Courseversity

Lesson

Combining groups

Primary EducationGrade 1MathematicsCV-PRI-G01-MATH-OPS-U01-L0245–60 min

You will learn

  • Combine two groups to find the total.
  • Count all to find the sum.
  • Show that the order of the groups does not change the total.
  • Write the addition sentence for combined 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

The lesson in 60 seconds

  1. Combine means put two groups together.
  2. Count all to find the total.
  3. 3 + 4 and 4 + 3 have the same total.
  4. Write what you did: 3 + 4 = 7.

Words to know

combine
Put together.
group
Things that are together.
total
The number you get when you add.
sentence
A number sentence, like 3 + 2 = 5.

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.

4
3
4 + 3 = 7

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.

Remember: Combine groups and count all. Changing the order does not change the total: 4 + 3 = 3 + 4.

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.

Show the steps and answer
  1. Write 6 + 1.
  2. Count on 1 from 6: 7.

Answer: 6 + 1 = 7

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?
Think about it: what did you notice?

Both orders give 7. 5 + 2 = 2 + 5.

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

Question 1. 4 + 3 = ?

7.

Question 2. Is 2 + 6 the same as 6 + 2?

Yes, both equal 8.

Question 3. 5 red and 1 blue. How many in all?

5 + 1 = 6.

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?

Show a sample answer

5 + 3 = 8 birds.

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

Show a sample answer

4 + 6 = 10 mangoes.

7. Common mistakes

Mistake: Thinking that 2 + 5 and 5 + 2 give different answers.
Fix: The order does not change the total. Check with counters.
Another mistake: Thinking 3 + 4 and 4 + 3 have different totals.
Fix: Swap the groups and count again. The total is still 7.
Another mistake: Counting only one group.
Fix: Count the first group and then the second group. Say the total last.

8. Lesson summary and revision card

I can…

  • I can combine two groups to find the total.
  • I can count all to find the sum.
  • I can show that order does not change the total.
  • I can write the addition sentence for combined groups.

9. Check and master

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

1. 4 + 3 = ?

2. Which is the same as 5 + 2?

3. 6 + 1 = ?

4. Combine 3 stars and 3 stars. How many stars?

5. Which sentence matches 2 red and 4 blue counters?

6. 2 + 6 = ?

7. Which is the same as 4 + 3?

8. 5 + 4 = ?

9. Combine 4 stars and 2 stars. How many stars?

10. Which sentence matches 3 red and 5 blue counters?

11. If 6 + 3 = 9, what is 3 + 6?

12. What is the total of 1 and 8?

Challenge 1. If 7 + 2 = 9, what is 2 + 7?

Challenge 2. Sam says 7 + 2 is harder than 2 + 7. Is he right?

Your result appears here after you answer every question.

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.

Marking guide and model answers
  1. 9 [1]
  2. 6 + 3 [1]
  3. 9 books [1]; 5 + 4 = 9 [1]
  4. 10 [1]. Order does not change the total [1].
  5. Correct drawing [1]; 3 + 5 = 8 [1]

Score guide: 7 to 8 = secure. 5 to 6 = nearly there, revise the parts you missed. Under 5 = work through the lesson again with a grown-up.

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

Question Expected response Marks
5 + 2 = __ 7 2
2 + 5 = __ 7 2
6 + 3 = __ 9 2
4 + 4 = __ 8 2
Is 1 + 6 the same as 6 + 1? (yes or no) yes 2
Total 10

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

Objective Bronze (Developing) Silver (Proficient) Gold (Advanced)
O1 Combine two groups to find the total Shows this with help from an adult or a picture Does this independently and explains how they know Explains it clearly and uses it in a new situation
O2 Count all to find the sum Shows this with help from an adult or a picture Does this independently and explains how they know Explains it clearly and uses it in a new situation
O3 Show that the order of the groups does not change the total Shows this with help from an adult or a picture Does this independently and explains how they know Explains it clearly and uses it in a new situation
O4 Write the addition sentence for combined groups Shows this with help from an adult or a picture Does this independently and explains how they know Explains it clearly and uses it in a new situation

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

1–5. Objectives, prerequisites, materials, preparation, duration

Lesson objectives. Learners will: combine two groups to find the total; count all to find the sum; show that the order of the groups does not change the total; write the addition sentence for combined groups.

Prerequisite knowledge. Lesson 1: the meaning of addition.

Materials. Counters (stones, seeds or bottle tops), paper, pencils, board or chalkboard. Low-resource options: use stones, seeds, sticks, bottle tops or drawings in the sand or on the board instead of printed materials.

Preparation. Gather the counters and draw the example pictures on the board before the lesson.

Suggested duration. 45–60 minutes. It can be split into two shorter sessions.

6–9. Teaching procedure, explanation notes, guided and independent activities

Introduction (5 min). Start with the Discover situation and let learners suggest ideas before you teach.

Explanation (10 min). Teach the Understand section with real objects first, then pictures, then symbols and words.

Guided activity (10 min). You need 10 counters in two colours. Learners follow the Explore steps in pairs.

Independent activity (10 min). Learners complete the independent practice and the worksheet.

Assessment and reflection (5 min). Ask each learner to say one thing they learned and how they know it.

Key questions. What happens if we swap the groups? Which number is easier to start with? How do you know the total?

Teacher explanation notes. Use the concrete, pictorial, abstract order: real objects first, then pictures, then symbols and words. Return to real objects whenever a learner needs support.

10–12. Differentiation, formative assessment, common misconceptions

Support. Use real objects and work with a partner; say each step aloud together. Extension. Ask learners to make up their own example and explain it to a partner.

Formative assessment. Listen to learner explanations, ask “how do you know?”, and check the independent work.

Misconceptions. Thinking that 2 + 5 and 5 + 2 give different answers. The order does not change the total. Check with counters.

13–15. Assessment questions, answer keys, marking scheme

Use the quiz and worksheet on this page. The 8-mark exam practice scheme, the 10-mark scheme and all answers are in the answer sections above. Re-check every answer and the marking scheme before publication.

16–19. Remediation, enrichment, homework, teacher reflection

Remediation. Combine two groups of 1 to 3 counters, count all, then swap the groups. Enrichment. Invite learners to find or create three more examples at home or in the classroom and explain them. Homework. See above.

Teacher reflection. After teaching, record: which concepts learners understood; which misconceptions occurred; which activities worked; which learners need more practice; and what to improve next time.

Sources and standards

This lesson is based on the sources below, and no official endorsement is claimed. Reference starting points named in the Courseversity standard: Common Core State Standards for Mathematics, Cambridge Primary and the IB Primary Years Programme. Where a standard code is named, it points to the official framework.

Official standards for this topic area. Common Core State Standards for Mathematics (official site): Grade 1 » Operations & Algebraic Thinking; Grade 1 » Number & Operations in Base Ten. These pages list the standards that cover this topic area; read them alongside the lesson.

Research used to shape this lesson. Common Core 1.OA.B.3 (order and addition); Cambridge Primary Mathematics Stage 1. These sources informed the lesson.

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