You will learn
- Use a basic fact to multiply multiples of ten.
- Count zeros.
- Multiply by 100 and 1,000.
- Solve a related problem.
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 the basic facts first.
- Then add the zeros.
- Count all the zeros in both factors.
- Check the size of the answer.
Words to know
10, 20, 30 …
A times-table fact.
The digit 0.
Value by position.
1. Discover: trays of eggs
A farmer has 6 crates with 40 eggs each. How could 6 × 4 help find the total?
2. Understand: multiples of ten
Multiply the basic fact, then add the zeros.
- 6 × 40: 6 × 4 = 24, then one zero: 240.
- 30 × 50: 3 × 5 = 15, then two zeros: 1,500.
- 7 × 300: 7 × 3 = 21, then two zeros: 2,100.
- 20 × 900: 2 × 9 = 18, then three zeros: 18,000.
Idea 1: Basic fact
8 × 70: 8 × 7 = 56, then add one zero: 560.
Idea 2: Count zeros
60 × 80: 6 × 8 = 48, then two zeros: 4,800. 5 × 400: 5 × 4 = 20, then two zeros: 2,000.
Idea 3: Thousands
20 × 900: 2 × 9 = 18, then three zeros: 18,000. 4 × 5,000: 4 × 5 = 20, then three zeros: 20,000.
Why add zeros? Each ten or hundred moves the digits one place left.
3. Worked examples
Example 1 (I show you): One zero
8 × 70
- 8 × 7 = 56.
Answer: 560
Example 2 (We do it together): Two zeros
60 × 80
- 6 × 8 = 48, then two zeros.
Answer: 4,800
Example 3 (You try): Three zeros
4 × 5,000
Show the steps and answer
- 4 × 5 = 20, then three zeros.
Answer: 20,000
Did you know?
The fact 6 × 8 = 48 gives 60 × 80 = 4,800 too.
Why this matters
This trick makes big multiplications quick.
4. Explore: zero trick
You need paper.
- Write 6 × 40.
- Multiply 6 × 4.
- Count the zeros.
- Write the answer.
Think about it: what did you notice?
240.
5. Practise
Say it in a sentence
Use these starters when you talk about the lesson. Say them out loud.
- The basic fact is ___ × ___ = ___.
- There are ___ zeros in all.
- So the product is ___.
- I check the size by ___.
Guided practice
Question 1. 6 × 40?
240.
Question 2. 30 × 50?
1,500.
Question 3. 7 × 300?
2,100.
Independent practice
Level 1: Start
- 8 × 70
- 60 × 80
- 5 × 400
- 20 × 900
- 4 × 5,000
Level 2: Grow
- 6 × 80
- 40 × 50
- 9 × 300
Level 3: Stretch
- 70 × 600
- 8 × 7,000
- Ben says 30 × 40 = 120 because 3 × 4 = 12 and he added one zero. What is wrong?
Answers are in the answer key below. Try first, then check.
6. Apply: everyday mathematics
6 crates hold 40 eggs each. How many eggs?
Show a sample answer
240 eggs.
Another one. A school buys 60 boxes of 40 pencils. How many pencils?
Show a sample answer
6 × 4 = 24, then two zeros: 2,400 pencils.
7. Common mistakes
Fix: Count zeros in both numbers.
Fix: Count the zeros in both numbers.
Fix: Keep every zero, including the one in the product.
8. Lesson summary and revision card
- I can use a basic fact.
- I can count zeros.
- I can multiply by 100 and 1,000.
- I can solve related problems.
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
- Use the basic fact.
- Count all the zeros.
- Place value stays.
11. Next lesson
Next lesson: Two-digit 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 8 × 70. [2 marks]
- Find 60 × 80. [2 marks]
- Find 5 × 400. [2 marks]
- Find 20 × 900. [2 marks]
- Ali says 4 × 5,000 = 2,000. Is he right? Explain. [3 marks]
Total: 11 marks.
Marking guide and model answers
- 8 × 7 = 56 [1]; 560 [1]
- 6 × 8 = 48 [1]; 4,800 [1]
- 5 × 4 = 20 [1]; 2,000 [1]
- 2 × 9 = 18 [1]; 18,000 [1]
- No [1]. 4 × 5 = 20, then three zeros [1]. It is 20,000 [1].
Score guide: 10 to 11 = secure. 7 to 9 = nearly there, revise the parts you missed. Under 7 = work through the lesson again with a grown-up.
Printable worksheet
- 8 × 70
- 60 × 80
- 5 × 400
- 20 × 900
- 4 × 5,000
- 6 × 40 =
- 30 × 50 =
- 7 × 300 =
- 60 × 80 =
- 4 × 5,000 =
Homework
Make five problems with multiples of ten and solve them.
Answer key and marking scheme
| Question | Expected response | Marks |
|---|---|---|
| 8 × 70 | 560 | 2 |
| 60 × 80 | 4,800 | 2 |
| 5 × 400 | 2,000 | 2 |
| 20 × 900 | 18,000 | 2 |
| 4 × 5,000 | 20,000 | 2 |
| Total | 10 |
Practice answers: Worksheet: 1 560; 2 4,800; 3 2,000; 4 18,000; 5 20,000.
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): 6 240; 7 1,500; 8 2,100; 9 4,800; 10 20,000.
Independent practice answers. Level 1: 1 560; 2 4,800; 3 2,000; 4 18,000; 5 20,000. Level 2: 1 480; 2 2,000; 3 2,700. Level 3: 1 42,000; 2 56,000; 3 There are two zeros in all, so 30 × 40 = 1,200..
Mastery and remediation
| Objective | Bronze (Developing) | Silver (Proficient) | Gold (Advanced) |
|---|---|---|---|
| O1 Use a basic fact to multiply multiples of ten | 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 Count zeros | 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 by 100 and 1,000 | 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 Solve a related problem | 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: Dropping a zero. Count zeros in both numbers.
- Explain another way: use real objects first, then pictures.
- Show a simpler example: Practise multiplying by 10 and 100.
- 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 tens, hundreds and thousands using basic facts. You do not need to be good at mathematics to help.
- Practise with prices like 40 items at 50 each.
- Ask: what is the basic fact?
- Count the zeros 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: use a basic fact to multiply multiples of ten; count zeros; multiply by 100 and 1,000; solve a related problem.
Prerequisite knowledge. Lessons 1 and 2.
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 is the basic fact? How many zeros in all?
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. Dropping a zero. Count zeros in both numbers.
13–15. Assessment questions, answer keys, marking scheme
Use the quiz and worksheet on this page. The 11-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 multiplying by 10 and 100. 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 3.NBT.A.3 and 4.NBT.B.5; Cambridge Primary Mathematics Stage 4 (multiplying by multiples of ten). These sources informed the lesson; no official alignment is claimed.