You will learn
- Multiply by a 2-digit number.
- Multiply a 4-digit number by a 2-digit number.
- Use partial products.
- Check with 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
- Break the 2-digit number into tens and ones.
- Multiply by each part to get partial products.
- Add the partial products.
- Estimate to check the answer.
Words to know
One part of the product.
A step-by-step method.
Carry.
The answer.
1. Discover: school supplies
A school orders 26 cartons with 345 pencils in each. How many pencils?
2. Understand: multiplying
- 345 × 26 = 345 × 20 + 345 × 6 = 6,900 + 2,070 = 8,970.
- 1,248 × 34 = 37,440 + 4,992 = 42,432.
- 507 × 48 = 20,280 + 4,056 = 24,336.
Estimate first: 345 × 26 ≈ 350 × 25 = 8,750. Close to 8,970.
Idea 1: Partial products
123 × 12 = 123 × 10 + 123 × 2 = 1,230 + 246 = 1,476.
Idea 2: Bigger numbers
456 × 23 = 456 × 20 + 456 × 3 = 9,120 + 1,368 = 10,488.
Idea 3: Zeros
1,000 × 45 = 45,000. 302 × 15 = 3,020 + 1,510 = 4,530.
Why split? Small steps are easier and easier to check.
3. Worked examples
Example 1 (I show you): Multiply
123 × 12
- × 10 and × 2.
Answer: 1,476
Example 2 (We do it together): Multiply
456 × 23
- × 20 and × 3.
Answer: 10,488
Example 3 (You try): Multiply
302 × 15
Show the steps and answer
- × 10 and × 5.
Answer: 4,530
Did you know?
Partial products are the steps hidden inside the column method.
Why this matters
Multiplying large numbers is used in prices, areas and populations.
4. Explore: multiply
You need paper.
- Write 345 × 26.
- Multiply by 6.
- Multiply by 20.
- Add.
Think about it: what did you notice?
8,970.
5. Practise
Say it in a sentence
Use these starters when you talk about the lesson. Say them out loud.
- I split the number into ___ and ___.
- The partial products are ___ and ___.
- Added together they make ___.
- My estimate was ___.
Guided practice
Question 1. 345 × 26?
8,970.
Question 2. 1,248 × 34?
42,432.
Question 3. 507 × 48?
24,336.
Independent practice
Level 1: Start
- 123 × 12
- 456 × 23
- 1,000 × 45
- 302 × 15
- 2,506 × 8
Level 2: Grow
- 34 × 12
- 215 × 11
- 60 × 35
Level 3: Stretch
- 1,234 × 21
- 805 × 36
- Ana says 45 × 12 = 90 + 5 = 95. What is wrong?
Answers are in the answer key below. Try first, then check.
6. Apply: everyday mathematics
26 cartons with 345 pencils. How many?
Show a sample answer
8,970.
Another one. A hall has 28 rows of 36 seats. How many seats?
Show a sample answer
36 × 28 = 720 + 288 = 1,008 seats
7. Common mistakes
Fix: Write a zero first.
Fix: Multiplying by 20 means × 2 then × 10.
Fix: Line up the place values.
8. Lesson summary and revision card
- I can multiply by a 2-digit number.
- I can multiply a 4-digit number by a 2-digit number.
- I can use partial products.
- I can check by estimating.
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
- Partial products.
- Shift for tens.
- Estimate to check.
11. Next lesson
Next lesson: Multidigit division. 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 123 × 12. [3 marks]
- Find 456 × 23. [3 marks]
- Find 1,000 × 45. [1 mark]
- Find 302 × 15. [3 marks]
- Ben says 302 × 15 = 3,035. Is he right? Explain. [3 marks]
Total: 13 marks.
Marking guide and model answers
- 123 × 10 = 1,230 [1]; 123 × 2 = 246 [1]; 1,476 [1]
- 456 × 20 = 9,120 [1]; 456 × 3 = 1,368 [1]; 10,488 [1]
- 45,000 [1]
- 3,020 [1]; 1,510 [1]; 4,530 [1]
- No [1]. 302 × 10 = 3,020 and 302 × 5 = 1,510 [1]. The answer is 4,530 [1].
Score guide: 12 to 13 = secure. 8 to 11 = nearly there, revise the parts you missed. Under 8 = work through the lesson again with a grown-up.
Printable worksheet
- 123 × 12
- 456 × 23
- 1,000 × 45
- 302 × 15
- 2,506 × 8
- 345 × 26 =
- 1,248 × 34 =
- 507 × 48 =
- 123 × 12 =
- 1,000 × 45 =
Homework
Multiply three 3-digit numbers by 14.
Answer key and marking scheme
| Question | Expected response | Marks |
|---|---|---|
| 123 × 12 | 1,476 | 2 |
| 456 × 23 | 10,488 | 2 |
| 1,000 × 45 | 45,000 | 2 |
| 302 × 15 | 4,530 | 2 |
| 2,506 × 8 | 20,048 | 2 |
| Total | 10 |
Practice answers: Worksheet: 1 1,476; 2 10,488; 3 45,000; 4 4,530; 5 20,048.
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 8,970; 7 42,432; 8 24,336; 9 1,476; 10 45,000.
Independent practice answers. Level 1: 1 1,476; 2 10,488; 3 45,000; 4 4,530; 5 20,048. Level 2: 1 408; 2 2,365; 3 2,100. Level 3: 1 25,914; 2 28,980; 3 45 × 10 = 450 and 45 × 2 = 90, so 540..
Mastery and remediation
| Objective | Bronze (Developing) | Silver (Proficient) | Gold (Advanced) |
|---|---|---|---|
| O1 Multiply by a 2-digit number | 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 a 4-digit number by a 2-digit number | 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 Use partial products | 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 with 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 the shift (zero) in the tens row. Write a zero first.
- Explain another way: use real objects first, then pictures.
- Show a simpler example: Practise 3-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 by 2-digit numbers. You do not need to be good at mathematics to help.
- Multiply prices by quantities.
- Ask: what are the partial products?
- Estimate before you calculate.
- 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 by a 2-digit number; multiply a 4-digit number by a 2-digit number; use partial products; check with estimation.
Prerequisite knowledge. Grade 4 multiplication.
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. What are the partial products? Does the answer fit my estimate?
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 the shift (zero) in the tens row. Write a zero first.
13–15. Assessment questions, answer keys, marking scheme
Use the quiz and worksheet on this page. The 13-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 3-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 5 » Operations & Algebraic Thinking; Grade 5 » 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 5.NBT.B.5; Cambridge Primary Mathematics Stage 5 (multiplication). These sources informed the lesson.