You will learn
- Write powers of 10 with exponents.
- Read 10³ as 1,000.
- Multiply and divide by powers of 10.
- Explain the pattern of zeros.
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
- A power of ten is 10 multiplied by itself.
- The exponent counts the tens.
- 10³ = 1,000 has 3 zeros.
- Multiply or divide by moving digits.
Words to know
10 multiplied by itself.
Tells how many 10s.
The number multiplied.
Digits 0.
1. Discover: 1, 10, 100 …
1,000 is 10 × 10 × 10. Is there a short way to write that?
2. Understand: powers of ten
- 10² = 10 × 10 = 100; 10³ = 1,000; 10⁶ = 1,000,000.
- The exponent tells how many zeros follow the 1.
- 45 × 10³ = 45,000 (three places left).
- 3,200 ÷ 10² = 32 (two places right).
Idea 1: Powers
10⁴ = 10 × 10 × 10 × 10 = 10,000. 10⁶ = 1,000,000.
Idea 2: Multiply
7 × 10² = 7 × 100 = 700. 6.5 × 10 = 65.
Idea 3: Divide
8,000 ÷ 10³ = 8,000 ÷ 1,000 = 8.
Why zeros? The exponent tells how many zeros 10 to that power has.
3. Worked examples
Example 1 (I show you): Power
10⁴
- Four tens.
Answer: 10,000
Example 2 (We do it together): Multiply
7 × 10²
- × 100.
Answer: 700
Example 3 (You try): Divide
8,000 ÷ 10³
Show the steps and answer
- ÷ 1,000.
Answer: 8
Did you know?
10⁶ is a million: one with six zeros.
Why this matters
Powers of ten write huge and tiny numbers neatly.
4. Explore: powers
You need paper.
- Write 10², 10³, 10⁴.
- Count the zeros.
- Compute 45 × 10³.
- Compute 3,200 ÷ 10².
Think about it: what did you notice?
45,000; 32.
5. Practise
Say it in a sentence
Use these starters when you talk about the lesson. Say them out loud.
- 10 to the power ___ means ___ tens.
- It has ___ zeros.
- The answer is ___.
- I move the digits ___ places.
Guided practice
Question 1. 10³?
1,000.
Question 2. 45 × 10³?
45,000.
Question 3. 3,200 ÷ 10²?
32.
Independent practice
Level 1: Start
- 10⁴
- 10⁶ in digits
- 7 × 10²
- 8,000 ÷ 10³
- 6.5 × 10
Level 2: Grow
- 10²
- 6 × 10³
- 4,000 ÷ 10²
Level 3: Stretch
- 25 × 10⁴
- 3,000,000 ÷ 10⁵
- Ben says 10⁵ = 50,000. What is wrong?
Answers are in the answer key below. Try first, then check.
6. Apply: everyday mathematics
A bag holds 10³ grams. How many grams?
Show a sample answer
1,000.
Another one. Write 5,000,000 as 5 times a power of ten.
Show a sample answer
5 × 10⁶
7. Common mistakes
Fix: 10³ = 10 × 10 × 10.
Fix: 10³ means 10 × 10 × 10, not 10 × 3.
Fix: The exponent equals the number of zeros.
8. Lesson summary and revision card
- I can write powers of 10 with exponents.
- I can read 10³ as 1,000.
- I can multiply and divide by powers of 10.
- I can explain the pattern of zeros.
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
- Exponent = zeros.
- Move places left to multiply.
- Move right to divide.
11. Next lesson
Next lesson: Numerical expressions. 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.
- Write 10⁴ in digits. [2 marks]
- Write 10⁶ in digits. [1 mark]
- Find 7 × 10². [2 marks]
- Find 8,000 ÷ 10³. [2 marks]
- Ali says 10³ = 30. Is he right? Explain. [3 marks]
Total: 10 marks.
Marking guide and model answers
- 10 × 10 × 10 × 10 [1]; 10,000 [1]
- 1,000,000 [1]
- 10² = 100 [1]; 700 [1]
- ÷ 1,000 [1]; 8 [1]
- No [1]. 10³ = 10 × 10 × 10, not 10 × 3 [1]. It is 1,000 [1].
Score guide: 9 to 10 = secure. 6 to 8 = nearly there, revise the parts you missed. Under 6 = work through the lesson again with a grown-up.
Printable worksheet
- 10⁴
- 10⁶ in digits
- 7 × 10²
- 8,000 ÷ 10³
- 10³
- 10³ =
- 10⁴ =
- 45 × 10³ =
- 3,200 ÷ 10² =
- 10⁶ =
Homework
Write the powers of 10 from 10¹ to 10⁷.
Answer key and marking scheme
| Question | Expected response | Marks |
|---|---|---|
| 10⁴ | 10,000 | 2 |
| 10⁶ in digits | 1,000,000 | 2 |
| 7 × 10² | 700 | 2 |
| 8,000 ÷ 10³ | 8 | 2 |
| 10³ | 1,000 | 2 |
| Total | 10 |
Practice answers: Worksheet: 1 10,000; 2 1,000,000; 3 700; 4 8; 5 1,000.
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 1,000; 7 10,000; 8 45,000; 9 32; 10 1,000,000.
Independent practice answers. Level 1: 1 10,000; 2 1,000,000; 3 700; 4 8; 5 65. Level 2: 1 100; 2 6,000; 3 40. Level 3: 1 250,000; 2 30; 3 10⁵ = 10 × 10 × 10 × 10 × 10 = 100,000..
Mastery and remediation
| Objective | Bronze (Developing) | Silver (Proficient) | Gold (Advanced) |
|---|---|---|---|
| O1 Write powers of 10 with exponents | 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 Read 10³ as 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 |
| O3 Multiply and divide by powers of 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 |
| O4 Explain the pattern of 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 |
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 10³ = 30. 10³ = 10 × 10 × 10.
- Explain another way: use real objects first, then pictures.
- Show a simpler example: Multiply 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 learns powers of ten and the pattern of zeros. You do not need to be good at mathematics to help.
- Count zeros in big numbers together.
- Ask: how many tens are multiplied?
- Relate to thousand and million.
- 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: write powers of 10 with exponents; read 10³ as 1,000; multiply and divide by powers of 10; explain the pattern of zeros.
Prerequisite knowledge. Lessons 1 to 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 many tens? How many zeros?
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 10³ = 30. 10³ = 10 × 10 × 10.
13–15. Assessment questions, answer keys, marking scheme
Use the quiz and worksheet on this page. The 10-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 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 5.NBT.A.2; Cambridge Primary Mathematics Stage 5 and 6 (powers of ten). These sources informed the lesson; no official alignment is claimed.