The idea, step by step
Pairs decide whether a number is even
An even number of objects makes pairs with none left over. An odd number leaves one object without a partner. Zero is even: there is no unpaired object.
Only the ones digit decides whether a whole number is odd or even. Endings 0, 2, 4, 6 and 8 are even; endings 1, 3, 5, 7 and 9 are odd. Tens, hundreds and thousands can already be paired.
Use pairs to explain a rule
Two odd groups each have one leftover. When joined, those two leftovers make a new pair. So odd + odd is even. Joining an even group and an odd group still leaves one unpaired object: even + odd is odd.
Multiplying makes equal groups. If either factor is even, objects can be paired within or across the groups, making an even product. An odd number of odd groups leaves one unpaired object, so odd × odd is odd. Test a rule with small examples and explain why the pairs work.
A common trap
Calling 1,024 odd because its first digit is 1.
Instead: Look at the ones digit, not the first digit. It ends in 4, so it is even.
See the thinking
Classify a large number
Is 8,137 odd or even? Explain without drawing 8,137 dots.
- Its ones digit is 7.
- Seven ones make three pairs and one leftover. The thousands, hundreds and tens add no leftover.
Predict a total
Without adding fully, decide whether 215 + 387 is odd or even.
- Both numbers end in odd digits.
- Each odd group has one leftover. The two leftovers pair together.
Check your understanding
Must 6 × 13 be odd or even?
Show answer
Even.
Six equal groups can be paired together. A product with an even factor is even.
Your turn
6 questions · 9 marks · Work at your own pace.
Read the questions online
- List the even numbers: 17, 28, 40, 53, 66.1 mark
- Is 7,205 odd or even? Give a reason.1 mark
- Complete the rule: even + even is ____.1 mark
- Without finding the exact total, classify 4,018 + 723.2 marks
- Give two different odd numbers whose sum is 20.2 marks
- A learner says odd × odd is always even. Use a calculation to disprove this and state the correct rule.2 marks
Read the worked solutions
Equivalent correct methods earn the corresponding marks. Include units where asked.
- List the even numbers: 17, 28, 40, 53, 66.1 mark
Their ones digits are 8, 0 and 6.
28, 40 and 66. - Is 7,205 odd or even? Give a reason.1 mark
The last digit determines the leftover after pairing.
Odd, because its ones digit is 5. - Complete the rule: even + even is ____.1 mark
Joining two groups made entirely of pairs still gives complete pairs.
Even. - Without finding the exact total, classify 4,018 + 723.2 marks
4,018 is even and 723 is odd.
Even + odd is odd.
Odd. - Give two different odd numbers whose sum is 20.2 marks
Check that both numbers are odd and their sum is 20.
For example, 7 and 13. Other valid pairs include 1 and 19, 3 and 17, or 9 and 11. - A learner says odd × odd is always even. Use a calculation to disprove this and state the correct rule.2 marks
Both factors are odd, but 15 is odd: the proposed rule is false.
An odd number of odd groups leaves one object unpaired.
For example, 3 × 5 = 15. Odd × odd is odd.
Curriculum reference & lesson scope
Australian Curriculum v9 and SA Curriculum Mathematics
Place-value revision; odd/even properties; addition/subtraction strategies; missing values; rounding/checking.
Official curriculum source ↗