Lesson 14 | Percent and Scaling | 7th Grade Mathematics

Objective

Use a scale to determine actual measurements.

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

Interpret a scale in a scale drawing.
Use a scale in a scale drawing to find actual measurements using strategies such as a table, equation, or proportion.

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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

Vincent proposes an idea to the student government at his school to install a basketball hoop along with a court, as shown in the diagram below. The school administration tells Vincent that in order for his plan to be approved, it must fit in the empty lot on the school property. The empty lot measures 25 feet by 75 feet.

Will the lot be big enough for the court Vincent planned? Justify your answer.

Guiding Questions

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References

EngageNY Mathematics Grade 7 Mathematics > Module 1 > Topic D > Lesson 18 — Example 1

Grade 7 Mathematics > Module 1 > Topic D > Lesson 18 of the New York State Common Core Mathematics Curriculum from EngageNY and Great Minds. © 2015 Great Minds. Licensed by EngageNY of the New York State Education Department under the CC BY-NC-SA 3.0 US license. Accessed Dec. 2, 2016, 5:15 p.m..

Modified by Fishtank Learning, Inc.

Problem 2

A projector is connected to your computer and projects onto a large wall. The projector enlarges what is on your computer screen by a scale factor of 325%. An image on your computer is $${8 {1\over2}}$$ inches long. What is the length of the projected image on your wall?

Guiding Questions

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Problem 3

Sherry designed her garden as shown below in the diagram.

a. After designing the garden, Sherry decided to build the garden 75% of the size represented in the diagram. What will be the outside dimensions of the actual garden?

b. If Sherry plans to use a wire fence to go around the garden and to divide each section of the garden, how much fence does she need?

c. The fence costs $3.25 per foot plus 7% sales tax. What is the total cost of the fence?

Guiding Questions

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References

EngageNY Mathematics Grade 7 Mathematics > Module 4 > Topic C > Lesson 14 — Example 2

Grade 7 Mathematics > Module 4 > Topic C > Lesson 14 of the New York State Common Core Mathematics Curriculum from EngageNY and Great Minds. © 2015 Great Minds. Licensed by EngageNY of the New York State Education Department under the CC BY-NC-SA 3.0 US license. Accessed Dec. 2, 2016, 5:15 p.m..

Modified by Fishtank Learning, Inc.

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 company sells rugs online on their website. The image of one rug on the website measures $$2\frac{1}{2}"$$ by $$3\frac{1}{4}"$$. The scale for the image that corresponds to the actual size of the rug is $$1$$ inch: $$2\frac{1}{2}$$ feet. Find the actual measurements of the rug.

Student Response

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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.

Include images of pictures (such as from a catalog or magazine) with a given scale, and ask what the actual measurements are (do not include any area problems); include some percent scales.

EngageNY Mathematics Grade 7 Mathematics > Module 1 > Topic D > Lesson 18 — Exercises, Examples, and Problem Set

Lesson 13

Lesson 15

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

Anchor Problems

Problem 1

Guiding Questions

References

Problem 2

Guiding Questions

Problem 3

Guiding Questions

References

Problem Set

Target Task

Student Response

Additional Practice

Lesson Map

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