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Algebraic thinking. When one number is near a Hundred. When One Number Is Near a Hundred. 98 + 48 Add on 2 - to make a tidy number 97 + 38 Similar but add on three 96 + 87 Generalisation is what always works Number added on changed, but reason for didn’t - PowerPoint PPT Presentation
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Algebraic thinking
When one number is near a Hundred
Level 1 Level 2 Level 3 Level 4 Level 4-5
1-1 CA CAI AC EA AA AM AP
AddSub
9% 32% 40% 19%
AddSub
1% 14% 39% 37% 8%
MultDiv
1% 8% 19% 35% 25% 11%
MultDiv
2% 12% 27% 34% 20% 5%
PropRatio
12% 23% 28% 27% 9%
PropRatio
1% 16% 29% 17% 31% 5%
Level 1 Level 2 Level 3 Level 4 Level 4-5
1-1 CA CAI AC EA AA AM AP
AddSub
1% 14% 39% 37% 8%
AddSub
5% 26% 46% 23%
MultDiv
2% 12% 27% 34% 20% 5%
MultDiv
6% 16% 32% 30% 16%
PropRatio
1% 16% 29% 17% 31% 5%
PropRatio
6% 23% 17% 41% 12%
When One Number Is Near a Hundred98 + 48Add on 2 - to make a tidy number
97 + 38Similar but add on three
96 + 87Generalisation is what always works
• Number added on changed, but reason for didn’t• Know that what you add on, you must subtract
Algebraic thinking
98 + 48 = (98 + ) + (48 _____
If I do this…
What do I do here?
Algebraic thinking
98 + 48 = (98 + ) + (48 - )
Algebraic Thinking
98 + 47 =
– Here = means get the answer
Algebraic Thinking
97 + 96 = 98 + 95
– Is this true?– Here = means balance
Algebraic Thinking
98 + 84 = 95 + 87
– Wrong structure– Must be up and down
Algebraic Thinking
84 + 39 = 81 + 41
– And be the same amount
Algebraic Thinking
61 + 58 = 59 +
64 + = 61 + 38
Algebraic Thinking
6 + = 9 +
Insert a pair of numbers that make this true
Algebraic Thinking
6 + = 9 +
Write a statement to link these that is always true
Algebraic Thinking
7 + = 11 +
Make a general statement
Algebraic Thinking
10 + = 6 +
Make a general statement
Algebraic Thinking
41 + n = 43 + _______
– Don’t simplify, use the structure
Algebraic Thinking
41 + n = 43 + (n - 2)
– Because 41 goes up 2, n must go down 2
