Primary 5 maths · Whole numbers · About 12 minutes
Multiply and divide by 10, 100, 1000 and their multiples
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, 1000 and their multiples
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 4000 ÷ 1000.
| First quantity | Operation | Second quantity |
|---|---|---|
| 4000 | / | 1000 |
Keep the units and place values aligned. 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.
Keep the units and place values aligned First quantity Operation Second quantity 4000 / 1000 Keep the units and place values aligned. Read each value with the heading above its column.
4000 ÷ 1000 asks how many 1000s make 4000.
Keep the units and place values aligned First quantity Operation Second quantity 4000 / 1000 Calculate 4000 ÷ 1000.
4
Keep the units and place values aligned. Read each value with the heading above its column.
4000 ÷ 1000 asks how many 1000s make 4000.
Keep the units and place values aligned First quantity Operation Second quantity 4000 / 1000 Keep the units and place values aligned. Read each value with the heading above its column.
1000 × 4 = 4000.
Keep the units and place values aligned First quantity Operation Second quantity 4000 / 1000 Keep the units and place values aligned. Read each value with the heading above its column.
So 4000 ÷ 1000 = 4.
Keep the units and place values aligned First quantity Operation Second quantity 4000 / 1000 Keep the units and place values aligned. Read each value with the heading above its column.
Check the result against the question we started with.
4 × 1000 = 4000.
We found 4. Division finds how many equal-sized units make the total.
Keep the units and place values aligned First quantity Operation Second quantity 4000 / 1000
Common mistakes to discuss
- Adding a zero. Multiplying by 10 moves every digit one place left; it does not append a character. 2.5 × 10 is 25, not 2.50.
Check your understanding
- Multiply and divide by 10, 100, 1000 and their multiples
- 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.
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