You will learn
- Write equal groups as repeated addition.
- Find the total by adding.
- Read the sign × as groups of.
- Match a picture to a multiplication sentence.
Version 0.2 · expanded edition · expert review pending Standards alignment: pending verification. Written in the style of common primary school assessments. No exam result is promised.
Student lesson
- Equal groups can be written as repeated addition.
- Add the same number again and again.
- The sign × means groups of.
- 3 × 4 means 3 groups of 4.
Words to know
Adding the same number again and again.
Find the total of equal groups.
Groups of.
The answer to a multiplication.
1. Discover: rows of seats
There are 4 rows of benches with 3 children on each. Instead of counting one by one, we can write 3 + 3 + 3 + 3. What is the total?
2. Understand: repeated addition
Repeated addition adds the same number again and again: 4 + 4 + 4 = 12.
We can write this shorter with the sign × (times): 3 groups of 4 is 3 × 4 = 12. The answer, 12, is the product.
2 + 2 + 2 + 2 = 8 is 4 groups of 2, so 4 × 2 = 8.
Idea 1: Repeated addition
Repeated addition means adding the same number again and again. 5 + 5 + 5 = 15.
Idea 2: Multiplication
We can write repeated addition as multiplication. 4 + 4 + 4 = 3 × 4. The sign × is read times or groups of. The answer is called the product.
Idea 3: Match a picture
3 plates with 4 cakes each: 4 + 4 + 4 = 12 and 3 × 4 = 12.
Why? Multiplying is a short way to add equal groups.
3. Worked examples
Example 1 (I show you): Add
5 + 5 + 5 = ?
- 5 + 5 = 10.
- 10 + 5 = 15.
Answer: 15
Example 2 (We do it together): Write as multiplication
Write 4 + 4 + 4 as a multiplication.
- There are 3 fours.
Answer: 3 × 4
Example 3 (You try): Read ×
What does 3 × 4 mean?
Show the steps and answer
- × means groups of.
Answer: 3 groups of 4
Did you know?
The sign × was first used about 400 years ago.
Why this matters
Multiplication saves time when we add equal groups.
4. Explore: add and times
You need counters and paper.
- Make 3 groups of 4.
- Write 4 + 4 + 4.
- Write 3 × 4 = 12.
- Make 4 groups of 2 and write both ways.
Think about it: what did you notice?
4 + 4 + 4 = 3 × 4 = 12; 2 + 2 + 2 + 2 = 4 × 2 = 8.
5. Practise
Say it in a sentence
Use these starters when you talk about the lesson. Say them out loud.
- ___ + ___ + ___ = ___.
- ___ groups of ___ is ___.
- ___ × ___ = ___.
- The product is ___.
Guided practice
Question 1. 5 + 5 + 5 = ?
15.
Question 2. Write 4 + 4 + 4 as a multiplication.
3 × 4.
Question 3. What does 3 × 4 mean?
3 groups of 4.
Independent practice
Level 1: Start
- 5 + 5 + 5
- 3 + 3 + 3 + 3
- Write 2 + 2 + 2 as a multiplication.
- 4 × 5 = ?
- 6 + 6 = ?
Level 2: Grow
- 4 + 4 + 4 = ___.
- Write 5 + 5 + 5 + 5 as a multiplication.
- 3 × 3 = ___.
Level 3: Stretch
- 8 + 8 + 8 = ___.
- A picture shows 4 plates with 3 cakes each. Write the sentence.
- Ali says 3 × 4 is 3 + 4 = 7. What is wrong?
Answers are in the answer key below. Try first, then check.
6. Apply: everyday mathematics
A shop has 4 shelves with 5 tins on each. Write a multiplication and the total.
Show a sample answer
4 × 5 = 20 tins.
Another one. 5 baskets each hold 2 fruits. Write repeated addition and multiplication.
Show a sample answer
2 + 2 + 2 + 2 + 2 = 10; 5 × 2 = 10
7. Common mistakes
Fix: 3 × 4 means 3 groups of 4: 4 + 4 + 4.
Fix: Use groups of: 3 × 4 is three groups of four.
Fix: The first number is the groups, the second is how many in each.
8. Lesson summary and revision card
- I can write equal groups as repeated addition.
- I can find the total by adding.
- I can read × as groups of.
- I can match a picture to a multiplication.
9. Check and master
Answer all 14 questions. You will see feedback after each one.
Your result appears here after you answer every question.
10. Key takeaways
- Repeated addition adds equal groups.
- × means groups of.
- The answer is the product.
11. Next lesson
Next lesson: Arrays. 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.
- 5 + 5 + 5 = ? [1 mark]
- Write 2 + 2 + 2 + 2 as a multiplication. [2 marks]
- What does 3 × 4 mean? [1 mark]
- Draw or describe 3 × 5 and find the product. [3 marks]
- Ben says 2 × 6 is 8. Is he right? Explain. [3 marks]
Total: 10 marks.
Marking guide and model answers
- 15 [1]
- 4 × 2 [2]. Give 1 mark for 4 twos.
- 3 groups of 4 [1]
- 3 groups of 5 [1]; 5 + 5 + 5 [1]; 15 [1]
- No [1]. 2 × 6 is 2 groups of 6 [1]. 6 + 6 = 12 [1].
Score guide: 9 to 10 = secure. 6 to 8 = nearly there, revise the parts you missed. Under 6 = work through the lesson again with a grown-up.
Printable worksheet
- 5 + 5 + 5
- 3 + 3 + 3 + 3
- 2 + 2 + 2 as ×
- 4 × 5
- 6 + 6
- 2 + 2 + 2 = ___.
- Write 3 + 3 + 3 + 3 as a multiplication.
- 5 × 2 = ___.
- 10 + 10 + 10 = ___.
- 6 + 6 = ___ = 2 × 6.
Homework
Write three repeated additions and their × sentences with objects at home.
Answer key and marking scheme
| Question | Expected response | Marks |
|---|---|---|
| 5 + 5 + 5 | 15 | 2 |
| 3 + 3 + 3 + 3 | 12 | 2 |
| 2 + 2 + 2 as × | 3 × 2 | 2 |
| 4 × 5 | 20 | 2 |
| 6 + 6 | 12 | 2 |
| Total | 10 |
Practice answers: Worksheet: 1 15; 2 12; 3 3 × 2; 4 20; 5 12.
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 6; 7 4 × 3; 8 10; 9 30; 10 12.
Independent practice answers. Level 1: 1 15; 2 12; 3 3 × 2 = 6; 4 20; 5 12. Level 2: 1 12; 2 4 × 5; 3 9. Level 3: 1 24; 2 4 × 3 = 12; 3 3 × 4 is 3 groups of 4: 4 + 4 + 4 = 12..
Mastery and remediation
| Objective | Bronze (Developing) | Silver (Proficient) | Gold (Advanced) |
|---|---|---|---|
| O1 Write equal groups as repeated addition | 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 Find the total by adding | 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 Read the sign × as groups of | 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 Match a picture to a multiplication sentence | 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 |
Proposed Courseversity thresholds for this page: Bronze = at least 8 of 12 core questions correct; Silver = all 12; Gold = all 12 plus both challenge questions. A badge is never a full record of progress.
If a learner struggles
- Find the misconception: Reading 3 × 4 as 3 + 4. 3 × 4 means 3 groups of 4: 4 + 4 + 4.
- Explain another way: use real objects first, then pictures.
- Show a simpler example: Use counters in groups and add them one group at a time.
- Guided practice: work through one example together and let the learner try the next one.
- Reassess: use the quiz again or the worksheet.
- Move on when the learner shows Silver-level evidence independently.
For parents and guardians
In this lesson your child writes equal groups as repeated addition and multiplication. You do not need to be good at mathematics to help.
- Use coins in rows to write repeated addition.
- Say 3 × 4 as 3 groups of 4.
- Ask: how many is 2 × 5?
- 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: write equal groups as repeated addition; find the total by adding; read the sign × as groups of; match a picture to a multiplication sentence.
Prerequisite knowledge. Lesson 1.
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 counters and paper. 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. How many groups? How many in each? What is 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. Reading 3 × 4 as 3 + 4. 3 × 4 means 3 groups of 4: 4 + 4 + 4.
13–15. Assessment questions, answer keys, marking scheme
Use the quiz and worksheet on this page. The 10-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. Use counters in groups and add them one group at a time. 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
Alignment is pending verification and no external 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. Specific standard codes will be added once checked against the official documents.
Research used to shape this lesson. Common Core 2.OA.C.4 (repeated addition); Cambridge Primary Mathematics Stage 2. These sources informed the lesson; no official alignment is claimed.