You will learn
- Say that each place is 10 times the right.
- Say that each place is 1/10 of the left.
- Compare values of the same digit.
- Multiply and divide by 10.
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
- Each place is 10 times the place to its right.
- Each place is 1/10 of the place to its left.
- Multiplying by 10 moves digits one place left.
- Dividing by 10 moves digits one place right.
Words to know
Value by position.
×10.
÷10.
0 to 9.
1. Discover: 444
In 444, the three 4s have different values. How do they relate to one another?
2. Understand: relationships
- In 444: the 4 in the hundreds is 400, ten times the 4 in the tens (40), which is ten times the 4 in the ones (4).
- 500,000 ÷ 10 = 50,000.
- 7,000 × 10 = 70,000.
Moving a digit one place left makes it ten times bigger; one place right makes it one tenth.
Idea 1: Times 10
3,000 × 10 = 30,000. Each digit moves one place to the left.
Idea 2: Divide by 10
800,000 ÷ 10 = 80,000. 9,000 ÷ 100 = 90.
Idea 3: Same digit
In 55 the left 5 is worth 50 and the right 5 is worth 5. The left one is 10 times the right one. 60 × 100 = 6,000.
Why a pattern? Our number system is built on tens.
3. Worked examples
Example 1 (I show you): × 10
3,000 × 10
- One place left.
Answer: 30,000
Example 2 (We do it together): ÷ 10
800,000 ÷ 10
- One place right.
Answer: 80,000
Example 3 (You try): × 100
60 × 100
Show the steps and answer
- Two places left.
Answer: 6,000
Did you know?
A digit does not change when it moves; its place does.
Why this matters
This pattern is the key to multiplying and dividing by 10, 100 and 1,000.
4. Explore: shift
You need a place value chart.
- Write 4 in the ones.
- Move it to the tens.
- Move it to the hundreds.
- Compare the values.
Think about it: what did you notice?
4, 40, 400.
5. Practise
Say it in a sentence
Use these starters when you talk about the lesson. Say them out loud.
- The digits move ___ places.
- To the left / right because ___.
- The new number is ___.
- The left digit is ___ times the right.
Guided practice
Question 1. 400 is how many times 40?
10.
Question 2. 500,000 ÷ 10?
50,000.
Question 3. 7,000 × 10?
70,000.
Independent practice
Level 1: Start
- 3,000 × 10
- 800,000 ÷ 10
- The 5 in 55: left is how many times right?
- 60 × 100
- 9,000 ÷ 100
Level 2: Grow
- 4,500 × 100
- 70,000 ÷ 10
- 2,500 ÷ 100
Level 3: Stretch
- 90 × 10,000
- 4,800,000 ÷ 1,000
- Ben says 5,000 × 10 = 5,010. What is wrong?
Answers are in the answer key below. Try first, then check.
6. Apply: everyday mathematics
A school has 4,500 books. A bigger school has 10 times as many. How many?
Show a sample answer
45,000.
Another one. A school has 4,500 pupils. A bigger school has 10 times as many. How many pupils?
Show a sample answer
4,500 × 10 = 45,000
7. Common mistakes
Fix: Use the place.
Fix: Multiply: move digits left.
Fix: Divide moves digits right.
8. Lesson summary and revision card
- I can say each place is 10 times the place to its right.
- I can say each place is 1/10 of the left.
- I can compare values of the same digit.
- I can multiply and divide by 10.
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
- Left ×10.
- Right ÷10.
- Place decides value.
11. Next lesson
Next lesson: Expanded form. 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 3,000 × 10. [2 marks]
- Find 800,000 ÷ 10. [2 marks]
- In 55, how many times is the left 5 worth the right 5? [2 marks]
- Find 60 × 100. [2 marks]
- Ali says 9,000 ÷ 100 = 900. Is he right? Explain. [3 marks]
Total: 11 marks.
Marking guide and model answers
- Digits move one place left [1]; 30,000 [1]
- Digits move one place right [1]; 80,000 [1]
- 50 and 5 [1]; 10 times [1]
- Two places left [1]; 6,000 [1]
- No [1]. ÷ 100 moves two places right [1]. It is 90 [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
- 3,000 × 10
- 800,000 ÷ 10
- 60 × 100
- 9,000 ÷ 100
- 400 is ___ times 40
- 500,000 ÷ 10 =
- 7,000 × 10 =
- 400 is how many times 40?
- 3,000 × 10 =
- 60 × 100 =
Homework
Make a chart showing what happens when you multiply 25 by 10, 100 and 1,000.
Answer key and marking scheme
| Question | Expected response | Marks |
|---|---|---|
| 3,000 × 10 | 30,000 | 2 |
| 800,000 ÷ 10 | 80,000 | 2 |
| 60 × 100 | 6,000 | 2 |
| 9,000 ÷ 100 | 90 | 2 |
| 400 is ___ times 40 | 10 | 2 |
| Total | 10 |
Practice answers: Worksheet: 1 30,000; 2 80,000; 3 6,000; 4 90; 5 10.
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 50,000; 7 70,000; 8 10; 9 30,000; 10 6,000.
Independent practice answers. Level 1: 1 30,000; 2 80,000; 3 10 times; 4 6,000; 5 90. Level 2: 1 450,000; 2 7,000; 3 25. Level 3: 1 900,000; 2 4,800; 3 Multiplying by 10 moves each digit one place left: 50,000..
Mastery and remediation
| Objective | Bronze (Developing) | Silver (Proficient) | Gold (Advanced) |
|---|---|---|---|
| O1 Say that each place is 10 times the right | 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 Say that each place is 1/10 of the left | 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 Compare values of the same 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 Multiply and divide by 10 | 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: Thinking the 4s in 444 have the same value. Use the place.
- Explain another way: use real objects first, then pictures.
- Show a simpler example: Practise ×10 on small 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 learns how places relate by tens. You do not need to be good at mathematics to help.
- Multiply prices by 10 and 100.
- Ask: which way do the digits move?
- Use a place value chart.
- 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: say that each place is 10 times the right; say that each place is 1/10 of the left; compare values of the same digit; multiply and divide by 10.
Prerequisite knowledge. Lesson 1.
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 a place value chart. 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. Which way do the digits move? How many places?
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. Thinking the 4s in 444 have the same value. Use the place.
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 ×10 on small 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.A.1 and 5.NBT.A.2; Cambridge Primary Mathematics Stage 5 (place value). These sources informed the lesson; no official alignment is claimed.