Multiplying and Dividing by Powers of 10: a week of ready-to-teach maths
Five days of lessons for Year 6 Number. Print this pack and the week is prepared: each day has a one-page plan and a student worksheet, plus number and power cards, a mini-check and every answer.
Start here: five minutes to Monday
- Skim the week at a glance on the next page.
- Print the five days. Each day is two A4 sheets: a plan and a worksheet.
- Cut out the number and power cards once; one set per pair serves Days 1 to 4.
- Open the free interactive unit on your board. Every plan tells you which picture to show and which buttons to press.
- Teach straight from the plan. Timings, talk prompts, misconceptions and answers are all on the one page.
No maths background needed
This pack is written for the busy generalist teacher. Each plan explains the idea in plain words, lists the misconceptions children bring, and gives the answers. The big idea of the week: multiplying by 10 makes every digit worth ten times as much, so each digit moves one place to the left; dividing by 10 moves each one place to the right. The decimal point stays where it is and the digits slide past it, which is why “add a zero” fails for decimals. A multiple such as 300 is a fact and a power of 10 together: 3 × 100.
One day, one lesson
The five lessons fill a week of maths, one lesson of about 50 minutes a day. Run them in order: each day stands on the one before. Every plan marks a split point if your timetable runs two shorter sessions.
Words to watch
Say “the digits move” rather than “the point moves”: both give the same answer, but only the first explains it. A power of 10 is 10, 100, 1000 and so on; a multiple of a power of 10 is a number like 20, 300 or 4000. No calculators this week: the descriptor asks for place value and times-table facts.
The week at a glance
One lesson a day for a week. Each day stands on the day before, so run them in order.
| Day | Lesson | Children learn and do | On screen |
|---|---|---|---|
| 1 | Ten times bigger | Multiply decimals by 10, 100 and 1000 by moving every digit left, with zeros holding empty places | Multiplying by 10; Powers of 10 |
| 2 | Ten times smaller | Divide by 10, 100 and 1000 by moving every digit right, and use multiplying to check | Dividing by powers of 10 |
| 3 | Multiples of 10, 100 and 1000 | Multiply by 20, 300 or 4000 with a times-table fact and a power of 10 | Multiplying by multiples of 10 |
| 4 | Dividing by multiples | Divide by 20, 300 or 400 with a division fact and a power of 10 | Dividing by multiples of 10 |
| 5 | Estimate and check | Round to estimate, judge an answer, and convert measures by powers of 10 | Estimating to check |
How the week builds
Day 1 multiplies by powers of 10; Day 2 divides by them; Day 3 multiplies by their multiples with a times-table fact; Day 4 divides by multiples; and Day 5 estimates, checks and converts measures. It builds on the Year 4 work of multiplying and dividing whole numbers by multiples and powers of 10, and on the Year 5 work with decimals to thousandths. It leads to the next unit, fractions, decimals and percentages of a quantity, and to Year 7, where numbers are written in expanded notation with powers of 10.
Materials for the week (one trip)
- From the classroom: scissors, pencils, this pack printed.
- Cut out once, use all week: the twelve number cards and twelve power cards, one set per pair.
- Optional for Day 5: a metre ruler, a 1 L jug and kitchen scales to show the conversions.
Words for the word wall
power of 10, place value, digit, decimal point, place holder, multiple, product, quotient, estimate, round, reasonable, convert
Dear families
This week in maths, Year 6 multiplies and divides decimals by 10, 100 and 1000, and by numbers like 20 and 300, without a calculator. We think of the digits sliding left or right across the decimal point, and we estimate to check every answer.
Try this at home
- Prices: if one item costs $2.45, what do 10 cost? 100? Say how the digits move.
- Measures: how many millimetres are in 3.5 cm? How many metres is 250 cm?
- Shopping: 20 stickers cost $4.60. How much is one? (Halve, then divide by 10.)
- Ask why 2.5 × 10 is not 2.50.
My numbers this week
Fill one row a day. Find a decimal at home (price, length, mass), then multiply it by 10 and divide it by 10.
| Day | My decimal | × 10 | ÷ 10 |
|---|---|---|---|
| Monday | |||
| Tuesday | |||
| Wednesday | |||
| Thursday | |||
| Friday |
Printed from the free seegongsik Multiplying and Dividing by Powers of 10 teaching pack · seegongsik.com/au/y6/number/AC9M6N06/pack
Ten times bigger
Multiplying by 10 makes every digit worth ten times as much, so each digit moves one place to the left and an empty place gets a zero. Children slide digits across a place-value chart for × 10, × 100 and × 1000, and see why “add a zero” fails for decimals.
We are learning to
- multiply decimals by 10, 100 and 1000 by moving every digit to the left,
- use a zero to hold an empty place,
- explain why adding zeros to the end does not work for decimals.
Success criteria
- I can work out 0.035 × 100 and say how far each digit moved.
- I can explain why 2.5 × 100 is not 2.500.
You need
The worksheet, one per child, and the cut-out number and power cards, one set per pair.
Lesson flow (about 50 minutes)
| 10 min | Slide left Show the two pictures on the board (see the box). Children say each answer before you press. Ask: “When 3.5 became 35, which digit is now in the tens place? What is it worth now?” |
| 25 min | On the chart Children write 3.45 and its products in the chart in Part A, then work through Part B. Ask: “0.6 × 1000: the 6 moves three places. Which places are empty, and what goes in them?” |
| 15 min | Point slide Children do Parts C and D. Then pairs play Point slide (cut-outs) with the × power cards only. Ask: “Mia says 2.5 × 100 = 2.500. What would you show Mia on the chart?” |
Two half-sessions instead? Split after Part A; start Session B with the Powers of 10 picture.
Watch for these ideas
- Adding zeros to the end: 2.5 × 100 is 250; 2.500 still equals 2.5.
- Moving the digits the wrong way. Multiplying by 10 makes the number bigger, so the digits move left.
- Losing a place holder: 0.6 × 1000 is 600, not 6.
Answers
- Part A: 3.45 × 10 = 34.5; 3.45 × 100 = 345; 3.45 × 1000 = 3450.
- Part B: 0.42 × 10 = 4.2; 2.5 × 100 = 250; 0.6 × 1000 = 600; 0.035 × 100 = 3.5; 12.7 × 10 = 127; 0.008 × 1000 = 8.
- Part C: 100, 1000, 0.56.
- Part D: Mia is wrong. Each digit moves two places left: 2.5 × 100 = 250.
Ten times bigger
A. Slide the digits left
3.45 is in the chart. Write each product on its own row.
| thousands | hundreds | tens | ones | tenths | hundredths | thousandths | ||
|---|---|---|---|---|---|---|---|---|
| 3.45 | 3 | . | 4 | 5 | ||||
| × 10 | . | |||||||
| × 100 | . | |||||||
| × 1000 | . |
B. Work these out
0.42 × 10 = ________
2.5 × 100 = ________
0.6 × 1000 = ________
0.035 × 100 = ________
12.7 × 10 = ________
0.008 × 1000 = ________
C. Find the missing number
0.37 × ______ = 37
4.2 × ______ = 4200
______ × 100 = 56
D. Is Mia right?
Mia says 2.5 × 100 = 2.500, “because you add two zeros”. Is Mia right? Explain with the chart.
______________________________________________________________________
Ten times smaller
Dividing by 10 makes every digit worth a tenth as much, so each digit moves one place to the right. Zeros fill any empty places between the point and the first digit: 7 ÷ 100 is 0.07. Multiplying back undoes a division, which makes it a quick check.
We are learning to
- divide by 10, 100 and 1000 by moving every digit to the right,
- write the zeros a quotient needs after the decimal point,
- check a division by multiplying back.
Success criteria
- I can work out 6.3 ÷ 100 and 56 ÷ 1000.
- I can use 3.6 × 100 = 360 to say what 360 ÷ 100 is.
You need
The worksheet, one per child, and the cut-out number and power cards, one set per pair.
Lesson flow (about 50 minutes)
| 10 min | Slide right Show the dividing picture on the board (see the box). Children say each answer before you press. Ask: “7 ÷ 10: there is nothing to the right of the 7. Where does it go, and what fills the ones?” |
| 25 min | On the chart Children write 45 and its quotients in the chart in Part A, then work through Part B. Ask: “Why does 56 ÷ 1000 need a zero straight after the point?” |
| 15 min | Undo it Children do Parts C and D. Then pairs play Point slide (cut-outs) with all the power cards. Ask: “If 3.6 × 100 = 360, what is 360 ÷ 100? Why is there nothing to work out?” |
Two half-sessions instead? Split after Part A; start Session B with Point slide.
Watch for these ideas
- Moving the digits the wrong way. Dividing makes the number smaller, so the digits move right.
- Dropping a needed zero: 6.3 ÷ 100 is 0.063, not 0.63.
- Thinking a whole number divided by 10 stays whole: 7 ÷ 10 = 0.7.
Answers
- Part A: 45 ÷ 10 = 4.5; 45 ÷ 100 = 0.45; 45 ÷ 1000 = 0.045.
- Part B: 320 ÷ 100 = 3.2; 7 ÷ 10 = 0.7; 6.3 ÷ 100 = 0.063; 2500 ÷ 1000 = 2.5; 0.8 ÷ 10 = 0.08; 56 ÷ 1000 = 0.056.
- Part C: 360 ÷ 100 = 3.6; 250 ÷ 1000 = 0.25; 70.4 ÷ 10 = 7.04.
- Part D: 5 ÷ 100 and 0.5 ÷ 10 are both 0.05, so they are equal.
Ten times smaller
A. Slide the digits right
45 is in the chart. Write each quotient on its own row.
| thousands | hundreds | tens | ones | tenths | hundredths | thousandths | ||
|---|---|---|---|---|---|---|---|---|
| 45 | 4 | 5 | . | |||||
| ÷ 10 | . | |||||||
| ÷ 100 | . | |||||||
| ÷ 1000 | . |
B. Work these out
320 ÷ 100 = ________
7 ÷ 10 = ________
6.3 ÷ 100 = ________
2500 ÷ 1000 = ________
0.8 ÷ 10 = ________
56 ÷ 1000 = ________
C. Undo it
3.6 × 100 = 360, so 360 ÷ 100 = ________
0.25 × 1000 = 250, so 250 ÷ 1000 = ________
7.04 × 10 = 70.4, so 70.4 ÷ 10 = ________
D. Which is bigger?
Which is bigger: 5 ÷ 100 or 0.5 ÷ 10? Or are they equal? Show how you know.
______________________________________________________________________
Multiples of 10, 100 and 1000
To multiply by 300, multiply by 3 and then by 100: a times-table fact does the work and the power of 10 moves the digits. The order does not matter, so children choose whichever step is easier first.
We are learning to
- split a multiple such as 300 into a fact and a power of 10,
- multiply a decimal by the fact, then move the digits,
- solve money and measurement problems this way.
Success criteria
- I can work out 0.7 × 600 and show both steps.
- I can explain why 0.6 × 300 is more than 100 but less than 1000.
You need
The worksheet, one per child.
Lesson flow (about 50 minutes)
| 10 min | Fact, then slide Run the multiplying vote on the board (see the box). Children choose before each press. Ask: “0.6 × 300: what is 0.6 × 3? What does the × 100 do then?” |
| 25 min | Split the multiple Children write both steps for each product in Part A. Ask: “For 0.08 × 50, is it easier to multiply by 5 first or by 10 first?” |
| 15 min | Stories Children solve the stories in Part B and write their own in Part C. Ask: “300 tickets at $2.50: why must the answer be more than $500 but less than $1000?” |
Two half-sessions instead? Split after Part A; start Session B with the first story.
Watch for these ideas
- Adding the two steps instead of doing one after the other: 0.6 × 300 is 0.6 × 3 × 100.
- Forgetting the power of 10: 0.08 × 50 is 4, not 0.4.
- Fact slips with decimals: 0.7 × 6 = 4.2, so 0.7 × 600 = 420.
Answers
- Part A: 0.4 × 20 = 0.4 × 2 × 10 = 0.8 × 10 = 8; 1.5 × 300 = 1.5 × 3 × 100 = 4.5 × 100 = 450; 0.08 × 50 = 0.08 × 5 × 10 = 0.4 × 10 = 4; 2.3 × 4000 = 2.3 × 4 × 1000 = 9.2 × 1000 = 9200; 0.7 × 600 = 0.7 × 6 × 100 = 4.2 × 100 = 420; 0.06 × 3000 = 0.06 × 3 × 1000 = 0.18 × 1000 = 180.
- Part B: (1) $750; (2) 8 m; (3) 48 kg.
- Part C: answers will vary; check that the multiple was split into a fact and a power of 10.
Multiples of 10, 100 and 1000
A. Fact first, then slide
Split the multiple into a fact and a power of 10. Write both steps.
0.4 × 20 = 0.4 × 2 × 10 = ________ × 10 = ________
1.5 × 300 = 1.5 × 3 × 100 = ________ × 100 = ________
0.08 × 50 = 0.08 × 5 × 10 = ________ × 10 = ________
2.3 × 4000 = 2.3 × 4 × 1000 = ________ × 1000 = ________
0.7 × 600 = 0.7 × 6 × 100 = ________ × 100 = ________
0.06 × 3000 = 0.06 × 3 × 1000 = ________ × 1000 = ________
B. Stories
1. A concert ticket costs $2.50. How much do 300 tickets cost?
Working: ________________________________ Answer: ________
2. A floor tile is 0.4 m long. How long is a row of 20 tiles?
Working: ________________________________ Answer: ________
3. A bag of rice weighs 1.2 kg. What do 40 bags weigh?
Working: ________________________________ Answer: ________
C. Your own
Write a story that needs × 400 for a partner. Solve it on the back.
______________________________________________________________________
Dividing by multiples
To divide by 20, divide by 2 and then by 10: the division fact does the work and the power of 10 moves the digits right. Children write both steps and check the answer by multiplying back.
We are learning to
- split a divisor such as 400 into a fact and a power of 10,
- divide by the fact, then move the digits right,
- check a quotient by multiplying it back.
Success criteria
- I can work out 4.8 ÷ 20 and 360 ÷ 400 and show both steps.
- I can check a quotient by multiplying.
You need
The worksheet, one per child.
Lesson flow (about 50 minutes)
| 10 min | Fact, then slide Run the dividing vote on the board (see the box). Children choose before each press. Ask: “4.8 ÷ 20: why divide by 2 first? What does the ÷ 10 do then?” |
| 25 min | Split the divisor Children write both steps for each quotient in Part A, then check two of them by multiplying. Ask: “6.3 ÷ 3: how does 63 ÷ 3 help?” |
| 15 min | Stories Children solve the stories in Part B. Ask: “One pencil costs $0.24. How can we check it by multiplying?” |
Two half-sessions instead? Split after Part A; start Session B with the first story.
Watch for these ideas
- Dividing by the fact but forgetting the power of 10: 4.8 ÷ 20 is 0.24, not 2.4.
- Moving the digits left after dividing. A quotient by 400 is smaller, so the digits move right.
- Stuck on 6.3 ÷ 3: think 63 tenths ÷ 3 = 21 tenths, so 6.3 ÷ 3 = 2.1.
Answers
- Part A: 4.8 ÷ 20 = 4.8 ÷ 2 ÷ 10 = 2.4 ÷ 10 = 0.24; 360 ÷ 400 = 360 ÷ 4 ÷ 100 = 90 ÷ 100 = 0.9; 6.3 ÷ 30 = 6.3 ÷ 3 ÷ 10 = 2.1 ÷ 10 = 0.21; 1.2 ÷ 40 = 1.2 ÷ 4 ÷ 10 = 0.3 ÷ 10 = 0.03; 900 ÷ 300 = 900 ÷ 3 ÷ 100 = 300 ÷ 100 = 3; 5.6 ÷ 800 = 5.6 ÷ 8 ÷ 100 = 0.7 ÷ 100 = 0.007.
- Part B: (1) $0.24; (2) 9 m; (3) 0.008 kg = 8 g.
Dividing by multiples
A. Fact first, then slide
Split the divisor into a fact and a power of 10. Write both steps.
4.8 ÷ 20 = 4.8 ÷ 2 ÷ 10 = ________ ÷ 10 = ________
360 ÷ 400 = 360 ÷ 4 ÷ 100 = ________ ÷ 100 = ________
6.3 ÷ 30 = 6.3 ÷ 3 ÷ 10 = ________ ÷ 10 = ________
1.2 ÷ 40 = 1.2 ÷ 4 ÷ 10 = ________ ÷ 10 = ________
900 ÷ 300 = 900 ÷ 3 ÷ 100 = ________ ÷ 100 = ________
5.6 ÷ 800 = 5.6 ÷ 8 ÷ 100 = ________ ÷ 100 = ________
Check two of them by multiplying: ______________________________________________
B. Stories
1. A packet of 20 pencils costs $4.80. How much is one pencil?
Working: ________________________________ Answer: ________
2. A 360 m running track is marked into 40 equal sections. How long is each section?
Working: ________________________________ Answer: ________
3. A 2.4 kg bag of flour is shared into 300 equal scoops. How much is in each scoop, in kilograms and in grams?
Working: ________________________________ Answer: ________
Estimate and check
Rounding the decimal to one non-zero digit gives a quick estimate: 3.9 × 200 is about 4 × 200 = 800. Children estimate first, calculate exactly, and use the estimate to catch an answer whose digits moved the wrong number of places. Then they convert measures, which are powers of 10 at work.
We are learning to
- estimate a product or quotient by rounding,
- judge whether an answer is reasonable and fix it when it is not,
- convert between metric units by multiplying or dividing by 10, 100 or 1000.
Success criteria
- I can estimate 3.9 × 200 in my head and say whether 7.8 is a sensible answer.
- I can change 450 cm into metres and explain which way the digits move.
You need
The worksheet, one per child; a metre ruler, a 1 L jug and kitchen scales are a bonus for Part C.
Lesson flow (about 50 minutes)
| 10 min | Is it reasonable? Run the estimate check on the board (see the box). Children choose before each press. Ask: “3.2 × 100 = 32? Without working it out, how do you know it is wrong?” |
| 25 min | Estimate, then calculate Children estimate and calculate each line of Part A, then judge the answers in Part B. Ask: “0.48 × 30: what friendly number is close to 0.48?” |
| 15 min | Measures Children convert the measures in Part C. Finish with the self-check quiz on the board as a class game. Ask: “Why does changing kilometres to metres make the number bigger?” |
Two half-sessions instead? Split after Part A; start Session B with the answers in Part B.
Watch for these ideas
- Rounding to a whole number when the decimal is less than 1: 0.48 rounds to 0.5, not 0.
- Trusting a neat-looking answer: 36 ÷ 400 = 0.9 looks tidy but is ten times too big.
- Converting the wrong way: a smaller unit needs more of them, so centimetres to metres divides.
Answers
- Part A: 3.9 × 200: about 800, exact 780; 0.48 × 30: about 15, exact 14.4; 61 ÷ 20: about 3, exact 3.05; 8.4 ÷ 40: about 0.2, exact 0.21.
- Part B: 75 is wrong; it is 750; 24 is right; 4200 is right; 0.9 is wrong; it is 0.09.
- Part C: 2.5 km = 2500 m; 450 cm = 4.5 m; 0.75 L = 750 mL; 3600 g = 3.6 kg; 8.5 cm = 85 mm.
Estimate and check
A. Estimate, then calculate
| Calculation | Estimate (round first) | Exact answer |
|---|---|---|
| 3.9 × 200 | ||
| 0.48 × 30 | ||
| 61 ÷ 20 | ||
| 8.4 ÷ 40 |
B. Right or wrong?
Estimate each one. Tick the right answers; fix the wrong ones.
| Someone’s answer | Estimate | Right? | Fixed answer |
|---|---|---|---|
| 2.5 × 300 = 75 | |||
| 0.6 × 40 = 24 | |||
| 4.2 × 1000 = 4200 | |||
| 36 ÷ 400 = 0.9 |
C. Convert the measures
2.5 km = ________ m
450 cm = ________ m
0.75 L = ________ mL
3600 g = ________ kg
8.5 cm = ________ mm
Number cards
Cut out the twelve number cards and the twelve power cards on the next sheet, once. Pairs use them on Days 1 to 4.
Point slide (Days 1 to 4)
- Shuffle the number cards into one pile and the power cards into another.
- Each player turns over one card from each pile and works out the answer without a calculator.
- Say how far each digit moved, and which way: “3.5 × 100: every digit moved two places left, so 350.”
- The bigger answer wins all four cards. Equal answers: both put their cards back.
Day 1: use only the × power cards. Teacher note: the largest possible answer is 160 × 1000 = 160 000; the smallest is 0.3 ÷ 100 = 0.003.
Power cards
Every number card has at most one decimal place, so no answer needs more than three.
Teacher note: a quick check for any pair, for example 3.5 × 100 = 350: multiplying makes the number bigger, dividing makes it smaller.
What we know: Multiplying and Dividing by Powers of 10
Work on your own. No calculator. Show your thinking if you can.
- 4.7 × 100 = ________
- 0.035 × 1000 = ________
- 52 ÷ 100 = ________
- 6.3 ÷ 10 = ________
- 0.8 × 300 = ________ (show both steps)
- 7.2 ÷ 40 = ________ (show both steps)
- Estimate 3.9 × 200. Is 7.8 a sensible answer? Why? ______________________________
- A packet of 20 stickers costs $4.20. How much is one sticker? ________
How did this week feel? Circle one: I can teach it · I am getting there · I need more help
Answers and marking guide
Answers
- 470.
- 35.
- 0.52.
- 0.63.
- 0.8 × 300 = 0.8 × 3 × 100 = 2.4 × 100 = 240.
- 7.2 ÷ 40 = 7.2 ÷ 4 ÷ 10 = 1.8 ÷ 10 = 0.18.
- About 4 × 200 = 800, so 7.8 is not sensible; the exact answer is 780.
- $0.21 (4.2 ÷ 20 = 4.2 ÷ 2 ÷ 10 = 2.1 ÷ 10 = 0.21).
A quick three-level guide
| Idea | Working towards | At standard | Beyond |
|---|---|---|---|
| Powers of 10 (Q1 to Q4) | adds or removes zeros instead of moving digits | multiplies and divides by 10, 100 and 1000 with zeros as place holders | explains the move as each digit changing its value |
| Multiples (Q5, Q6) | uses the fact but forgets the power of 10 | splits a multiple into a fact and a power of 10 and shows both steps | chooses the easier order of the two steps |
| Estimating (Q7) | rounds but does not compare | estimates by rounding and judges an answer | says how many places a wrong answer is out |
| Problems (Q8) | cannot choose the operation | chooses the operation and gives money to two places | checks the answer by multiplying back |
Eight questions, four ideas. A child at standard answers most questions and can say why, with digits moving across the point, a fact and a power of 10, or an estimate.
Weekly class record
Jot a tick as you move around the room; the mini-check fills any gaps. A tick a day is plenty.
| Name | Multiply by powers | Divide by powers | Multiply by multiples | Divide by multiples | Estimate and measure |
|---|---|---|---|---|---|
The five columns are the five days: multiplying by powers of 10, dividing by them, multiplying by multiples, dividing by multiples, and estimating and measures.