Curriculum / Math / 7th Grade / Unit 5: Percent and Scaling / Lesson 12
Math
Unit 5
7th Grade
Lesson 12 of 19
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Define and identify scale images.
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.
The foundational standards covered in this lesson
5.NF.B.5 — Interpret multiplication as scaling (resizing), by:
5.NF.B.5.A — Comparing the size of a product to the size of one factor on the basis of the size of the other factor, without performing the indicated multiplication.
5.NF.B.5.B — Explaining why multiplying a given number by a fraction greater than 1 results in a product greater than the given number (recognizing multiplication by whole numbers greater than 1 as a familiar case); explaining why multiplying a given number by a fraction less than 1 results in a product smaller than the given number; and relating the principle of fraction equivalence a/b = (n×a)/(n×b) to the effect of multiplying a/b by 1.
7.RP.A.2 — Recognize and represent proportional relationships between quantities.
The essential concepts students need to demonstrate or understand to achieve the lesson objective
Suggestions for teachers to help them teach this lesson
This lesson introduces a new topic in this unit on scale drawings. In this lesson, students understand what it means to be a scale copy of another image and they begin to make connections to proportionality and percent. In the lessons that follow, students will investigate these relationships further to define and use scale factor and percent in various applications.
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Problems designed to teach key points of the lesson and guiding questions to help draw out student understanding
These are scale giants:
These are NOT scale giants:
What do you think makes a giant scale? What makes a giant NOT scale?
Marcellus the Giant by Eli Luberoff is made available by Desmos. Copyright © 2017 Desmos, Inc. Accessed Dec. 27, 2017, 11 a.m..
Five figures are shown below.
a. Which figures are scale images of Figure 1? Explain your reasoning why.
b. Which figures are not scale images of Figure 1? Explain your reasoning why.
Polygon 2 is a scaled copy of Polygon 1. Use the image to answer the questions.
a. Name 2 sets of corresponding points between Polygon 1 and Polygon 2.
b. Name 2 sets of corresponding line segments between Polygon 1 and Polygon 2.
c. Name 2 sets of corresponding angles between Polygon 1 and Polygon 2.
A set of suggested resources or problem types that teachers can turn into a problem set
Give your students more opportunities to practice the skills in this lesson with a downloadable problem set aligned to the daily objective.
A task that represents the peak thinking of the lesson - mastery will indicate whether or not objective was achieved
Li drew two images of the letter T in a grid, as shown below.
Li says the larger T is a scaled image of the smaller T because the larger T is twice the height of the smaller T. Do you agree with Li? Explain why or why not.
An example response to the Target Task at the level of detail expected of the students.
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.
Lesson 11
Lesson 13
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.
Find the percent given a part and the whole.
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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.
Find the percent of increase or decrease given the original and new amounts.
Solve percent problems fluently, including percent increase and decrease.
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.
Solve percent applications involving measurement and percent error.
Topic D: Scale Drawings
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.
Use scales in maps to find actual distances between locations.
Use scales in floor plans to find actual measurements and dimensions.
Compute actual areas from scale drawings.
Draw scale drawings at different scales.
Create a scale floor plan (optional).
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