The Aussie Fir Tree
The Aussie Fir Tree It grows down under
Stage 1
Stage 2
Stage 3
Stage 4
Stage 5
4
The Aussie Fir Tree It grows down under
2. Describe how the pattern is growing?
3. How many unit squares are needed to build a Stage 10 Aussie Fir Tree? Show your work.
4. Given any stage number n, determine a closed form equation to determine the amount of unit squares needed to build the tree.
5. Your mate tells you that exactly 274 unit squares will make an Aussie Fir Tree. He is wrong. Explain to him why his statement is false. (c) joint copyright Silicon Valley Mathematics Initiative, SCALE, New York City DOE, 2010.
5
Now, choose four quadratic functions from p.204 in the book and graph them!
Name TASK
Date
S-Pattern Task1
1
2
3
4
5
1. What patterns do you notice in the set of figures?
2. Sketch the next two figures in the sequence.
1
1 Adapted
from Foreman, L.C. & Bennett, A.B., Jr. (1995). Visual Mathematics: Course II, lessons 1-10. Salem, OR: Math Learning Center.
© 2015 University of Pittsburgh
3. Describe a figure in the sequence that is larger than the 20th figure without drawing it.
TASK
4. Determine an equation for the total number of tiles in any figure in the sequence. Explain your equation and show how it relates to the visual diagram of the figures.
5. If you knew that a figure had 9802 tiles in it, how could you determine the figure number? Explain.
6. Is there a linear relationship between the figure number and the total number of tiles? Why or why not?
2 © 2015 University of Pittsburgh
Stage 1
Stage 2
Stage 3
Stage 4
Stage 5
4
The Aussie Fir Tree It grows down under
2. Describe how the pattern is growing?
3. How many unit squares are needed to build a Stage 10 Aussie Fir Tree? Show your work.
4. Given any stage number n, determine a closed form equation to determine the amount of unit squares needed to build the tree.
5. Your mate tells you that exactly 274 unit squares will make an Aussie Fir Tree. He is wrong. Explain to him why his statement is false. (c) joint copyright Silicon Valley Mathematics Initiative, SCALE, New York City DOE, 2010.
5
Now, choose four quadratic functions from p.204 in the book and graph them!
Name TASK
Date
S-Pattern Task1
1
2
3
4
5
1. What patterns do you notice in the set of figures?
2. Sketch the next two figures in the sequence.
1
1 Adapted
from Foreman, L.C. & Bennett, A.B., Jr. (1995). Visual Mathematics: Course II, lessons 1-10. Salem, OR: Math Learning Center.
© 2015 University of Pittsburgh
3. Describe a figure in the sequence that is larger than the 20th figure without drawing it.
TASK
4. Determine an equation for the total number of tiles in any figure in the sequence. Explain your equation and show how it relates to the visual diagram of the figures.
5. If you knew that a figure had 9802 tiles in it, how could you determine the figure number? Explain.
6. Is there a linear relationship between the figure number and the total number of tiles? Why or why not?
2 © 2015 University of Pittsburgh
