Primary 5 Foundation maths · Operations · About 12 minutes
Multiply and divide by 10, 100 and 1000 and their multiples without a calculator
Track a named digit and the value of its old and new columns.
Start the interactive lesson →Open practice activity
What you will learn
- Multiply and divide by 10, 100 and 1000 and their multiples without a calculator
Models used: number sentences, stories, tables.
Before you start
Ten times as much
Three tens and two ones make 32.
The number at the top of each column is the value of one counter in that column.
Three tens and two ones make 32.
The digits occupy different places because their values change. Thinking about units also works for division.
The number at the top of each column is the value of one counter in that column.
Make every unit ten times as large. Three tens become three hundreds; two ones become two tens.
A digit tells us how many units there are. Its position tells us what size those units are; that is why a zero can matter.
The number at the top of each column is the value of one counter in that column.
The result is 320. Divide by ten to return each unit to its previous size.
32 × 10 = 320; 320 ÷ 10 = 32
A digit tells us how many units there are. Its position tells us what size those units are; that is why a zero can matter.
What did the picture help us see?
The result is 320. Divide by ten to return each unit to its previous size.
Worked example: A new example, together
Calculate 200 ÷ 100.
| Total to share | Number of equal shares |
|---|---|
| 200 | 100 |
The unknown is the amount in one share. Read each value with the heading above its column.
Track a named digit and the value of its old and new columns.
Division finds how many equal-sized units make the total.
The unknown is the amount in one share. Total to share Number of equal shares 200 100 The unknown is the amount in one share. Read each value with the heading above its column.
200 ÷ 100 asks how many 100s make 200.
The unknown is the amount in one share. Total to share Number of equal shares 200 100 Calculate 200 ÷ 100.
2
The unknown is the amount in one share. Read each value with the heading above its column.
200 ÷ 100 asks how many 100s make 200.
The unknown is the amount in one share. Total to share Number of equal shares 200 100 The unknown is the amount in one share. Read each value with the heading above its column.
100 × 2 = 200.
The unknown is the amount in one share. Total to share Number of equal shares 200 100 The unknown is the amount in one share. Read each value with the heading above its column.
So 200 ÷ 100 = 2.
The unknown is the amount in one share. Total to share Number of equal shares 200 100 The unknown is the amount in one share. Read each value with the heading above its column.
Check the result against the question we started with.
2 × 100 = 200.
We found 2. Division finds how many equal-sized units make the total.
The unknown is the amount in one share. Total to share Number of equal shares 200 100
Common mistakes to discuss
- Adding a zero. Multiplying by 10 moves every digit one place left. 4.3 × 10 is 43, and 200 ÷ 100 is 2 rather than “200 with zeros removed”.
Check your understanding
- Multiply and divide by 10, 100 and 1000 and their multiples without a calculator
- justify multiplication or division by powers of ten with place value
- check the answer against the original quantities and units
Explain your reasoning to an adult, then try a fresh question in the interactive lesson. A result from one attempt is not proof of lasting mastery.
Try this lesson →Related Primary 5 Foundation lessons
- Add and subtract up to three-digit numbers without a calculatorAdd and subtract up to three-digit numbers without a calculator · About 12 minutes
- Mentally add and subtract ones, tens and hundredsMentally add and subtract ones, tens and hundreds · About 12 minutes
- Multiply and divide up to two digits by one digit without a calculatorMultiply and divide up to two digits by one digit without a calculator · About 12 minutes
- Use the order of operations and bracketsUse the order of operations and brackets · About 12 minutes
- Recall multiplication and division factsRecall multiplication and division facts · About 12 minutes