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# Algebraic Proof

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by

## Mr Mattock

on 25 October 2015

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#### Transcript of Algebraic Proof

Algebraic Proof
Starter
Writing algebraically
Match the algebraic expression to the description
Prove it

Try moving the shaded pattern around the grid. What happens?
Starter
It is 8 times more
Try moving the shaded pattern around the grid. What happens?
It is always 8 times more
Proof and Explanation
What do the outer 8 expressions simplify to when you add them? How does this prove the result we spotted?

Can we explain from each grid why this is happening?
Proof and Explanation
What do the outer 8 expressions simplify to when you add them? How does this prove the result we spotted?
n-8+n-7+n-6+n-1+n+1+n+6+n+7+n+8 = 8n which is 8x the middle.
Can we explain from each grid why this is happening?
The pairs opposite each other add to 2n, so with 4 pairs this makes 8n.
Prove that the top number can be predicted from the
bottom left number.
Prove it
The top number is just the first number add 2 then multiplied by 9 (or multiplied by 9 and add 18)
Proving results
A two digit number is made by reversing the digits of a different two digit number. Prove the the difference between two such numbers will always be a multiple of 9.
L.O. - To prove results using algebra

Proving results
A two digit number is made by reversing the digits of a different two digit number. Prove the the difference between two such numbers will always be a multiple of 9.
The two numbers are 10x + y and 10y + x.
The difference is (10x + y) - (10y + x) = 10x - x + y - 10y
= 9x - 9y = 9(x - y).
Which is a multiple
of 9.
Proving results
Prove the sum of the squares of 2 consecutive numbers is odd.
Proving results
Prove the sum of the squares of 2 consecutive numbers is odd.
n + (n+1) =
n + n + 2n + 1 =
2n + 2n + 1 =
2(n + n) + 1
Which is an odd number (of the form
2 x something + 1)
2
2
2
2
2
2
Main Activity 2
Prove the results on the algebraic proof sheet.
Writing algebraically
Main Activity 2
1). (2n+1) - (2n - 1) = (4n + 4n + 1) - (4n - 4n + 1) = 8n
2
2
2
2
2). (2n+1) + (2n - 1) = (4n + 4n + 1) + (4n - 4n + 1) = 8n +2 = 4(2n ) + 1
2
2
2
2
2
2
3). (10x + y) + (10y + x) = 11x + 11y = 11(x + y)
4). (2n) + (2n - 1) = 4n + 4n + 4n + 1 = 8n + 4n + 1 = 4(2n + n) + 1
2
2
2
2
2
2
5). n + (n+1) + (n+2) + (n+3) + (n+4) = n + n + 2n + 1 + n + 4n + 4 +
n + 6n + 9 + n + 8n + 16 = 5n + 20n + 30 = 5(n + 4n + 6)
2
2
2
2
2
2
2
2
2
2
2
2
6). 1000x + 100y + 10x + y = 1010x + 101y = 101(10x + y)
Key
Examples

Activities
Activity