You will learn
- Multiply 3-digit by 1-digit.
- Multiply 4-digit by 1-digit.
- Multiply 3-digit by 2-digit.
- Check by estimation.
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
- Multiply each place from the right.
- Carry when a product is 10 or more.
- Use partial products for 2-digit factors.
- Check by estimation.
Words to know
More than one digit.
Carry.
Part of the answer.
The usual written method.
1. Discover: bigger problems
A school buys 346 books for each of 7 classes. How many books?
2. Understand: multidigit multiplication
Multiply each place and regroup.
- 346 × 7: 300×7 = 2,100; 40×7 = 280; 6×7 = 42. Sum 2,422.
- 1,234 × 5: 1,000×5 = 5,000; 200×5 = 1,000; 30×5 = 150; 4×5 = 20. Sum 6,170.
- 245 × 13 = 2,450 + 735 = 3,185.
Idea 1: 3-digit
508 × 6: 500 × 6 = 3,000 and 8 × 6 = 48. Total 3,048.
Idea 2: 4-digit
1,005 × 8: 1,000 × 8 = 8,000 and 5 × 8 = 40. Total 8,040.
Idea 3: By 2 digits
245 × 13: 245 × 10 = 2,450 and 245 × 3 = 735. Total 3,185.
Why estimate? 245 × 13 is about 250 × 10 = 2,500 to 3,000, so 3,185 is sensible.
3. Worked examples
Example 1 (I show you): Zeros inside
508 × 6
- 3,000 and 48.
Answer: 3,048
Example 2 (We do it together): 4-digit
1,005 × 8
- 8,000 and 40.
Answer: 8,040
Example 3 (You try): 3-digit by 2-digit
245 × 13
Show the steps and answer
- 2,450 and 735.
Answer: 3,185
Did you know?
The standard algorithm is partial products written in short form.
Why this matters
Multiplying bigger numbers is needed for money, area and planning.
4. Explore: long multiplication
You need paper.
- Write 346 × 7.
- Multiply each digit.
- Add partial products.
- Estimate: 350 × 7 ≈ 2,450.
Think about it: what did you notice?
2,422.
5. Practise
Say it in a sentence
Use these starters when you talk about the lesson. Say them out loud.
- I multiply the ___ first.
- I carry ___.
- The partial products are ___ and ___.
- The total is ___.
Guided practice
Question 1. 346 × 7?
2,422.
Question 2. 1,234 × 5?
6,170.
Question 3. 245 × 13?
3,185.
Independent practice
Level 1: Start
- 508 × 6
- 1,005 × 8
- 346 × 7
- 245 × 13
- 222 × 4
Level 2: Grow
- 413 × 2
- 1,100 × 5
- 125 × 12
Level 3: Stretch
- 2,345 × 4
- 306 × 25
- Ben says 508 × 6 = 348. What is wrong?
Answers are in the answer key below. Try first, then check.
6. Apply: everyday mathematics
346 books for each of 7 classes. Total?
Show a sample answer
2,422 books.
Another one. A farm packs 125 eggs in each of 24 crates. How many eggs?
Show a sample answer
125 × 20 = 2,500 and 125 × 4 = 500, so 3,000 eggs.
7. Common mistakes
Fix: Keep every place.
Fix: Add the carry to the next product.
Fix: Keep every place in its column.
8. Lesson summary and revision card
- I can multiply 3-digit by 1-digit.
- I can multiply 4-digit by 1-digit.
- I can multiply 3-digit by 2-digit.
- I can check by estimation.
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
- Multiply each place.
- Regroup carefully.
- Check by estimating.
11. Next lesson
Next lesson: Estimating products. 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.
- Find 508 × 6. [3 marks]
- Find 1,005 × 8. [2 marks]
- Find 346 × 7. [3 marks]
- Find 245 × 13. [3 marks]
- Ali says 222 × 4 = 808. Is he right? Explain. [3 marks]
Total: 14 marks.
Marking guide and model answers
- 500 × 6 = 3,000 [1]; 8 × 6 = 48 [1]; 3,048 [1]
- 8,000 and 40 [1]; 8,040 [1]
- 2,100, 280 and 42 [1]; add them [1]; 2,422 [1]
- 245 × 10 = 2,450 [1]; 245 × 3 = 735 [1]; 3,185 [1]
- No [1]. 800 + 80 + 8 [1]. It is 888 [1].
Score guide: 12 to 14 = secure. 9 to 11 = nearly there, revise the parts you missed. Under 9 = work through the lesson again with a grown-up.
Printable worksheet
- 508 × 6
- 1,005 × 8
- 346 × 7
- 245 × 13
- 222 × 4
- 346 × 7 =
- 1,234 × 5 =
- 245 × 13 =
- 508 × 6 =
- 1,005 × 8 =
Homework
Multiply three 3-digit numbers by 6 and check.
Answer key and marking scheme
| Question | Expected response | Marks |
|---|---|---|
| 508 × 6 | 3,048 | 2 |
| 1,005 × 8 | 8,040 | 2 |
| 346 × 7 | 2,422 | 2 |
| 245 × 13 | 3,185 | 2 |
| 222 × 4 | 888 | 2 |
| Total | 10 |
Practice answers: Worksheet: 1 3,048; 2 8,040; 3 2,422; 4 3,185; 5 888.
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 2,422; 7 6,170; 8 3,185; 9 3,048; 10 8,040.
Independent practice answers. Level 1: 1 3,048; 2 8,040; 3 2,422; 4 3,185; 5 888. Level 2: 1 826; 2 5,500; 3 1,500. Level 3: 1 9,380; 2 7,650; 3 He treated 5 as 5 ones. 500 × 6 = 3,000, so the answer is 3,048..
Mastery and remediation
| Objective | Bronze (Developing) | Silver (Proficient) | Gold (Advanced) |
|---|---|---|---|
| O1 Multiply 3-digit by 1-digit | 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 Multiply 4-digit by 1-digit | 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 Multiply 3-digit by 2-digit | 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 Check by estimation | 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: Forgetting zero when a digit is 0. Keep every place.
- Explain another way: use real objects first, then pictures.
- Show a simpler example: Practise 2-digit × 1-digit.
- 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 multiplies three- and four-digit numbers. You do not need to be good at mathematics to help.
- Use prices of items in bulk.
- Ask for an estimate first.
- Check each carry together.
- 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: multiply 3-digit by 1-digit; multiply 4-digit by 1-digit; multiply 3-digit by 2-digit; check by estimation.
Prerequisite knowledge. Lesson 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. 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. Did I carry? Do I have all the partial products?
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. Forgetting zero when a digit is 0. Keep every place.
13–15. Assessment questions, answer keys, marking scheme
Use the quiz and worksheet on this page. The 14-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. Practise 2-digit × 1-digit. 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 4 » Operations & Algebraic Thinking; Grade 4 » 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 4.NBT.B.5 (multiply a 4-digit by 1-digit, 2-digit by 2-digit); Cambridge Primary Mathematics Stage 4 and 5 (written multiplication). These sources informed the lesson.