Exploring Houses

1. Exploring Houses Austin Fischer Kristen Stoll Vanessa Vertin

2. Building Houses Determine the total number of pieces for each house. Sketch House 5, House 6, and House 7.

3. Building Houses What do you notice from House 2  House 3? What do you notice from House 4  House 5? Do you see a pattern? Predict House 15 Recursive... vs. Explicit… 45 y=# of pieces n=house # y=3n a =3 a =a ∙3 1 n n-1

4. Your Initials • Make growing patterns using an initial in your name. • Size 1, Size 2, Size 3, Size 4 • Make table or chart to organize information • How does your letter change from step to step? • Can you write an equation to find the nth size?

5. Garden Patterns Draw Garden 5 for Pattern A and Pattern B Pattern for Pattern A… Pattern for Pattern B… How does Pattern A relate to Pattern B? Add 3 to each garden Add 5 to each garden

6. Stamps Draw Size 5 • Recursive • vs. • Explicit a =10 a =a +6 1 n n-1 y=# of stamps n=# of rods y=6n+4 • What happens to the number of stamps if each rod is 3 units long? • 4 units?

7. Dots Using a peg board, construct Shape 5. Do you see a pattern? Add two for each new shape

8. Which formula is the best? Recursive Explicit

9. Hints to Teachers • Allow students to use physical materials. • Students could have difficulties dealing with squares AND triangles in the same pattern. • Use material students can glue to paper to display in classroom. • Some initials could cause difficulties. • Have students organize information in a chart or table.