Add by combining two sets

What you will learn

• Add by combining two sets

Models used: number sentences, stories, diagrams.

Before you start

• Use ordinal numbers from first to tenth

Put two groups together

We have 2 counters and add 1 more. How many are there altogether? (2 + 1)

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

   Here are 2 blue counters and 1 orange counter.

   The first group is already counted. Holding 8 and counting on 5 is quicker and safer than starting at one.

   2

   1

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

   Start at 2. Count on 1: 3.

   2

   3

   1

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

   So 2 + 1 = 3.

   2 + 1 = 3

   2

   3

   1

Worked example: A new example, together

What is 3 + 8?

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

   Let’s make 10 first. 3 needs 7 more to make 10.

   38

2. So we split 8 into 7 and 1.

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

   3 + 7 = 10. Then 10 + 1 = 11.

   3 + 7 = 10 · 10 + 1 = 11

   38

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

   Use the picture and the steps we have just followed to finish this question.

   38
   What is 3 + 8?

   11

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

   So 3 + 8 = 11.

   3 + 8 = 11

   38

Common mistakes to discuss

• Counting the first set again. The first group is already counted. Hold 8 in mind and count on 5 more, rather than starting from one.

Check your understanding

• Add by combining two sets
• join two groups by counting on from the larger
• 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.