Supplies |
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Play-dough, plastic knife, two counting boards (one with whole numbers and one with fractions), tokens, 3" by 5" index card |
Procedure |
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1. On the 3" by 5" index card, write these fractions: Cut them out to use as labels. |
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| 2. Now flatten your clay into a pancake. You can stick the label 1 into it. Put a token on 1 on the fraction board. |
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| 3. Cut the clay (as best you can) into two halves with a straight cut. Roll them into balls. Stick the two labels 1/2 into the two pieces. Remove the 1 token on the fraction board and replace it by two tokens on 1/2. |
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| 4. Cut one of the 1/2 pieces into 3 equal pieces; roll them into balls. Put 1/6 labels on each of them. Remove one token on 1/2 on the fraction board and replace it with 3 tokens on 1/6. |
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| 5. Cut the other 1/2 piece into 5 equal pieces; roll into balls. Put 1/10 labels on each of them. Remove the other token on 1/2 on the fraction board, and replace it with 5 tokens on 1/10. |
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| 6. Cut one of the 1/6 clay pieces into two equal pieces; roll into balls. Put 1/12 labels on each one. Remove one token on 1/6 on the fraction board, and replace it with 2 tokens on 1/12. |
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| 7. Cut one of the 1/10 pieces into 2 equal pieces. Put 1/20 labels on each of them. Remove one token from 1/10 on the board, and replace it with 2 tokens on 1/20. |
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| 8. Cut one of the 1/12 pieces into five equal pieces; roll into balls. Put 1/60 labels on each one (!). Remove one token from 1/12 on the board, and replace it with 5 tokens on 1/60. |
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| 9. Cut one of the 1/20 pieces into 3 equal pieces; roll into balls. Put 1/60 labels on each one. Remove one token from 1/20 on the board, and replace it with 3 tokens on 1/60. |
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10. Now you have these tokens on the board: 1/6: 2 tokens 1/10: 4 tokens 1/12: 1 token 1/20: 1 token 1/60: 8 tokens Copy this pattern of tokens onto the whole number board. |
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| 11. Now simplify the whole numbers. What do you get? One! |
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This is only one partition of "1" into a sum of fractions.
Can you find others, for example, using fifths? The fractions you need must appear on the counting board!
And you may need to make new labels. Just experiment!
There are other ways to "traverse" the board above. Can you find some?