Problem Set
EngageNY Mathematics Grade 7 Mathematics > Module 1 > Topic D > Lesson 21 — Problem Set
Open Up Resources Grade 7 Unit 1 Lesson 10 — Practice Problems

Lesson 17

Lesson 19

Lesson Map

Topic A: Percent, Part, and Whole

Define percent and convert between fractions, decimals, and percentages. Solve percent problems mentally with benchmark percentages.

7.RP.A.3

Find percent of a number when given percent and the whole.

7.NS.A.3 7.RP.A.3

Find the whole given a part and percent.

7.NS.A.3 7.RP.A.3

Find the percent given a part and the whole.

7.NS.A.3 7.RP.A.3

Topic B: Percent Increase and Decrease

Find a new amount given the original and a percent increase or decrease.

7.EE.A.2 7.RP.A.3

Find the original amount given a new amount after a given percent increase or decrease.

7.EE.A.2 7.RP.A.3

Find the percent of increase or decrease given the original and new amounts.

7.RP.A.3

Solve percent problems fluently, including percent increase and decrease.

7.EE.A.2 7.RP.A.3

Topic C: Percent Applications

Solve percent applications involving discount, tax, and tip.

7.EE.B.3 7.RP.A.3

Solve percent applications involving simple interest, commissions, and other fees.

7.EE.B.3 7.RP.A.3

Solve percent applications involving measurement and percent error.

7.EE.B.3 7.RP.A.3

Topic D: Scale Drawings

Define and identify scale images.

7.G.A.1

Define and determine scale factor between two scale images. Use scale factor to draw scale images.

7.G.A.1 7.RP.A.3

Use a scale to determine actual measurements.

7.G.A.1 7.RP.A.3

Use scales in maps to find actual distances between locations.

7.G.A.1 7.RP.A.3

Use scales in floor plans to find actual measurements and dimensions.

7.G.A.1 7.RP.A.3

Compute actual areas from scale drawings.

7.G.A.1 7.RP.A.3

Draw scale drawings at different scales.

7.G.A.1 7.RP.A.3

Create a scale floor plan (optional).

7.G.A.1 7.RP.A.3

Percent and Scaling

Objective

Common Core Standards

Core Standards

Geometry

Ratios and Proportional Relationships

Foundational Standards

Ratios and Proportional Relationships

Criteria for Success

Tips for Teachers

Lesson Materials

Anchor Problems

Problem 1

Guiding Questions

Problem 2

Guiding Questions

References

Problem Set

Target Task

Student Response

Additional Practice

Lesson Map

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