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 drawings. They discover that the relationship between the perimeter of figures is the same as the relationship between the corresponding sides of the figures. In other words, the same scale factor used to scale a figures side lengths is the same multiplier for comparing the perimeters. This works because perimeter is a linear measure. For instance, a reactangle with side lengths a and b has a perimeter of 2(a + b). If we scale the side lengths by a factor of n, the new perimeter is 2(an + bn) or 2n(a + b). A conceptual challenge students may encounter is believing the perimeter scaled by n and not 2n.
The concept is developed through work with a rectangle, which students manipulate to see how the perimeter changes as the dimensions are scaled up and down.
This work helps students deepen their understanding of equivalence because as students study the proportional relationship between original figures and scale drawings, they will extend the idea of equivalent ratios to include figures that are proportionally equivalent.
Students engage in Mathematical Practice 6 (attend to precision) as they ensure that the scale factor includes the proper units, for example if the dimensions of the original figure are in feet and the scale drawing dimensions are in inches, the scale factor must account for that.
Key vocabulary:
- original figure
- perimeter
- proportion
- ratio
- scale drawing
- scale factor
Special materials needed:
- grid paper
- optional: geo boards and rubber bands
