1. starter × Odd Even + Odd Even
Complete the table using the word odd or even.
Give an example for each ×
Odd
Even +
Odd
Even

2. starter × Odd Even + Odd Even
Complete the table using the word odd or even.
Give an example for each ×
Odd
Even +
Odd
Even

3. For addition and multiplication
Proof of Odd and Even
For addition and multiplication

4. Proof of odd and even Objective
To understand how to prove if a number is odd or even through addition or multiplication
Success criteria
Represent an even number
Represent an odd number
Prove odd + odd = even
Prove odd + even = odd
Prove even + even = even
Prove odd × odd = odd
Prove odd × even = even
Prove even × even = even

5. Key words Integer Odd Even Arbitrary Variable Addition Multiplication
Proof
Constant
Factor

6. How to represent an even number
All even numbers have a factor of 2
All even numbers can be represented as
Where n is any integer value
2=2×1 14= 2×7 62=2×31 2n

7. How to represent an odd number
All odd numbers are even numbers minus 1
All odd numbers can be represented as
Where n is any integer value
3 = = =
2n – 1 or 2n + 1

8. Proof that odd + odd = even
Odd numbers can be written 2n – 1
Let m, n be any integer values
odd + odd = 2n m - 1
= 2n + 2m - 2
factorise
= 2(n + m - 1)
This must be an even number as it has a factor of 2

9. Proof that odd + even = odd
Odd numbers can be written 2n – 1
Even numbers can be written 2m
Let m, n be any integer values
odd + even = 2n m
= 2n + 2m - 1
partially factorise
= 2(n + m) - 1
This must be an odd number as this shows a number that has a factor of 2 minus 1

10. Proof that even + even = even
Even numbers can be written 2n
Let m, n be any integer values
even + even = 2n + 2m
factorise
= 2(n + m)
This must be an even number as it has a factor of 2

11. Proof that odd × odd = odd
Odd numbers can be written 2n – 1
Let m, n be any integer values
odd × odd = (2n – 1)(2m – 1)
= 4mn - 2m – 2n + 1
partially factorise
= 2(2nm - m - n) + 1
This must be an odd number as this shows a number that has a factor of 2 plus 1

12. Proof that odd × even = even
Odd numbers can be written 2n – 1
Even numbers can be written 2m
Let m, n be any integer values
odd × even = (2n – 1)2m
= 4mn - 2m
partially factorise
= 2(mn - m)
This must be an even number as it has a factor of 2

13. Proof that even × even = even
Even numbers can be written 2n
Let m, n be any integer values
even + even = (2n)2m = 4mn
partially factorise
= 2(2mn)
This must be an even number as it has a factor of 2

14. Exercise 1
Prove that three odd numbers add together to give an odd number.
Prove that three even numbers add together to give an even number
Prove that two even and one odd number add together to give an odd number
Prove that two even and one odd number multiplied together give an even number

15. Exercise 1 answers 2n – 1 + 2m – 1 + 2r – 1
= 2n + 2m + 2r – 2 – 1 = 2(n + m + r – 1) – 1
2n + 2m + 2r
= 2(n + m + r – 1)
2n + 2m + 2r – 1
= 2(n + m + r) – 1
(2n)(2m)(2r – 1)
= 4mn(2r – 1) = 8mnr – 4mn = 2(4mnr – 2mn)

16. Word match
Formula that represent area have terms which have order two formula have terms that have order three that have terms of order are neither length, area or volume. Letters are used to represent lengths and when a length is multiplied by another we obtain an Constants are that do not represent length as they have no units associated with them. The letter π is often used in exam questions to represent a
Formula, area, length, numbers, constant, Volume, represent, mixed, Greek

17. Word match answers
Formula that represent length have terms which have order two. Volume formula have terms that have order three. Formula that have terms of mixed order are neither length, area or volume. Letters are used to represent lengths and when a length is multiplied by another length we obtain an area. Constants are numbers that do not represent length as they have no units associated with them. The Greek letter π is often used in exam questions to represent a constant

18. Title - review Objective To Success criteria Level – all To list
Level – most
To demonstrate
Level – some
To explain

19. Review whole topic
Key questions