# The Art of Dilation (Cultural Connections)

**Main Resources**

Project Description (pdf)

WebQuest Slides (pdf)

WebQuest Slides (pdf)

**Handouts**

1. Similar Problems (pdf)

2. Inventing Rules (pdf)

3. Polygon Equations (pdf)

4. More Similar Triangles (pdf)

5. Ladder Crossing (pdf)

6. The Shortest Path (pdf)

7. Introduction to Dilation (pdf)

8. Dilation & Scaling Factors (pdf)

9. More Scaling Factors (pdf)

10. Dilation Practice (pdf)

11. Scaling Factors Summary (pdf)

12. Dilation Puzzles (pdf)

13. What is Preserved? (pdf)

14. Dilation Transformation (pdf)

15. Copy Machine (pdf)

16. Repeated Dilations (pdf)

17. Billy Bear (pdf)

18. Isometric Dot Paper (pdf)

2. Inventing Rules (pdf)

3. Polygon Equations (pdf)

4. More Similar Triangles (pdf)

5. Ladder Crossing (pdf)

6. The Shortest Path (pdf)

7. Introduction to Dilation (pdf)

8. Dilation & Scaling Factors (pdf)

9. More Scaling Factors (pdf)

10. Dilation Practice (pdf)

11. Scaling Factors Summary (pdf)

12. Dilation Puzzles (pdf)

13. What is Preserved? (pdf)

14. Dilation Transformation (pdf)

15. Copy Machine (pdf)

16. Repeated Dilations (pdf)

17. Billy Bear (pdf)

18. Isometric Dot Paper (pdf)

## Topics covered include:

Similarity and Congruence

- Further developing intuitive ideas about the meaning of “same shape” and learning the formal definition of similar (in contrast to last year’s study of congruent)
- Discovering the special properties of triangles in connection with similarity, as well as other features of triangles as special polygons

Proportional Reasoning and the Algebra of Proportions

- Understanding the meaning of proportionality in connection with similarity
- Developing equations of proportionality from situations involving similar figures
- Understanding the role of proportionality in nongeometric situations
- Developing techniques for solving equations involving fractional expressions

Polygons and Angles

- Developing angle sum formulas for triangles and other polygons
- Discovering the properties of angles formed by a transversal across parallel lines
- Discovering the triangle inequality and investigating its extension to polygons

Logical Reasoning and Proof

- Working with the concept of counterexample in understanding the criteria for similarity

Experiments and Data Analysis

- Planning and carrying out controlled experiments
- Collecting and analyzing data
- Identifying key features in graphs of data

Mathematical Modeling

- Using a geometric diagram to represent a real-world situation
- Using scale drawings to solve problems
- Applying properties of similar triangles to real-world situations
- Exploring how models provide insight in a variety of situations