Braids for Days
By: Daisy Lefler and Gillian Hooper
Problem Intro:
Claire is braiding Sophie's hair with three strands. Sophie wants her hair braided so the braid has returned to its original position.
A)
-If Claire has already done 27 loops in Sophie's hair, how many times has the braid repeated and how many looks until it repeats again.
B)
-Now try with any number of starting loops.
C)
-Create a table with the information you found in problem B.
Challenge option:
-Now try with four or more strands.
Write-Up:
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Problem Statement
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Process: Describe your thinking process during this problem. What ideas worked? What ideas didn’t work? Where did you get stuck and how did you get unstuck?
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Solution: Give specific examples of your solution. If you did find a solution explain what you have. If you found a formula prove that it works.
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Reflection: Reflect on this problem. Include two habits of a mathematician.
Sat Problem:
In the figure above, three wires are braided. That is, by starting in order A, B, C, the outer left wire A is brought over wire B to the middle position, forming the order shown in step 1, then the outer right wire C is brought to the new middle position shown in step 2, and so on, alternately bring each new left and each new right wire to the middle. At what number step does the briad first repeat the original order A, B, C?
A. 3
B. 4
C. 5
D. 6
E. 7
Adapted from ¨The Official SAT Study Guide by CollegeBoard¨ (New York Collegeboard, 2009)