Lesson 1: What are Scaled Copies?
Let’s explore scaled copies.
Illustrative Math Unit 7.1, Lesson 1 (printable worksheets)
Lesson 1 Summary
The following diagram describes some characteristics of a scaled copy and how to tell whether or not a figure is a scaled copy of another figure.
Lesson 1.1 Printing Portraits
Here is a portrait of a student. Move the slider under each image, A–E, to see it change.
- Which images are most like the original? Which are least like the original? Explain your reasoning.
- Some of the sliders make scaled copies of the original portrait. Which of the Portraits A–E do you think are scaled copies? Explain your reasoning.
- What do you think “scaled copy” means?
Lesson 1.2 Scaling F
On the top left is the original drawing of the letter F. There are also several other drawings.
- Identify all the drawings that are scaled copies of the original letter F drawing. Explain how you know.
- Examine all the scaled copies more closely, specifically, the lengths of each part of the letter F. How do they compare to the original? What do you notice?
- On the grid, draw a different scaled copy of the original letter F.
Lesson 1.3 Pairs of Scaled Polygons
Your teacher will give you a set of cards that have polygons drawn on a grid. Mix up the cards and place them all face up.
- Take turns with your partner to match a pair of polygons that are scaled copies of one another.
a. For each match you find, explain to your partner how you know it’s a match.
b. For each match your partner finds, listen carefully to their explanation, and if you disagree, explain your thinking.
- When you agree on all of the matches, check your answers with the answer key. If there are any errors, discuss why and revise your matches.
- Select one pair of polygons to examine further. Use the grid below to produce both polygons. Explain or show how you know that one polygon is a scaled copy of the other.
Are you ready for more?
Is it possible to draw a polygon that is a scaled copy of both Polygon A and Polygon B? Either draw such a polygon, or explain how you know this is impossible.
Lesson 1 Practice Problems
- Is it possible to draw a polygon that is a scaled copy of both Polygon A and Polygon B? Either draw such a polygon, or explain how you know this is impossible.
- Tyler says that Figure B is a scaled copy of Figure A because all of the peaks are half as tall.
Do you agree with Tyler? Explain your reasoning.
- Here is a picture of the Rose Bowl Stadium in Pasadena, CA.
Here are some copies of the picture. Select all the pictures that are scaled copies of the original picture.
- Complete each equation with a number that makes it true.
The Open Up Resources math curriculum is free to download from the Open Up Resources website and is also available from Illustrative Mathematics.
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