Mathematics K–6 · Years 3–4
Odd or even: pairing counters
Number and algebra
This site has no interactive model of its own. Where a step or a material names a Concept Studio model, simulation or tool, it has not been built; an external simulation a step names (for example PhET) is not part of this site.
The idea
An even number of counters pairs up with none left over, an odd number has one left over, and pairing shows why two odd numbers add to an even number.
What you need
- 40 counters
- a strip of paper with two rows of boxes (a two-row frame)
- number cards 1 to 30
- a recording table with columns number, pairs, left over, odd or even
How to do it
- Draw a number card, count out that many counters and place them in the two-row frame, filling both rows in step. Record the pairs and whether one is left over.
- Do this for every number from 1 to 20 and look at the pattern of odd and even down the table.
- Take 13 counters (odd) and 15 counters (odd) in separate frames. Push the two frames together and see what happens to the two leftovers.
- Repeat with 12 and 15, then with 12 and 14, and record whether each sum is odd or even.
- Test the rule on numbers ending in 0, 2, 4, 6 and 8 and on numbers ending in 1, 3, 5, 7 and 9 to link odd and even to the last digit.
What you should see
13 counters make 6 pairs with 1 left over, and 15 make 7 pairs with 1 left over; pushed together the two leftovers form a pair, so 28 makes 14 pairs with none left over. Odd plus odd is even, odd plus even is odd (12 and 15 give 27, one left over) and even plus even is even. Every number ending in 0, 2, 4, 6 or 8 pairs with none left over and every number ending in 1, 3, 5, 7 or 9 has one left over.
What changes
This activity lists no variables to change, measure and keep the same.
Common misconceptions
Each of these ideas is wrong, and the activity is a chance to test it.
- Odd plus odd is odd because both numbers are odd.
- A number is odd if it has an odd number of digits.
Safety card
Hazards
- none beyond ordinary classroom materials
Controls
- none needed
Note
No chemicals or heat are used, so the NSW Department of Education Chemical Safety in Schools package is not needed; ordinary classroom supervision under the school's usual risk management.
Curriculum references
The NSW syllabus outcomes and Australian Curriculum v9 codes this activity supports. They are references, not a verified or complete curriculum alignment.
Sources
The pages the author read to write this activity.