You will learn
- Multiply 2-digit by 1-digit.
- Multiply 2-digit by 2-digit.
- 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
- Split the number into tens and ones.
- Multiply each part.
- Add the partial products.
- Estimate to check.
Words to know
A part of the product.
Carry to the next place.
A box showing parts.
About.
1. Discover: bags of rice
12 bags hold 34 kg of rice each. How much in all? Can you split 12 into 10 and 2?
2. Understand: two-digit multiplication
Break one number into tens and ones.
- 23 × 4 = 20 × 4 + 3 × 4 = 80 + 12 = 92.
- 34 × 12 = 34 × 10 + 34 × 2 = 340 + 68 = 408.
- 25 × 14 = 250 + 100 = 350.
Check: 34 × 12 ≈ 30 × 10 = 300; 408 is close.
Idea 1: 2-digit by 1-digit
46 × 3: 40 × 3 = 120 and 6 × 3 = 18. 120 + 18 = 138.
Idea 2: Bigger
52 × 6: 50 × 6 = 300 and 2 × 6 = 12. 300 + 12 = 312.
Idea 3: 2-digit by 2-digit
34 × 12: 34 × 10 = 340 and 34 × 2 = 68. 340 + 68 = 408.
Why partial products? They show where every part comes from.
3. Worked examples
Example 1 (I show you): Split
46 × 3
- 120 and 18.
Answer: 138
Example 2 (We do it together): Split
52 × 6
- 300 and 12.
Answer: 312
Example 3 (You try): Two digits
34 × 12
Show the steps and answer
- 340 and 68.
Answer: 408
Did you know?
An area model draws each partial product as a box.
Why this matters
Multiplying 2-digit numbers is useful in shopping and measuring.
4. Explore: partial products
You need paper.
- Write 34 × 12.
- 34 × 10 = 340.
- 34 × 2 = 68.
- Add.
Think about it: what did you notice?
408.
5. Practise
Say it in a sentence
Use these starters when you talk about the lesson. Say them out loud.
- I split ___ into ___ and ___.
- The partial products are ___ and ___.
- Their sum is ___.
- My estimate is ___.
Guided practice
Question 1. 23 × 4?
92.
Question 2. 34 × 12?
408.
Question 3. 25 × 14?
350.
Independent practice
Level 1: Start
- 46 × 3
- 52 × 6
- 34 × 12
- 25 × 14
- 21 × 21
Level 2: Grow
- 38 × 4
- 64 × 5
- 15 × 12
Level 3: Stretch
- 27 × 13
- 45 × 22
- Kofi says 34 × 12 = 68 + 34 = 102. What is wrong?
Answers are in the answer key below. Try first, then check.
6. Apply: everyday mathematics
12 bags hold 34 kg each. Total kg?
Show a sample answer
408 kg.
Another one. A hall has 16 rows of 25 chairs. How many chairs?
Show a sample answer
25 × 10 = 250 and 25 × 6 = 150, so 400 chairs.
7. Common mistakes
Fix: 340, not 34.
Fix: The tens digit means tens, so 40 × 3, not 4 × 3.
Fix: Multiply each part, then add.
8. Lesson summary and revision card
- I can multiply 2-digit by 1-digit.
- I can multiply 2-digit by 2-digit.
- I can use partial products.
- I can check with 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
- Split the number.
- Add partial products.
- Estimate to check.
11. Next lesson
Next lesson: Multidigit multiplication. 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 46 × 3. [2 marks]
- Find 52 × 6. [2 marks]
- Find 34 × 12. [3 marks]
- Find 25 × 14. [3 marks]
- Ana says 21 × 21 = 42. Is she right? Explain. [3 marks]
Total: 13 marks.
Marking guide and model answers
- 120 and 18 [1]; 138 [1]
- 300 and 12 [1]; 312 [1]
- 34 × 10 = 340 [1]; 34 × 2 = 68 [1]; 408 [1]
- 25 × 10 = 250 [1]; 25 × 4 = 100 [1]; 350 [1]
- No [1]. 21 × 20 = 420 [1]; 420 + 21 = 441 [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
- 46 × 3
- 52 × 6
- 34 × 12
- 25 × 14
- 21 × 21
- 23 × 4 =
- 46 × 3 =
- 34 × 12 =
- 25 × 14 =
- 21 × 21 =
Homework
Solve ten 2-digit multiplications and check with estimates.
Answer key and marking scheme
| Question | Expected response | Marks |
|---|---|---|
| 46 × 3 | 138 | 2 |
| 52 × 6 | 312 | 2 |
| 34 × 12 | 408 | 2 |
| 25 × 14 | 350 | 2 |
| 21 × 21 | 441 | 2 |
| Total | 10 |
Practice answers: Worksheet: 1 138; 2 312; 3 408; 4 350; 5 441.
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 92; 7 138; 8 408; 9 350; 10 441.
Independent practice answers. Level 1: 1 138; 2 312; 3 408; 4 350; 5 441. Level 2: 1 152; 2 320; 3 180. Level 3: 1 351; 2 990; 3 He must multiply by 10 and by 2: 340 + 68 = 408..
Mastery and remediation
| Objective | Bronze (Developing) | Silver (Proficient) | Gold (Advanced) |
|---|---|---|---|
| O1 Multiply 2-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 2-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 |
| 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 tens in the second row. 340, not 34.
- Explain another way: use real objects first, then pictures.
- Show a simpler example: Use arrays to multiply 12 × 4.
- 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 two-digit numbers using partial products. You do not need to be good at mathematics to help.
- Ask your child to split the number.
- Check with an estimate.
- Draw an area model 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 2-digit by 1-digit; multiply 2-digit by 2-digit; use partial products; check with estimation.
Prerequisite knowledge. Lesson 3.
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. How do I split it? What are 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 the tens in the second row. 340, not 34.
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. Use arrays to multiply 12 × 4. 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 up to 2-digit by 2-digit); Cambridge Primary Mathematics Stage 4 (written multiplication). These sources informed the lesson.