Make Pairs to Test Even or Odd
Decide whether all objects can be grouped into pairs.
Supplied materials
- Paper and pencil, or a trusted adult to read aloud.
- Supplied group: fourteen drawn counters.
Learn the idea
A pair has exactly two objects. An even number can be put into pairs with no object left over. An odd number leaves one unpaired object. Pairing checks the whole group without needing to remember a list of even numbers.
You can move one object from each pair into a top row and the other into a bottom row. For an even total, these rows have equal numbers. Fourteen makes seven pairs and can be written as two equal groups of seven.
- Draw fourteen counters and circle each pair.
- Check that all counters have one partner; count seven pairs.
- Write 14 = 7 + 7, then try eleven counters and look for a leftover.
See the method in action
Fourteen counters form seven pairs with none left over: 14 = 7 + 7. Eleven form five pairs and one leftover: 11 = 5 + 5 + 1, so eleven is odd.
Check your reasoning
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See the answer and explanation
16 = 8 + 8
There are eight objects in each of two equal groups. 8 + 8 = 16; this is an even total. Seven plus nine totals sixteen but does not describe two equal groups.
Take it further
Change the total to seventeen. Eight pairs use sixteen counters and one is left, so seventeen is odd: 17 = 8 + 8 + 1.
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