AC9M4N02 • Homework

Properties of Odd and Even Numbers worksheet

Use this printable homework sheet for written working, application and reflection alongside the online learning activities.

Open practice

Written practice: draw, explain and check

These eight tasks cover the whole topic. Show your model or reasoning before checking the answers. The PDF includes space to write and an answer guide.

  1. Draw 19 counters and circle as many pairs as possible. State the number of pairs and leftovers, then explain whether 19 is odd or even.

  2. Explain why 2 408 is even. Your explanation must connect the ones digit with complete pairs in the tens, hundreds and thousands.

  3. There are 27 whole pencils for two children. Each child must receive the same number. Use as many pencils as possible without cutting them. How many does each get, how many remain, and what does this show?

  4. Predict odd or even for 46 + 28, 35 + 47 and 35 + 28. Explain each prediction using pairs and leftovers.

  5. Predict odd or even for 74 − 26, 75 − 27, 74 − 27 and 75 − 26. Explain how removing complete pairs or an unpaired one helps.

  6. Predict odd or even for 8 × 7 and 5 × 9. Use equal groups or an array to explain why one even factor changes the result.

  7. Draw a flowchart asking whether the ones digit is 0, 2, 4, 6 or 8. Label the Yes and No results, then use it to sort 0, 151, 286 and 403.

  8. A student writes 54 + 32 = 85. Use odd/even properties to show the error. Would changing the answer to 84 prove it correct? Explain and calculate the exact answer.

Answer guide for parents and teachers
  1. Nine pairs and one leftover; 19 is odd because one counter has no partner.
  2. Each group of ten, hundred and thousand can be fully paired. Eight ones make four more pairs, so there is no leftover and 2 408 is even.
  3. Each receives 13 pencils and one remains. 27 is odd, so it cannot be split into two equal whole-number groups using every pencil.
  4. Even, even, odd. Fully paired collections stay paired; two odd leftovers make a new pair; one odd leftover remains when combining odd and even.
  5. The results are even, even, odd and odd. For 74 − 26, remove 13 pairs from 37 pairs, leaving 24 pairs. For 75 − 27, remove 13 pairs and the single leftover from 37 pairs and a leftover, again leaving 24 pairs. For 74 − 27, removing 26 leaves 48, then removing one breaks a pair and leaves 47, odd. For 75 − 26, remove 13 complete pairs; the original single leftover remains, giving 49, odd.
  6. 8 × 7 is even: arrange eight groups of seven, then pair the groups to make four groups of fourteen; each fourteen can be completely paired. 5 × 9 is odd: pair within each of five groups of nine, leaving five single counters; these make two pairs with one left over.
  7. Yes leads to Even; No leads to Odd. Even: 0 and 286. Odd: 151 and 403. Zero divides into two equal groups of zero with none left over.
  8. 85 is odd, but even + even must be even. 84 is even but that does not prove it correct. The exact sum is 86; matching parity alone is not enough.