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Consider this unconventional way to count on the fingers of one hand. We count 1 on the thumb, 2 on the index finger, 3 on the middle finger, 4 on the ring finger, and 5 on the pinky.
Then we turn around and count 6 on the ring finger, 7 on the middle finger, 8 on the index finger, and 9 on the thumb. Then we turn around again and count 10 on the index finger, 11 on the ring finger... and so on. If we continue to count in this way, which finger are we on when we count the number 1000? |
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Response Videos
The response videos are categorized into groups. Compare the videos in each group. What features are shared among the solutions in the same group? What features make the groups different from each other? Would you propose a different grouping?
Response Group A
Andrea & Sara's video response
Ginny's video response
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Ashlyn's video response
Kendall's video response
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Don's video response
Wynne's video response
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Response Group B
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Shelby, Tasha, & Tommy's video response
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Jared's video response
Nathan's video response
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Logan's video response
Nathaniel's video response
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Response Group C
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Chris's video response
Maile's video response
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Kaylyn's video response
Paul's video response
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Follow-up Challenges
The response videos are categorized into groups. Compare the videos in each group. What features are shared among the solutions in the same group? What features make the groups different from each other? Would you propose a different grouping?
Don's solution is like the others in Group A and he gets the same answer, but there's a problem in the way he extends his pattern. What's the problem? Why does he still get the right answer?
Ginny's solution is also like the others in Group A, but there's a problem that leads her to a different answer. What's the problem? Compare her problem and Don's. How are they the same, how are they different?
Nathaniel notes that there are "five 20s in 100". How does this factor in to his solution? Can we apply this same kind of reasoning to solve the challenge in other ways?
Compare Chris's and Kaylyn's solutions. How are they the same? How are they different? What advice would you give to Kaylyn?
Describe Maile's approach in your own words. Does it always work? Can we use her strategy to determine which finger you will end on when counting up to the number 110?
Explore Paul's approach, which introduces the idea of modular arithmetic.
Don's solution is like the others in Group A and he gets the same answer, but there's a problem in the way he extends his pattern. What's the problem? Why does he still get the right answer?
Ginny's solution is also like the others in Group A, but there's a problem that leads her to a different answer. What's the problem? Compare her problem and Don's. How are they the same, how are they different?
Nathaniel notes that there are "five 20s in 100". How does this factor in to his solution? Can we apply this same kind of reasoning to solve the challenge in other ways?
Compare Chris's and Kaylyn's solutions. How are they the same? How are they different? What advice would you give to Kaylyn?
Describe Maile's approach in your own words. Does it always work? Can we use her strategy to determine which finger you will end on when counting up to the number 110?
Explore Paul's approach, which introduces the idea of modular arithmetic.