You will learn
- Multiply a decimal by a whole number.
- Multiply two decimals.
- Place the decimal point.
- Estimate to check.
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
- Multiply as if there were no decimal points.
- Count the decimal places in both factors.
- Put the same number of places in the product.
- Estimate to check.
Words to know
Answer.
Digits after the point.
A number multiplied.
About.
1. Discover: cost of cloth
Cloth costs 3.2 per metre. How much for 4 m? What about 0.6 × 0.3?
2. Understand: multiplying decimals
- 3.2 × 4 = 12.8.
- Ignore the points: 6 × 3 = 18. Count decimal places: 1 + 1 = 2. So 0.6 × 0.3 = 0.18.
- 2.5 × 1.2 = 3.00 = 3.
- 12.5 × 0.1 = 1.25.
Idea 1: By whole
1.5 × 4: 15 × 4 = 60 with one decimal place, so 6.0 = 6.
Idea 2: Two decimals
0.4 × 0.5: 4 × 5 = 20 with two decimal places, so 0.20 = 0.2. 2.5 × 1.2: 25 × 12 = 300 with two places, so 3.00 = 3.
Idea 3: By 0.1
12.5 × 0.1 = 1.25. 0.2 × 0.2 = 0.04.
Why count places? Each decimal place divides by 10.
3. Worked examples
Example 1 (I show you): Multiply
1.5 × 4
- 15 × 4.
Answer: 6
Example 2 (We do it together): Multiply
0.4 × 0.5
- 4 × 5, two places.
Answer: 0.2
Example 3 (You try): Multiply
0.2 × 0.2
Show the steps and answer
- 2 × 2, two places.
Answer: 0.04
Did you know?
Multiplying by 0.1 is the same as dividing by 10.
Why this matters
Multiplying decimals is used for prices per kilogram and areas.
4. Explore: multiply
You need paper.
- Multiply 6 × 3.
- Count places in both factors.
- Place the point.
- Estimate.
Think about it: what did you notice?
0.18.
5. Practise
Say it in a sentence
Use these starters when you talk about the lesson. Say them out loud.
- I multiply ___ × ___ = ___.
- There are ___ decimal places in total.
- So the product is ___.
- My estimate was ___.
Guided practice
Question 1. 3.2 × 4?
12.8.
Question 2. 0.6 × 0.3?
0.18.
Question 3. 2.5 × 1.2?
3.
Independent practice
Level 1: Start
- 1.5 × 4
- 0.4 × 0.5
- 2.5 × 1.2
- 12.5 × 0.1
- 0.2 × 0.2
Level 2: Grow
- 3.1 × 2
- 0.6 × 0.7
- 1.5 × 0.3
Level 3: Stretch
- 12.5 × 0.8
- 0.04 × 0.5
- Ben says 0.3 × 0.3 = 0.9. What is wrong?
Answers are in the answer key below. Try first, then check.
6. Apply: everyday mathematics
Cloth costs 3.2 per metre. Cost of 4 m?
Show a sample answer
12.8.
Another one. Beans cost 4.5 per kg. What do 0.6 kg cost?
Show a sample answer
4.5 × 0.6 = 2.7
7. Common mistakes
Fix: Add the decimal places.
Fix: Add the decimal places of both factors.
Fix: Multiplying by a number less than 1 gives a smaller result.
8. Lesson summary and revision card
- I can multiply a decimal by a whole number.
- I can multiply two decimals.
- I can place the decimal point.
- I can estimate to check.
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 as whole numbers.
- Count places.
- Estimate.
11. Next lesson
Next lesson: Dividing decimals in introductory contexts. 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 1.5 × 4. [2 marks]
- Find 0.4 × 0.5. [3 marks]
- Find 2.5 × 1.2. [3 marks]
- Find 12.5 × 0.1. [2 marks]
- Ali says 0.2 × 0.2 = 0.4. Is he right? Explain. [3 marks]
Total: 13 marks.
Marking guide and model answers
- 15 × 4 = 60 [1]; 6 [1]
- 4 × 5 = 20 [1]; two decimal places [1]; 0.2 [1]
- 25 × 12 = 300 [1]; two decimal places [1]; 3 [1]
- × 0.1 is ÷ 10 [1]; 1.25 [1]
- No [1]. 2 × 2 = 4 with two decimal places [1]. The answer is 0.04 [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
- 1.5 × 4
- 0.4 × 0.5
- 2.5 × 1.2
- 12.5 × 0.1
- 0.2 × 0.2
- 3.2 × 4 =
- 0.6 × 0.3 =
- 2.5 × 1.2 =
- 12.5 × 0.1 =
- 0.2 × 0.2 =
Homework
Multiply six pairs of decimals.
Answer key and marking scheme
| Question | Expected response | Marks |
|---|---|---|
| 1.5 × 4 | 6 | 2 |
| 0.4 × 0.5 | 0.2 | 2 |
| 2.5 × 1.2 | 3 | 2 |
| 12.5 × 0.1 | 1.25 | 2 |
| 0.2 × 0.2 | 0.04 | 2 |
| Total | 10 |
Practice answers: Worksheet: 1 6; 2 0.2; 3 3; 4 1.25; 5 0.04.
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 12.8; 7 0.18; 8 3; 9 1.25; 10 0.04.
Independent practice answers. Level 1: 1 6; 2 0.2; 3 3; 4 1.25; 5 0.04. Level 2: 1 6.2; 2 0.42; 3 0.45. Level 3: 1 10; 2 0.02; 3 3 × 3 = 9 with two decimal places is 0.09..
Mastery and remediation
| Objective | Bronze (Developing) | Silver (Proficient) | Gold (Advanced) |
|---|---|---|---|
| O1 Multiply a decimal by a whole 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 two decimals | 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 Place the decimal point | 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 Estimate to check | 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: Putting the point in the wrong place. Add the decimal places.
- Explain another way: use real objects first, then pictures.
- Show a simpler example: Multiply whole numbers.
- 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 decimals. You do not need to be good at mathematics to help.
- Work out prices by weight.
- Ask: how many decimal places in total?
- Estimate first.
- 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 a decimal by a whole number; multiply two decimals; place the decimal point; estimate to check.
Prerequisite knowledge. Lessons 5 and 6.
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 many decimal places in total? Is my answer reasonable?
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. Putting the point in the wrong place. Add the decimal places.
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. Multiply whole numbers. 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 5.NBT.B.7; Cambridge Primary Mathematics Stage 5 and 6 (multiplying decimals). These sources informed the lesson; no official alignment is claimed.