Odd or Even

Activities to try

1. 1

   Pair-them-up frame

   Why it works: A number is even when its objects pair with none left over and odd when exactly one is left over; because adding one either completes a pair or strands a single, odd and even alternate, and every even number is a double (n + n).

   1. Choose a number of counters (start up to 10, then up to 20) and drop them into a two-row frame so they arrange into pairs.
   2. Look at the result: if one counter is left with no partner the number is ODD; if every counter is matched the number is EVEN.
   3. Use a slider or counter to add one and remove one, watching whether the lone counter appears or disappears each time.
   4. Say out loud what changes each step: adding one either strands a single counter (makes it odd) or creates a new pair (makes it even).
   5. Use an 'equal addends' strip to write each even number as n + n (e.g. 8 = 4 + 4).
2. 2

   Predict then check with real counters

   Why it works: Parity is about whether everything pairs with nothing left over, not about size or whether the number can be split into any two groups; this reasoning generalises to larger numbers.

   1. Take a pile of counters (e.g. 13). Before touching them, predict whether they will all get a partner or whether one will be left over, and say why.
   2. Pair them two-by-two to check your prediction.
   3. Discuss: why is 13 odd but 12 even — what changes when you add one more?
   4. Tackle a friend's claim that 'zero is odd because there's nothing to pair', and decide whether 0 is odd or even.
   5. Try reasoning about a large number (e.g. 100 or 24 or 47): how could you tell odd or even without pairing every one?
3. 3

   Counting in 2s and the last-digit rule

   Why it works: Counting in 2s, the alternating number-track pattern, and the last-digit rule all describe the same pairing structure; the digit shortcut is a justified consequence of pairing, not a memorised fact.

   1. Count a group by 2s (hop along a number line in twos) to decide if the total is even, and compare this with the pairing result for the same number.
   2. Colour a number track by odd and even to reveal the alternating pattern.
   3. After the pairing meaning is secure, look at the ones digit of several numbers (e.g. 20, 12, 24, 16, 18, 47, 53) and notice which digits (0,2,4,6,8) go with even.
   4. State and justify the last-digit rule by reasoning that every ten makes 5 pairs with none left over, so whether there is a leftover depends only on the ones; then use it to predict the parity of a larger number.