You will learn
- Draw equal groups to show multiplication.
- Draw a bar model.
- Write a multiplication sentence for a picture.
- Find the product from a picture.
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
- Draw equal groups to show multiplication.
- A bar model uses equal boxes.
- Write a multiplication sentence for a picture.
- The product is the total.
Words to know
A drawing that shows an idea.
A bar divided into equal boxes.
Groups with the same number in each.
The answer to a multiplication.
1. Discover: plates of mangoes
You see 3 plates with 2 mangoes on each. Draw it. Which multiplication does your picture show?
2. Understand: multiplication pictures
A picture can show multiplication. Draw circles for the groups and dots for what is in each. 3 plates with 2 mangoes is 3 × 2 = 6.
A bar model uses equal boxes: three boxes of 2 make 6.
4 × 5: draw 4 groups of 5 dots. Count in 5s: 5, 10, 15, 20.
Idea 1: Draw groups
To show 3 × 2, draw 3 plates with 2 mangoes on each. Count all the mangoes: 2 + 2 + 2 = 6.
Idea 2: Bar model
A bar model is a bar split into equal boxes. 3 boxes of 5 show 3 × 5 = 15.
Idea 3: Picture to sentence
Look at the picture. Count the groups and the number in each group. Write groups × in each = total.
Why draw? A picture makes the meaning of multiplication clear.
3. Worked examples
Example 1 (I show you): Draw
Show 3 × 2 with a picture.
- 3 groups.
- 2 in each group.
- Total 6.
Answer: 3 × 2 = 6
Example 2 (We do it together): Bar model
A bar model has 3 boxes with 5 in each. What is the total?
- 5 + 5 + 5.
Answer: 15
Example 3 (You try): Write
4 groups of 5. Write a multiplication sentence.
Show the steps and answer
- 4 × 5.
- 5 + 5 + 5 + 5 = 20.
Answer: 4 × 5 = 20
Did you know?
Bar models are used all over the world to teach maths, from Singapore to Ghana.
Why this matters
Pictures help us understand multiplication before we learn the facts.
4. Explore: draw it
You need paper and a pencil.
- Draw 3 circles.
- Draw 2 dots in each circle.
- Count all the dots and write 3 × 2 = 6.
- Draw 4 groups of 5 and write 4 × 5.
Think about it: what did you notice?
3 × 2 = 6; 4 × 5 = 20.
5. Practise
Say it in a sentence
Use these starters when you talk about the lesson. Say them out loud.
- I draw ___ groups.
- There are ___ in each.
- The product is ___.
- My bar model has ___ boxes.
Guided practice
Question 1. 3 plates with 2 mangoes each?
3 × 2 = 6.
Question 2. 4 groups of 5?
4 × 5 = 20.
Question 3. 2 × 8?
16.
Independent practice
Level 1: Start
- 3 × 2
- 4 × 5
- 2 × 8
- 5 × 2
- 3 × 5
Level 2: Grow
- Draw 2 groups of 6. How many in all?
- 5 × 3 = ___.
- 6 × 2 = ___.
Level 3: Stretch
- A bar model has 4 boxes of 4. What is the total?
- 3 plates have 5 oranges each. How many oranges?
- Ben draws 4 groups of 3 and writes 4 × 3 = 7. What is wrong?
Answers are in the answer key below. Try first, then check.
6. Apply: everyday mathematics
A bar has 3 boxes with 5 in each. Write the multiplication and the total.
Show a sample answer
3 × 5 = 15.
Another one. Draw a bar model for 3 × 6 and find the product.
Show a sample answer
6 + 6 + 6 = 18
7. Common mistakes
Fix: Make each group the same.
Fix: Every group must have the same number.
Fix: Add the groups: 3 × 4 means 4 + 4 + 4.
8. Lesson summary and revision card
- I can draw equal groups for a multiplication.
- I can draw a bar model.
- I can write a multiplication sentence for a picture.
- I can find the product from a picture.
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
- Draw equal groups.
- Use a bar model.
- Count in equal jumps.
11. Next lesson
Next lesson: Multiplication facts for 2, 5 and 10. 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.
- Draw a picture for 2 × 3 and find the product. [2 marks]
- A bar model has 4 boxes of 5. Write the multiplication. [2 marks]
- 3 plates with 4 cakes each. Write the sentence. [2 marks]
- What is 5 × 2? [1 mark]
- Ali draws 3 groups of 2 and says the product is 5. Is he right? Explain. [3 marks]
Total: 10 marks.
Marking guide and model answers
- 2 groups of 3 [1]; 6 [1]
- 4 × 5 [1] = 20 [1]
- 3 × 4 [1] = 12 [1]
- 10 [1]
- No [1]. 3 × 2 means 2 + 2 + 2 [1] = 6 [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
- 3 × 2
- 4 × 5
- 2 × 8
- 5 × 2
- 3 × 5
- Draw 2 × 4. The product is ___.
- 3 groups of 3 = ___.
- A bar model with 5 boxes of 2. Total?
- 4 × 3 = ___.
- 2 × 5 = ___.
Homework
Draw two multiplication pictures. Write the sentence under each.
Answer key and marking scheme
| Question | Expected response | Marks |
|---|---|---|
| 3 × 2 | 6 | 2 |
| 4 × 5 | 20 | 2 |
| 2 × 8 | 16 | 2 |
| 5 × 2 | 10 | 2 |
| 3 × 5 | 15 | 2 |
| Total | 10 |
Practice answers: Worksheet: 1 6; 2 20; 3 16; 4 10; 5 15.
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 10; 9 12; 10 10.
Independent practice answers. Level 1: 1 6; 2 20; 3 16; 4 10; 5 15. Level 2: 1 12; 2 15; 3 12. Level 3: 1 16; 2 15; 3 He added. 3 + 3 + 3 + 3 = 12..
Mastery and remediation
| Objective | Bronze (Developing) | Silver (Proficient) | Gold (Advanced) |
|---|---|---|---|
| O1 Draw equal groups to show multiplication | 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 Draw a bar model | 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 Write a multiplication sentence for a picture | 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 Find the product from a picture | 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
- Find the misconception: Drawing groups of different sizes. Make each group the same.
- Explain another way: use real objects first, then pictures.
- Show a simpler example: Draw groups with counters first, then copy on paper.
- 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 uses pictures and bar models to show multiplication. You do not need to be good at mathematics to help.
- Draw groups of fruit or buttons and write the sentence.
- Draw a bar model with boxes and numbers.
- Ask: how many groups? How many in each?
- 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: draw equal groups to show multiplication; draw a bar model; write a multiplication sentence for a picture; find the product from a picture.
Prerequisite knowledge. Lessons 1 to 4.
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 paper and a pencil. 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 product?
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. Drawing groups of different sizes. Make each group the same.
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. Draw groups with counters first, then copy on paper. 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 2 » Operations & Algebraic Thinking; Grade 2 » 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 2.OA.C.4 (multiplication with pictures); Cambridge Primary Mathematics Stage 2. These sources informed the lesson.