Lesson plan

# 1. Identify similar shapes by applying scale factors (C)

teaches Common Core State Standards CCSS.Math.Content.8.G.A.3 http://corestandards.org/Math/Content/8/G/A/3
teaches Common Core State Standards CCSS.Math.Practice.MP6 http://corestandards.org/Math/Practice/MP6

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Lesson objective: Understand that a dilation of a two-dimensional shape produces a shape that is smaller than, larger than, or the same size as the original shape.

Students bring prior knowledge of proportionality from 7.RP.A.2. This prior knowledge is extended to dilations as students determine the impact when applying a scale factor to ordered pairs. A conceptual challenge students may encounter is both coordinates in an ordered pair must be multiplied by the same scale factor to form a similar shape.

The concept is developed through work with coordinate planes, which allow students to identify the coordinates of the preimage then apply the scale factor to the coordinates.

This work helps students deepen their understanding of equivalence because corresponding angles are congruent while the scale factor describes the relationship of the side lengths.

Students engage in Mathematical Practice 6 (attend to precision) as they identify relationships in similar shapes when they apply scale factors to coordinates. Students should notice that the angles remain the same while the sides may decrease, increase, or remain the same.

Key vocabulary:

• dilation
• enlargement
• reduction
• scale factor

Special materials needed:

• graph paper
• highlighters or colored pencils to assist students in identifying the various images