Recognise odd and even numbers

What you will learn

• Recognise odd and even numbers

Models used: number sentences, stories, tables.

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.

   Complete pairs use two at a time. One counter without a partner makes an odd count.

   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. Read one place at a time. Read each value with the heading above its column.

   Look for a counter left without a partner, not just the number of rows.

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

   Read one place at a time

   Place	Digit	Value
   hundreds	2	200
   tens	7	70
   ones	4	4

2. Read one place at a time. Read each value with the heading above its column.

   Every complete ten can be paired.

   Read one place at a time

   Place	Digit	Value
   hundreds	2	200
   tens	7	70
   ones	4	4

   Is 274 odd or even?

   Even

3. Read one place at a time. Read each value with the heading above its column.

   Every complete ten can be paired.

   Read one place at a time

   Place	Digit	Value
   hundreds	2	200
   tens	7	70
   ones	4	4

4. Read one place at a time. Read each value with the heading above its column.

   Check the ones digit.

   Read one place at a time

   Place	Digit	Value
   hundreds	2	200
   tens	7	70
   ones	4	4

5. Read one place at a time. Read each value with the heading above its column.

   274 pairs exactly, so it is even.

   Read one place at a time

   Place	Digit	Value
   hundreds	2	200
   tens	7	70
   ones	4	4

6. Read one place at a time. Read each value with the heading above its 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.

   Read one place at a time

   Place	Digit	Value
   hundreds	2	200
   tens	7	70
   ones	4	4

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
• explain odd and even counts using pairs
• 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.