Lesson 16 | Percent and Scaling | 7th Grade Mathematics

Objective

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

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 floor plan to understand what it tells you about the space.
Use a scale in a floor plan to find actual dimensions.
Determine a scale in a floor plan and use it to find missing dimensions.

Tips for Teachers

Suggestions for teachers to help them teach this lesson

This lesson introduces students to floor plans as scale drawings. They must make sense of what they are looking at and how the floor plan may represent an actual apartment. Using the measurements and/or scale given to them, they can find actual dimensions of the rooms in the apartments. Students should ask themselves if the measurements they find make sense in the context of an apartment space (MP.1). In Lesson 19, students will have the opportunity to create their own floor plans.

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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 floor plan for an apartment is shown below.

Find the actual dimensions of the rooms indicated in the table.

Room	Scale Drawing Dimensions	Actual Dimensions
Bedroom 2
Closet (above Bedroom 1)
Kitchen
Entire apartment

Guiding Questions

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References

EngageNY Mathematics Grade 7 Mathematics > Module 1 > Topic D > Lesson 19 — Source for image

Grade 7 Mathematics > Module 1 > Topic D > Lesson 19 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..

Problem 2

Travis is a realtor and is renting the apartment whose floor plan is shown below. He uses the floor plan to show potential renters how the apartment is laid out and the sizes of the rooms.

The living room and large bedroom are missing the actual dimensions. Travis knows that on the scale drawing of the floor plan, the kitchen measures 5.5 cm by 6.25 cm.

a. What is the scale of the floor plan?

b. What are the actual dimensions of the living room and the large bedroom if on the scale drawing they measure 7.5cm by 6.75 cm and 6.5 cm by 5.5 cm, respectively?

Guiding Questions

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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

At a lake, there is the option to rent a cabin to sleep in overnight. The floor plan shows the dimensions of the cabin (not including the backyard).

What are the actual dimensions of the cabin (not including the backyard)?

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.

Include problems where students are given a floor plan with a scale and must determine the actual measurements of the rooms.
Spiral in problems from Lessons 14 and 15.

EngageNY Mathematics Grade 7 Mathematics > Module 4 > Topic C > Lesson 14 — Examples and Problem Set; these problems are not about floor plans, but spiral in percent scale in finding actual measurements.

Lesson 15

Lesson 17

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

Anchor Problems

Problem 1

Guiding Questions

References

Problem 2

Guiding Questions

Problem Set

Target Task

Student Response

Additional Practice

Lesson Map

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