Combining groups

Version 0.2 · expanded edition · built from cited public sources Content is based on the official frameworks and sources listed under Sources and standards. No official endorsement is claimed. Written in the style of common primary school assessments. No exam result is promised.

Student lesson

Words to know

1. Discover: two teams

Team Red has 4 children. Team Blue has 3 children. If they join to make one big team, how many children are in the big team?

2. Understand: combining groups

To combine two groups, put them together and count all. Team Red (4) and Team Blue (3) make 7. We write 4 + 3 = 7.

If Blue comes first and Red second, we still get 7: 3 + 4 = 7. The order of the groups does not change the total.

Idea 1: Combine two groups

Put 3 red counters and 4 blue counters in one pile. You combined the groups. Count all: 7.

Idea 2: Count all, then count on

You can count all from one. A faster way is to start at the first number and count on: from 3, say 4, 5, 6, 7.

Why faster? You do not count the first group again.

Idea 3: Order does not change the total

3 + 4 = 7 and 4 + 3 = 7. If you swap the groups, the total stays the same.

Why? It is the same counters. We only changed the order we count them.

3. Worked examples

Example 1 (I show you): Add 3 + 4

Combine: 🟥🟥🟥 🟦🟦🟦🟦

1. Count the red: 3.
2. Count on the blue: 4, 5, 6, 7.

Answer: 3 + 4 = 7

Example 2 (We do it together): Swap the groups

Work out 5 + 2 and 2 + 5.

1. 5 + 2: start at 5, count on 6, 7.
2. 2 + 5: start at 2, count on 3, 4, 5, 6, 7.

Answer: Both are 7.

Example 3 (You try): Write the sentence

There are 6 beads and 1 bead. Write the sentence.

Did you know?

Adding in any order gives the same total. It is easier to start with the bigger number and count on.

Why this matters

We combine groups when we mix two baskets of fruit, join two teams or count coins from two pockets.

4. Explore: swap the groups

You need 10 counters in two colours.

1. Make 5 red counters and 2 blue counters. Count all.
2. Write 5 + 2 = 7.
3. Now swap: 2 blue then 5 red. Count all.
4. Write 2 + 5 = 7. What do you notice?

5. Practise

Say it in a sentence

Use these starters when you talk about the lesson. Say them out loud.

• I combined ___ and ___.
• The total is ___.
• ___ + ___ has the same total as ___ + ___.
• The addition sentence is ___.

Guided practice

Independent practice

Level 1: Start

1. 3 + 4 = __
2. 4 + 3 = __
3. What do you notice about 3 + 4 and 4 + 3?
4. Draw a group of 2 and a group of 5. How many altogether?
5. Write an addition sentence for 6 and 1.

Level 2: Grow

1. 5 + 3 = __
2. 3 + 5 = __
3. Combine 2 stars and 6 stars. How many?

Level 3: Stretch

1. If 6 + 4 = 10, what is 4 + 6?
2. Start with the bigger number and count on to work out 2 + 7.
3. Tom has 5 red and 3 blue marbles. Ana has 3 red and 5 blue marbles. Who has more?

Answers are in the answer key below. Try first, then check.

6. Apply: everyday mathematics

There are 5 birds on a tree and 3 birds on a wall. How many birds are there altogether?

Another one. You have 4 mangoes in one bag and 6 mangoes in another. How many mangoes in all?

7. Common mistakes

8. Lesson summary and revision card

9. Check and master

Answer all 14 questions. You will see feedback after each one.

Show my result

10. Key takeaways

• Combine groups by putting them together and counting all.
• The order does not change the total.
• Write the sentence with + and =.

11. Next lesson

Next lesson: Addition using objects. Keep going with the next idea in this course.

Exam practice

These questions are written in the style of common school and international primary assessments. Try them on your own, without looking back. Then check your answers in the marking guide. The marks are shown in brackets.

1. Work out 4 + 5. [1 mark]
2. Write another sum with the same total as 3 + 6. [1 mark]
3. Ben has 5 books. Mia has 4 books. How many books do they have altogether? Write the addition sentence. [2 marks]
4. If 8 + 2 = 10, what is 2 + 8? Explain. [2 marks]
5. Draw 3 circles and 5 circles. Write the addition sentence. [2 marks]

Total: 8 marks.

Printable worksheet

1. 5 + 2 = __
2. 2 + 5 = __
3. 6 + 3 = __
4. 4 + 4 = __
5. Is 1 + 6 the same as 6 + 1? (yes or no)
6. 4 + 4 = __
7. 2 + 7 = __
8. 7 + 2 = __
9. Write an addition sentence for 5 and 1.
10. Is 3 + 6 the same as 6 + 3?

Homework

Take 2 small piles of things at home, for example 4 and 3. Count the total. Swap the piles and count again. Tell a family member what you found.

Answer key and marking scheme

Practice answers: Worksheet: 1 7; 2 7; 3 9; 4 8; 5 yes.

Quiz answers: 1 A, 2 B, 3 C, 4 A, 5 B, 6 A, 7 B, 8 C, 9 A, 10 B, 11 C, 12 A, Challenge 1 C, Challenge 2 C.

Extra worksheet answers (items 6 onward): 6 8; 7 9; 8 9; 9 5 + 1 = 6; 10 Yes. Both are 9..

Independent practice answers. Level 1: 1 7; 2 7; 3 they are the same, because the order does not change the total; 4 2 + 5 = 7; 5 6 + 1 = 7. Level 2: 1 8; 2 8; 3 8. Level 3: 1 10; 2 Start at 7: 8, 9. The total is 9.; 3 They have the same, 8 each, because 5 + 3 = 3 + 5..

Mastery and remediation

Courseversity badge thresholds (overall quiz score): Gold = 90–100%; Silver = 80–89.9%; Bronze = 70–79.9%. A badge is never a full record of progress.

If a learner struggles

1. Find the misconception: Thinking that 2 + 5 and 5 + 2 give different answers. The order does not change the total. Check with counters.
2. Explain another way: use real objects first, then pictures.
3. Show a simpler example: Combine two groups of 1 to 3 counters, count all, then swap the groups.
4. Guided practice: work through one example together and let the learner try the next one.
5. Reassess: use the quiz again or the worksheet.
6. Move on when the learner shows Silver-level evidence independently.

For parents and guardians

In this lesson your child combines two groups and finds that order does not change the total. You do not need to be good at mathematics to help.

• Combine two small piles of beans and count all. Then swap the piles.
• Start from the bigger number and count on.
• Ask: what two groups make 8?
• Ask “how do you know?” after each answer, and listen.
• Praise effort, not only right answers. Mistakes are how we learn.
• Ten to fifteen minutes a day is better than one long session.

Teacher package