In this lesson, students analyze the effect of scaling on an area. The Warm-up builds on work students did in grade 8 evaluating square roots of small perfect squares and determining that some square roots are irrational. This practice with perfect squares primes them to recognize that dilating by a scale factor of multiplies areas by .

Knowing the relationship between scale factor and area is a basis for understanding how measurement and dimension are related in geometry. As students observe a pattern in the area of a figure after several different dilations, they are looking for regularity in repeated reasoning (MP8).

Technology isn’t required for this lesson, but there are opportunities for students to choose to use appropriate technology to solve problems. We recommend making technology available.