Find the missing part

What you will learn

• Find a missing part when the whole and one part are known
• Show a whole and its two parts with a number bond
• Explain why taking away finds a missing part

Models used: counters, number bonds, bar models, number lines, number sentences, stories.

Before you start

• Add by combining two sets
• Missing numbers in take-away

Why taking away finds the missing part

Count the blue counters: 5. Count the orange counters: 3. These are our two parts.

1. One counter stands for one object. The colours keep our two parts easy to follow.

   Count the blue counters: 5. Count the orange counters: 3. These are our two parts.

   5 blue

   3 orange

2. Each counter stands for one object. The separate groups are parts; count all the groups to find the whole.

   Put the two parts together. There are 8 counters altogether. We call all of them the whole.

   5 + 3 = 8

   The whole includes both colours. Count every counter once; none has been added or taken away.

   5 blue

   3 orange

3. Whole: 8. Blue part: 5. Orange part: 3.

   A number bond is a short way to show the same picture. The 8 at the top is the whole; 5 and 3 below are its parts.

   The circles show numbers, not extra counters. The branches connect each part to the whole it belongs to.

   8whole

   part5

   part3

4. Crossed blue counters: taken away. Orange counters without crosses: still here.

   Now take away the 5 blue counters. Crosses show the counters we removed. Count only the orange counters that remain.

   8 − 5 = 3

   Subtraction starts with the whole and removes one part. The other part is what remains.

   5 taken away

   3 orange
   If we put the 5 blue counters back, how many would there be?

   Eight again. The 3 orange counters and the 5 blue counters make the same whole: 3 + 5 = 8.

5. The numbers stay the same. We change which part of their story we are telling.

   Addition joins the parts. Subtraction finds one part when we know the whole and the other part.

   5 + 3 = 8 · 8 − 5 = 3

   8whole

   part5

   part3

Worked example

□ + 7 = 15

1. What are we trying to find?

   What does the box stand for?

   a missing part

2. Something plus 7 makes 15. So 15 is the whole and 7 is one part.

   15

   ?7

3. Show it as a number bond.

   15whole

   part?

   part7

4. Addition and subtraction undo each other. Take the part we know away from the whole.

5. Work it out.

   15 − 7 = ?

   What is 15 − 7?

   8

6. So the missing part is 8.

   □ = 8

7. Check by adding the parts.

   8 + 7 = 15 ✓

Common mistakes to discuss

• Adding the two numbers that are shown. In □ + 3 = 8 the 8 is the whole. The missing part must be smaller than 8, so 8 + 3 cannot be right.
• Counting the starting number again when counting on. Start at the part you know and say the next numbers: 4, 5, 6, 7, 8. Count the jumps, not the starting number.

Check your understanding

• find the missing number in □ + 3 = 8 and 5 + □ = 9
• show a whole and its parts with counters and a number bond
• use subtraction to find a missing part
• check a missing part by adding the parts

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.