Multiplying and Dividing by 10, 100 and 1000: a week of ready-to-teach maths

Five days of lessons for Year 4 Number. Print this pack and the week is prepared: each day has a one-page plan and a student worksheet, plus a cut-out place-value mat, digit cards and problem cards, a mini-check and every answer.

Start here: five minutes to Monday

1. Skim the week at a glance on the next page.
2. Print the five days. Each day is two A4 sheets: a plan and a worksheet.
3. Cut out the two card sheets once; the mat and cards are reused all week.
4. Open the free interactive unit on your board. Every plan tells you which picture to show and which buttons to press.
5. 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 is short: each place is worth ten times the place to its right. Multiply by 10 and every digit moves up one place; divide by 10 and every digit moves down one. The zero in 370 is not stuck on: it holds the empty ones place.

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.

Why not just add a zero?

“Add a zero” gives the right answer for 37 × 10, but it hides the reason and fails later with decimals (0.5 × 10 is 5, not 0.50). This pack always moves the digits on the place-value mat, so children see why the zero appears and can run the move backwards to divide.

The week at a glance

One lesson a day for a week. Each day stands on the day before, so run them in order.

How the week builds

Day 1 multiplies by 10 and shows why the digits shift; Day 2 runs the shift backwards to divide; Day 3 shifts two and three places for 100 and 1000; Day 4 turns the pattern into the count-the-zeros rule with its reason; and Day 5 uses multiples of ten (20, 300, 4000) to solve real problems in your head. It builds on place value and the times tables, and every written method for multiplying big numbers leans on it.

Materials for the week (one trip)

• From the classroom: scissors, pencils, this pack printed.
• Cut out once, use all week: the place-value mat, the digit cards and the problem cards in this pack. No maths equipment or calculators needed.

Words for the word wall

place value, digit, ones, tens, hundreds, thousands, ten-thousands, multiply, divide, ten times bigger, ten times smaller, power of 10, multiple of 10, shift

Dear families

This week in maths, Year 4 multiplies and divides by 10, 100 and 1000 in their heads. We learn why it works: each place is worth ten times the place to its right, so multiplying by 10 moves every digit one place to the left.

Try this at home

• Ask: if one ticket costs $4, what do 10 tickets cost? 100 tickets?
• Turn it round: $250 shared by 10 people is how much each?
• Use multiples of ten in the shops: 3 packs at $20 is 3 × 2 tens, which is 6 tens, $60.
• Ask your child to explain why 40 × 10 is 400, not 4000.

My times-ten facts this week

Fill one row a day. Choose a number and make it 10, 100 and 1000 times bigger.

Printed from the free seegongsik Multiplying and Dividing by 10, 100 and 1000 teaching pack · seegongsik.com/au/y4/number/AC9M4N05/pack

Ten times bigger

Children multiply by 10 on a place-value chart. Each place is worth ten times the place to its right, so making a number ten times bigger moves every digit one place to the left. The ones place is left empty, and a zero holds it.

We are learning to

• explain that each place is worth ten times the place to its right,
• multiply a whole number by 10 by moving every digit one place to the left,
• explain the zero in 370: it holds the empty ones place.

Success criteria

• I can multiply a number by 10 on the place-value chart.
• I can explain where the digits went and why there is a zero.

You need

The place-value mat and digit cards (cut-out sheet 1), one set per pair. The worksheet, one per child.

Lesson flow (about 50 minutes)

Two half-sessions instead? Split after 46 on the mat; start Session B with Part A.

Watch for these ideas

• “Just add a zero” with no reason. Ask where each digit went.
• Moving only the last digit: 213 × 10 as 2103. Every digit moves.
• Writing 705 × 10 as 7500, dropping the zero tens. Each digit keeps its own column.

Answers

• Part A: 46 × 10 = 460; 9 × 10 = 90; 213 × 10 = 2130; 705 × 10 = 7050.
• Part B: 65; 300; 100; 700. Part C: the 4 tens become 4 hundreds, so 40 × 10 = 400; zeros hold the empty tens and ones.

Ten times bigger

A. Multiply by 10. Write the answer’s digits in the chart.

B. Fill the gaps

______ × 10 = 650     30 × 10 = ______

1000 = ______ × 10     7 × 10 × 10 = ______

C. Explain why 40 × 10 = 400. Use the words tens and hundreds.

Ten times smaller

Children divide by 10 by running yesterday’s move backwards: every digit moves one place to the right and becomes ten times smaller. 250 ÷ 10 is 25, because 25 tens are 250.

We are learning to

• divide a whole number ending in 0 by 10 by moving every digit one place to the right,
• explain dividing by 10 as the reverse of multiplying by 10,
• check a division by multiplying back.

Success criteria

• I can divide a number by 10 on the place-value chart.
• I can check my answer by multiplying it by 10.

You need

The place-value mat and digit cards (cut-out sheet 1), one set per pair. The worksheet, one per child.

Lesson flow (about 50 minutes)

Two half-sessions instead? Split after 460 on the mat; start Session B with Part A.

Watch for these ideas

• Moving the digits the wrong way and making the number bigger. Ten times smaller means each digit drops a place.
• “Take off a zero” from the wrong place: 3050 ÷ 10 as 350. Every digit moves, zeros included.
• Thinking 90 ÷ 10 is 0 because the zero goes. The 9 tens become 9 ones.

Answers

• Part A: 430 ÷ 10 = 43; 90 ÷ 10 = 9; 1600 ÷ 10 = 160; 3050 ÷ 10 = 305. Part B: 56 × 10 = 560, so 560 ÷ 10 = 56; 208 × 10 = 2080, so 2080 ÷ 10 = 208.
• Part C: 700 ÷ 10 = 70; 5200 ÷ 10 = 520; 90 ÷ 10 = 9.

Ten times smaller

A. Divide by 10. Write the answer’s digits in the chart.

B. Times and divide undo each other

56 × 10 = ________,  so ________ ÷ 10 = 56

208 × 10 = ________,  so ________ ÷ 10 = 208

C. Circle the right answer, then check by multiplying by 10

700 ÷ 107000       70       7

5200 ÷ 10520       52       52 000

90 ÷ 10900       0       9

Two places, three places

Children multiply and divide by 100 and 1000. 100 is ten tens, so multiplying by 100 is multiplying by 10 twice: every digit moves two places. 1000 moves every digit three places. Dividing runs the same moves to the right.

We are learning to

• multiply by 100 by moving every digit two places left, and by 1000 by moving it three,
• divide by 100 and 1000 by moving every digit two or three places right,
• explain why: 100 is 10 × 10, and 1000 is 10 × 10 × 10.

Success criteria

• I can multiply and divide by 100 and 1000 in my head.
• I can show the move on the place-value chart.

You need

The place-value mat and digit cards (cut-out sheet 1), one set per pair. The worksheet, one per child.

Lesson flow (about 50 minutes)

Two half-sessions instead? Split after Part A; start Session B with 15 × 1000.

Watch for these ideas

• Moving one place for 100: 18 × 100 as 180. Each zero is one more place.
• Losing a zero already in the number: 40 × 100 as 400. The 4 tens become 4 thousands.
• Writing big answers without the space: 12500 for 12 500. Five digits get a space after the thousands.

Answers

• Part A: 18 × 100 = 1800; 15 × 1000 = 15 000. Parts B and C: 6 × 100 = 600; 18 × 100 = 1800; 40 × 100 = 4000; 125 × 100 = 12 500; 3 × 1000 = 3000; 15 × 1000 = 15 000; 20 × 1000 = 20 000.
• Part D: 900 ÷ 100 = 9; 4300 ÷ 100 = 43; 8000 ÷ 100 = 80; 7000 ÷ 1000 = 7; 16 000 ÷ 1000 = 16.

Two places, three places

A. Show the move on the chart

B. Multiply by 100

6 × 100 = ________18 × 100 = ________40 × 100 = ________125 × 100 = ________

C. Multiply by 1000

3 × 1000 = ________15 × 1000 = ________20 × 1000 = ________

D. Divide by 100 and 1000

900 ÷ 100 = ________4300 ÷ 100 = ________8000 ÷ 100 = ________7000 ÷ 1000 = ________16 000 ÷ 1000 = ________

Count the zeros, know the reason

Children turn the week’s pattern into a rule: the number of zeros in 10, 100 or 1000 tells you how many places to move. Then they test the rule on mistakes, so it stays a place-value move and not “stick zeros on”.

We are learning to

• use the number of zeros in 10, 100 or 1000 to know how many places the digits move,
• explain the rule: each zero is one more factor of ten, one more column,
• find and fix answers where the zeros were counted or placed wrongly.

Success criteria

• I can fill a table of times 10, 100 and 1000.
• I can find a wrong answer and explain the mistake.

You need

The place-value mat and digit cards (cut-out sheet 1), one set per pair, to check the claims. The worksheet, one per child.

Lesson flow (about 50 minutes)

Two half-sessions instead? Split after Part A; start Session B with the claims.

Watch for these ideas

• Mixing up the zeros already in the number with the zeros in 100. In 30 × 100 the 3 moves two places, from tens to thousands: 3000.
• Taking off the wrong number of zeros when dividing: 5000 ÷ 100 as 500.
• Using the rule without the reason, then trying it on 0.5 × 10. The digits still move one place.

Answers

• Part A: 4: 40, 400, 4000; 25: 250, 2500, 25 000; 60: 600, 6000, 60 000.
• Part B: Sam is wrong (30 × 100 = 3000); Lee is wrong (5000 ÷ 100 = 50); Ana is wrong (12 × 1000 = 12 000); Kit is right. Part C: two places, because 100 = 10 × 10; three places.

Count the zeros, know the reason

A. Fill the table

B. Right or wrong? Fix the wrong ones.

C. Finish the rule

Multiplying by 100 moves every digit ______ places to the left, because ______________________.

Multiplying by 1000 moves every digit ______ places to the left.

Multiples of ten in real problems

Children solve problems with multiples of ten, such as 300 × 4, in their heads. Split the multiple into a fact and a power of ten: 300 is 3 hundreds, so 300 × 4 is 3 × 4 hundreds, which is 12 hundreds, or 1200. Dividing works the same way backwards.

We are learning to

• split a multiple of ten into a known fact and a power of ten (300 is 3 hundreds),
• multiply and divide with multiples of ten without a calculator,
• write a number sentence for a story problem and say what the answer means.

Success criteria

• I can work out 300 × 4 and 1200 ÷ 300 in my head and explain how.
• I can solve a story problem and answer it in a sentence.

You need

The problem cards (cut-out sheet 2), one set per group of four. The worksheet, one per child.

Lesson flow (about 50 minutes)

Two half-sessions instead? Split after Part B; start Session B with the problem cards.

Watch for these ideas

• Multiplying the zeros too: 300 × 4 as 3 × 4 = 12, then forgetting the hundreds.
• Dividing the wrong way: 1200 ÷ 300 as 400. Ask how many 300s make 1200.
• An answer with no meaning. 40 is the number of trays, not eggs: say what the answer counts.

Answers

• Part A: 20 × 3 = 6 tens = 60; 300 × 4 = 12 hundreds = 1200; 50 × 6 = 30 tens = 300; 4000 × 2 = 8 thousands = 8000. Part B: 1200 ÷ 300 = 4; 800 ÷ 20 = 40; 1500 ÷ 500 = 3.
• Problem cards: 1. 120; 2. 1200; 3. 350; 4. 4; 5. 40; 6. 360; 7. 30; 8. 1000; 9. 4; 10. 480; 11. 30; 12. 2100.

Multiples of ten in real problems

A. Split it into a fact and a power of ten

20 × 3= 2 tens × 3 = ______ tens = ________

300 × 4= 3 hundreds × 4 = ______ hundreds = ________

50 × 6= 5 tens × 6 = ______ tens = ________

4000 × 2= 4 thousands × 2 = ______ thousands = ________

B. Share it

1200 ÷ 300= 12 hundreds ÷ 3 hundreds = ______

800 ÷ 20= 80 tens ÷ 2 tens = ______

1500 ÷ 500= 15 hundreds ÷ 5 hundreds = ______

C. Three problem cards I solved

Place-value mat and digit cards

Keep the mat whole. Cut out the digit cards. Put a number on the mat, one digit in each column, then slide every card left to multiply by 10 or right to divide by 10. The extra zero cards hold the empty places. One set per pair.

Digit cards

Teacher note: the cards are sized to sit inside a column of the mat. Two of every digit plus four extra zeros is enough for 125 × 100 = 12 500 or 15 × 1000 = 15 000, and every answer this week fits on the five columns.

Problem cards

Cut out the twelve cards (Day 5). Each one uses a multiple of ten. Write a number sentence, split the multiple of ten into a fact and a power of ten, and answer in a sentence.

Teacher note: the answers are at the foot of the Day 5 plan, card by card.

What we know: Multiplying and Dividing by 10, 100 and 1000

Work on your own, without a calculator. Show your thinking if you can.

1. 46 × 10 = __________
2. 3800 ÷ 10 = __________
3. 27 × 100 = __________
4. 9 × 1000 = __________
5. 56 000 ÷ 100 = __________
6. Fill the gaps: 64 × ______ = 6400    ______ ÷ 10 = 32
7. 40 × 7 = __________    600 × 3 = __________
8. Tickets cost $20 each. How much do 35 tickets cost? Show how you split it. ______________________________

Answers and marking guide

Answers

1. 460 (every digit one place left).
2. 380 (every digit one place right).
3. 2700 (two places left).
4. 9000 (three places left).
5. 560 (two places right).
6. 100; 320.
7. 280 (4 tens × 7 = 28 tens); 1800 (6 hundreds × 3 = 18 hundreds).
8. $700: 20 is 2 tens, and 2 tens × 35 = 70 tens.

A quick three-level guide

Eight questions, three ideas. A child at standard answers most questions without a calculator and explains them as digits moving places.

Weekly class record

Jot a tick as you move around the room; the mini-check fills any gaps. A tick a day is plenty.

The five columns are the five days: times 10, divide by 10, 100 and 1000, the zeros rule, and problems.