Recognise odd and even numbers

What you will learn

• Recognise odd and even numbers

Models used: number sentences, stories, diagrams.

Before you start

• Continue number patterns

Can everybody find a partner?

Six counters can make three complete pairs.

1. There are 3 groups, with 2 objects in each group. Count a group before counting them all.

   Six counters can make three complete pairs.

   2 + 2 + 2 = 3 × 2 = 6

2. Each bag is one group. Counters outside the bags are left over.

   Give the group one more counter. That counter has no partner.

   Equal sharing means every share has the same amount. Check both conditions: the shares match, and all the starting objects are accounted for.

   Group 1: 2

   Group 2: 2

   Group 3: 2

3. Each bag is one group. Counters outside the bags are left over.

   Six is even. Seven is odd because one is left without a partner.

   7 = 2 + 2 + 2 + 1

   Equal sharing means every share has the same amount. Check both conditions: the shares match, and all the starting objects are accounted for.

   Group 1: 2

   Group 2: 2

   Group 3: 2

Worked example: A new example, together

Is 274 odd or even?

1. The number at the top of each column is the value of one counter in that column.

   Make pairs. Look for a counter without a partner.

   Even numbers form complete pairs; odd numbers leave one over.

2. The number at the top of each column is the value of one counter in that column.

   Every complete ten can be paired.

   A digit tells us how many units there are. Its position tells us what size those units are; that is why a zero can matter.

   Is 274 odd or even?

   Even

3. The number at the top of each column is the value of one counter in that column.

   Check the ones digit.

   A digit tells us how many units there are. Its position tells us what size those units are; that is why a zero can matter.

4. The number at the top of each column is the value of one counter in that column.

   274 pairs exactly, so it is even.

   A digit tells us how many units there are. Its position tells us what size those units are; that is why a zero can matter.

5. The number at the top of each column is the value of one counter in that column.

   Check the result against the question we started with.

   274 = 2 × 137.

   We found Even. Even numbers form complete pairs; odd numbers leave one over.

Common mistakes to discuss

• Judging by size. Only the ones digit decides. 274 looks large but pairs exactly, so it is even; 13 is small and leaves one over, so it is odd.

Check your understanding

• Recognise odd and even numbers
• use pairs to tell odd from even
• check the answer against the original quantities and units

Explain your reasoning to an adult, then try a fresh question in the interactive lesson. A result from one attempt is not proof of lasting mastery.