Unit 2, Lesson 1
Projecting and Scaling
Grade 8
Preparation
Lesson Narrative
In this lesson, students build on the ideas from grade 7 that side lengths of scaled copies are proportional, and that the constant of proportionality relating the original lengths to the corresponding lengths in the scaled copy is the scale factor.
Students arrange a set of scaled copies of rectangles to share one angle and observe that the opposite vertices all lie on the same line (MP7). In future lessons, students will see that this is an example of a dilation, a geometric process that produces scaled copies, though it is not necessary that they make this connection in this lesson. A dilation scales the distance of all points from the center of dilation, which in this context is the shared vertex of the shared angle. An optional activity recalls work from grade 7 about scaled copies of rectangles.
Today’s activity is for students to individually reflect on the norms generated so far. During the Cool-down, students provide feedback on the norms, sharing those they agree with and those they feel need revision or removal. These suggestions will inform the next version of the classroom norms.
- Describe (orally) features of scaled copies of a rectangle.
- Identify rectangles that are scaled copies of one another.
Let’s explore scaling.
Required Materials
Activity 1
Activity 2
Activity 3
Required Preparation
Make a space for students to place their sticky notes at the end of the Warm-up. For example, hang a sheet of chart paper on a wall near the door.
If creating sets of rectangles for students ahead of time, prepare and label one set A–E for each pair of students:
- A: One full sheet, 8.5" x 11"
- B: One half sheet, 8.5" x 5.5"
- C: One quarter sheet, 4.25" x 5.5"
- D: One eighth sheet, 4.25" x 2.75"
- E: One sixteenth sheet, 2.125" x 2.75"
Each pair of students will also need a long straightedge (at least 14 inches long), such as a meter or yardstick. Alternatively, long straightedge can be created from newspaper by folding it as shown.
