Download Lesson 3.1

 The Empire State Building
has 102 floors and is
1250 feet high. How high
are you when you are
reach the 80th floor?
 Explain your reasoning.
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•
•
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Floor
Number
Height
(ft)
A 25-story building has floors at the
described heights. What recursive
sequence can describe the heights?
Find the height of the 4th and 10th
floors?
Which floor is 217 feet above ground?
How high is the 25th floor?
Basement
(0)
1
2
3
-4
9
22
35
4
… 10 …
… 25
… 217 …
Recursive Toothpick Pattern
Page 159
Materials Needed
Box of Toothpicks
 Step 1: Make Figures 1–3 of the pattern using as few
toothpicks as possible. How many toothpicks does it take to
reproduce each figure? How many toothpicks lie on the
perimeter of each figure?
 Step 2: Copy the table with enough rows for six figures of the
pattern. Make Figures 4–6 from toothpicks by adding
triangles in a row and complete the table.
 Step 3 What is the rule for finding the number of toothpicks
in each figure? What is the rule for finding the perimeter?
Use your calculator to create recursive routines for these
rules. Check that these routines generate the numbers in
your table.
 Step 4: Now make Figure 10 from toothpicks. Count the
number of toothpicks and find the perimeter. Does your
calculator routine give the same answers? Find the number of
toothpicks and the perimeter for Figure 25.
 Find the missing values in each sequence.
 7, 12, 17, ___, 27, ___, ___, 42, ___, 52
 5, 1, -3, ___, -11, -15, ___, ___, -27, ___
 -7, ___, -29, ___, -51, -62, ___, -84, ___
 2, -4, 8, -16, 32, ___, 128, -256, ___, ___
 Complete Problem #6 on page 162 in your
group. Be prepared to present your
solution.
 Complete problem 14 on page 164. Be
prepared to show your solution.
8  2(x  5)  14.8
Description
Undo
Result
Figure 1
Figure 2
Figure 3
 Consider the sequence of pentagons where
each side equals 1 unit and the area of
each pentagon is 1.73 square units.
 Complete the table for five figures.
Figure
Number
1
2
3
4
5
Perimeter
Number of
Toothpicks
Area
Figure 1
Figure 2
Figure 3
 Consider the sequence of pentagons where
each side equals 1 unit and the area of
each pentagon is 1.73 square units.
 Complete the table for five figures.
Figure
Number
Perimeter
Number of
Toothpicks
Area
1
5
5
1.73
2
8
9
1.73(2)=3.46
3
11
13
1.73(3)=5.19
4
14
17
1.73(4)=6.92
5
17
21
1.73(5)=8.65
Figure 1
Figure 2
Figure 3
 Write a recursive routine for the perimeter.
1,5 ;ans(1)  1, ans(2)  3
 Write a recursive routine for the area.
1,5 ;ans(1)  1, ans(2)  4
 Write a recursive routine for the number of
toothpicks.
1,1.73 ;ans(1)  1, ans(2)  1.73
Figure 1
Figure 2
Figure 3
 Find the perimeter of Figure 10.
 Which Figure has a perimeter of 47?
 Which Figure has an area of at least 34 square
units.
Figure
Number
1
2
3
4
5
Perimeter
Number of
Toothpicks
Area