8. (s poinms) Tom has learned the following facts well: .All the sums of whole n
ID: 3195779 • Letter: 8
Question
8. (s poinms) Tom has learned the following facts well: .All the sums of whole numbers that add to 10 or less-Tom knows these facts "forwards and backwards." For example, he knows not only that 5+2 is 7, but also that 7 decomposes into 5 plus 2 or 2 plus 5. . 10+1,10+2,10+3,....10+10. the doubles 1+1,2+2,3+3...,10+10 For each sum in this problem, show at least three different ways that Tom could use reasoning. together with the facts he knows well, to determine the sum. In each case, write equations that correspond to the strategies you describe. Take care to use parentheses appropriately and as needed a. 8+7Explanation / Answer
By using information given in the problem, the following possibilities arrived.
a) 8+7
1st way of Toms reasoning:
8+7 =
=(4+4)+(1+6) (Here 8 is decomposed as 4+4 and 7 is decomposed as 1+6)
=(4+6) + (4+1) (Tom knows 6+4 and 4+1)
=10 +5 (Tom knows 10+5).
2nd way of Toms reasoning:
8+7 =
=(4+4)+(5+2) (Here 8 is decomposed as 4+4 and 7 is decomposed as 5+2)
=(4+2) + 4+5 (Tom knows 4+2)
=(6+4) +5 (Tom knows 6+4)
=10 +5 (Tom knows 10+5).
3rd way of Toms reasoning:
8+7 =
=(3+5)+(5+2) (Here 8 is decomposed as 3+5 and 7 is decomposed as 5+2)
=(5+5)+(3+2) (Tom knows 5+5 and 3+2)
=10+5 (Tom knows 10+5).
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b) 6+7
1st way of Toms reasoning:
6+7 =
=(1+5)+(5+2) (Here 6 is decomposed as 1+5 and 7 is decomposed as 5+2)
=(5+5) + (1+2) (Tom knows 5+5 and 1+2)
=10 +3 (Tom knows 10+3).
2nd way of Toms reasoning:
6+7 =
=(3+3)+7 (Here 6 is decomposed as 3+3)
=(3+7) + 3 (Tom knows 3+7)
=10 + 3 (Tom knows 10+3).
3rd way of Toms reasoning:
6+7 =
=6+(4+3) (Here, 7 is decomposed as 4+3)
=(6+4)+3 (Tom knows 6+4)
=10+3 (Tom knows 10+3).
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c) 8+9
1st way of Toms reasoning:
8+9 =
=(4+4)+(3+6) (Here 8 is decomposed as 4+4 and 9 is decomposed as 3+6)
=(4+6) + (4+3) (Tom knows 4+6 and 4+3)
=10 +7 (Tom knows 10+7).
2nd way of Toms reasoning:
8+9 =
=(5+3)+(5+4) (Here 8 is decomposed as 5+3 and 9 is decomposed as 5+4)
=(5+5) + (3+4) (Tom knows 5+5 and 3+4)
=10 + 7 (Tom knows 10+7).
3rd way of Toms reasoning:
8+9 =
=(1+7)+(3+6) (Here 8 is decomposed as 1+7 and 9 is decomposed as 3+6)
=(7+3)+(1+6) (Tom knows 7+3 and 1+6)
=10+7 (Tom knows 10+7).
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