Lesson 6: Scaling and Area
About this lesson
This lesson is optional. In this lesson, students are introduced to how the area of a scaled copy relates to the area of the original shape. Students build on their grade 6 work with exponents to recognize that the area increases by the square of the scale factor by which the sides increased. Students will continue to work with the area of scaled shapes later in this unit and in later units in this course. Although the lesson is optional, it will be particularly helpful for students to have already had this introduction when they study the area of circles in a later unit.
In two of the activities in this lesson, students build scaled copies using pattern blocks as units of area. This work with manipulatives helps accustom students to a pattern that many find counterintuitive at first (MP8). (It is a common but false assumption that the area of scaled copies increases by the same scale factor as the sides.) After that, students calculate the area of scaled copies of parallelograms and triangles to apply the patterns they discovered in the handson activities (MP7).
Lesson overview

6.1 Warmup: Scaling a Pattern Block (10 minutes)
 There is a digital applet in this activity.

6.2 Optional Activity: Scaling More Pattern Blocks (10 minutes)
 Includes "Are you Ready for More?" extension problem
 There is a digital applet in this activity.
 6.3 Optional Activity: Area of Scaled Parallelograms and Triangles (15 minutes)
 Lesson Synthesis
 6.4 Cooldown: Enlarged Areas (5 minutes)
Learning goals:
 Calculate and compare (orally and in writing) the areas of multiple scaled copies of the same shape.
 Generalize (orally) that the area of a scaled copy is the product of the area of the original figure and the “square” of the scale factor.
 Recognize that a twodimensional attribute, like area, scales at a different rate than onedimensional attributes, like length and distance.
Learning goals (student facing):
 Let's build scaled shapes and investigate their areas.
Learning targets (student facing):
 I can describe how the area of a scaled copy is related to the area of the original figure and the scale factor that was used.
Required materials:
 pattern blocks
 preprinted slips, cut from copies of the blackline master
 geometry toolkits
Required preparation:
 Prepare to distribute the pattern blocks, at least 16 blue rhombuses, 16 green triangles, 10 red trapezoids, and 7 yellow hexagons per group of 3–4 students.
 Copy and cut up the Area of Scaled Parallelograms and Triangles blackline master so each group of 2 students can get 1 of the 2 shapes.
Glossary:
 area  Area is the number of square units that cover a twodimensional region, without any gaps or overlaps. For example, the area of region A is 8 square units. The area of the shaded region of B is \(\frac12\) square unit.
 Access the complete Grade 7 glossary.
Standards
 This lesson builds on the standard:CCSS.6.G.A.1MS.6.G.1MO.6.GM.A.1
 This lesson builds towards the standards:CCSS.7.G.B.4MS.7.G.4MO.7.GM.A.4bCCSS.7.G.B.6MS.7.G.6MO.7.GM.B.6aCCSS.7.RP.A.2.aMS.7.RP.2aMO.7.RP.A.2a
IM 6–8 Math was originally developed by Open Up Resources and authored by Illustrative Mathematics, and is copyright 20172019 by Open Up Resources. It is licensed under the Creative Commons Attribution 4.0 International License (CC BY 4.0). OUR's 6–8 Math Curriculum is available at https://openupresources.org/mathcurriculum/.
Adaptations and updates to IM 6–8 Math are copyright 2019 by Illustrative Mathematics, and are licensed under the Creative Commons Attribution 4.0 International License (CC BY 4.0).
Adaptations to add additional English language learner supports are copyright 2019 by Open Up Resources, and are licensed under the Creative Commons Attribution 4.0 International License (CC BY 4.0).
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