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Recursive Toothpick Pattern

The Empire State Building has 102 floors and is 1250 feet high. How high are you when you are reach the 80 th floor? Explain your reasoning. A 25-story building has floors at the described heights. What recursive sequence can describe the heights?

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Recursive Toothpick Pattern

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  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.

  2. 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?

  3. Recursive Toothpick Pattern Page 159 Materials Needed Box of Toothpicks

  4. 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.

  5. 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.

  6. 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, ___, ___

  7. Complete Problem #6 on page 162 in your group. Be prepared to present your solution.

  8. Complete problem 14 on page 164. Be prepared to show your solution.

  9. 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 1 Figure 2 Figure 3

  10. 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 1 Figure 2 Figure 3

  11. Write a recursive routine for the perimeter. • Write a recursive routine for the area. • Write a recursive routine for the number of toothpicks. Figure 1 Figure 2 Figure 3

  12. 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 1 Figure 2 Figure 3

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