Lesson plan

7. Areas of scale drawings are related by the square of the scale factor (C)

teaches Common Core State Standards CCSS.Math.Content.7.G.A.1 http://corestandards.org/Math/Content/7/G/A/1
teaches Common Core State Standards CCSS.Math.Practice.MP8 http://corestandards.org/Math/Practice/MP8
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Lesson objective: Understand that the area of a scale drawing is the product of the original area and the square of the scale factor.

Students bring prior knowledge of finding area by creating a figure with equal area from 6.G.A.1. This prior knowledge is extended to finding scaled area as students compare the ratio of the areas of scale drawings to the scale factor. A conceptual challenge students may encounter is thinking the scale factor is doubled instead of squared. 

The concept is developed through work with rectangular array, which illustrates how the original figure tiles the scale drawing by showing how many of the originals it would take to cover the scale drawing.

This work helps students deepen their understanding of operations because students operate with exponents and multiplication to find scaled area.

Students engage in Mathematical Practice 8 (look for and express regularity in repeated reasoning) as they generalize their findings from the table.

Key vocabulary:

  • exponents
  • original figure
  • proportions
  • scale drawings
  • scale factor
  • square (second power)

Special materials needed:

  • optional: algebra tiles