Even and odd numbers

What even and odd mean

A number is even if that many objects can be put into pairs with none left over, and odd if one is always left without a partner. Even numbers can also be split into two equal groups: 8 is 4 + 4. Odd numbers can't: 9 is 4 + 4 with 1 more.

On this page you choose how many counters to show, from 1 to 30. Press Pair up and the counters slide into pairs, two to a column, with a dashed loop around each pair. If one counter has no partner, it turns coral and is labeled. The readout says how many pairs there are, whether one is left over, and whether the number is even or odd. In Sort mode, eight number cards wait to go into the Even or Odd bin.

Why pairing helps

Children often learn "even numbers end in 0, 2, 4, 6 or 8" as a rule to remember. Pairing shows what even means. Once a child sees 14 as seven pairs, the rule about last digits makes sense: every ten pairs up perfectly, so only the ones digit can leave a counter over. Pairing also prepares for doubling and the 2 times table.

Common mix-ups

• Thinking a number with an odd tens digit is odd, such as calling 30 or 14 odd. Pair them up: nothing is left over.
• Believing 0 is neither even nor odd. Zero objects leave nobody without a partner, so 0 is even.
• Thinking odd numbers are "bigger" or "smaller" than even ones. They take turns: odd, even, odd, even.
• Guessing from how a number looks. In Sort, Check with counters lets a child pair it up instead.

A 10-minute even and odd routine

• Show 6 counters. Ask whether everyone will have a partner, then press Pair up.
• Press + once to show 7. Ask what happened to the new counter.
• Pair up 12 and 13, then ask the child to predict 20 and 21 before checking.
• Switch to Sort and let the child sort all eight cards, using Check with counters when unsure.
• Ask the child to explain how they could tell 28 is even without pairing up all 28 counters.

Where it fits by grade

• Kindergarten and Grade 1: counting, doubles and equal groups build the idea of pairs.
• Grade 2: decide whether a group of up to 20 objects has an odd or even number of members, by pairing or by counting in 2s, and write an even number as a sum of two equal addends (2.OA.C.3).
• England: Year 1 counts in multiples of twos, and Year 2 recalls the 2, 5 and 10 times tables, including recognizing odd and even numbers.

Learning more

Times tables are a skill on Eurekami's skill map, starting with counting in 2s, and Daily Practice brings them back when they start to fade. Lessons draw diagrams live from the numbers in each question.