In this unit students extend prior knowledge of ratio and proportion to relate the areas of scale drawings using scale factors. This unit builds towards Grade 8, Unit 3, which focuses on transformations and dilations. Students are likely to struggle with the idea of squaring the linear scale factor to find the area scale factor.
Key Concepts:
 Scale drawings may be larger, smaller, or the same size as an original drawing.
 Lengths of sides of pairs of scale drawings are proportional, resulting in proportional perimeters.
 Areas of pairs of scaled figures are related by the square of the scale factor.
Prior Knowledge Needed:
 Multiply fractions by whole numbers; (Grade 4, Unit 11; 4.NF.B.4)
 Interpreting multiplying fractions as scaling; (Grade 5, Unit 7; 5.NF.B.5)
 Finding area; (Grade 6, Unit 10; 6.G.A.1)
 Proportional relationships in scale drawings; (Grade 7, Unit 1; 7.G.A.4)
Units on the Horizon:
 Describe the effect of dilations on 2dimensional figures and understand similarity (Grade 8, Unit 3; 8.G.A.3)
Lessons

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 rectan...

Lesson objective: Compute scale drawing dimensions using scale factors. This lesson helps to build procedural skill with scaling figures up or down. A rectangle is used here because it supports student understanding of changing dimensions without changi...

Lesson objective: Apply scale factors to determine distances on a map given actual distances. This lesson provides an opportunity for students to apply their knowledge and understanding of scale drawings to a reallife situation. Students are asked to d...

Lesson objective: Understand that the proportional relationship between the corresponding sides of similar figures extends to the perimeters of the figures. Students' prior knowledge of proportional relationships is extended to perimeters of scale drawi...

Lesson objective: Compute perimeters of scale drawings using scale factors. This lesson helps to build procedural skill with determining scale values. A rectangle is used here because it enables students to see how the changing dimensions change the per...

Lesson objective: Apply scale factors to find the perimeters of actual buildings given a sketch of the buildings. This lesson provides an opportunity for students to apply their knowledge and understanding of scaled perimeters to a reallife situation. ...

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 ...

Lesson objective: Compute the area of scale figures by using the square of the scale factor and the original area. This lesson helps to build "procedural skill" with computing areas of scale figures using the square of a scale factor. Rectangular arrays...

Lesson objective: Apply scale factors to find the areas of scale drawings. This lesson provides an opportunity for students to apply their knowledge and understanding of scale drawings to a reallife situation. Students are asked to determine the amount...

Lesson objective: Apply scale factors to dimensions, perimeter and area. This lesson provides an opportunity for students to apply their knowledge and understanding of scale drawings to a reallife situation. Students are asked to reason about mathemati...