Lesson 1 Homework Practice Scale Drawings

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:

Lesson objective: Understand that scale drawings may be larger, smaller or the same size as an original figure.

Students bring prior knowledge of proportions from Grade 7, Unit 1; 7.G.A.4. This prior knowledge is extended to scaling dimensions of rectangles as students multiply by various scale factors. A conceptual challenge students may encounter is that dimensions must be scaled using multiplication, not addition. 

The concept is developed through work with photographs, which helps students recognize that each dimensions has to scale up or down by the same factor to keep from distorting the image. 

This work helps students deepen their understanding of numbers because the value of the scale factor relative to 1 determines whether the scale drawing is larger, smaller, or the same size as the original.

Students engage in Mathematical Practice 4 (Model with mathematics) as they scale factors to model the changes made to a rectangular photograph.

Key vocabulary:

  • original figure
  • proportions
  • scale drawing
  • scale factor

Special materials needed:

  • Optional: have students bring in school photos to enlarge or shrink.

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