AI generatedAlgebraKey Stage 3

Writing expressions for even and odd integers

Use and with integer .

  • State that the variable represents an integer when proving integer properties.
  • Use algebra to cover every permitted value. Factor out the divisor or 2 when helpful.
  • One counterexample disproves a universal statement; several examples do not prove it.

Example 1

Write expressions for an even integer and the odd integer 1 greater than it. State what your variable represents.

Even integerLet be any integer.
Odd integerAn even number plus an odd number is odd.
and , where is an integer.

Example 2

Write expressions for an even integer and the odd integer 3 greater than it. State what your variable represents.

Even integerLet be any integer.
Odd integerAn even number plus an odd number is odd.
and , where is an integer.

Your turn

Question 1

Write expressions for an even integer and the odd integer 5 greater than it. State what your variable represents.

Check answer
Even integerLet be any integer.
Odd integerAn even number plus an odd number is odd.
and , where is an integer.
Question 2

Write expressions for an even integer and the odd integer 7 greater than it. State what your variable represents.

Check answer
Even integerLet be any integer.
Odd integerAn even number plus an odd number is odd.
and , where is an integer.
Question 3

Write expressions for an even integer and the odd integer 9 greater than it. State what your variable represents.

Check answer
Even integerLet be any integer.
Odd integerAn even number plus an odd number is odd.
and , where is an integer.
Question 4

Write expressions for an even integer and the odd integer 11 greater than it. State what your variable represents.

Check answer
Even integerLet be any integer.
Odd integerAn even number plus an odd number is odd.
and , where is an integer.
Question 5

Write expressions for an even integer and the odd integer 13 greater than it. State what your variable represents.

Check answer
Even integerLet be any integer.
Odd integerAn even number plus an odd number is odd.
and , where is an integer.
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