- Multiply and divide decimals mentally by 10 or 100, and integers by 1000, and explain the effect
## Examples of what pupils should know and be able to do

Complete statements such as:

- $4\xf710=\square $
- $4\xf7\mathrm{\square}=0.04$
- $0.4\times 10=\mathrm{\square}$
- $0.4\times \mathrm{\square}=400$
- $0.4\xf710=\mathrm{\square}$
- $0.4\xf7\mathrm{\square}=0.004$
- $\mathrm{\square}\xf7100=0.04$
- $\mathrm{\square}\xf710=40$
- $\mathrm{\square}\times 1000=40,000$
- $\mathrm{\square}\times 10=400$

- Secondary mathematics exemplification: Multiply and divide numbers by 10, 100 and 1000
- Assessment example: Place value (space invaders): Aba (PDF-775 KB) Attachments

## Probing questions

- Why do $25\xf710$ and $250\xf7100$ give the same answer?
- This calculator display shows 0.001. Tell me what will happen when I multiply by 100. What will the display show?
- I divide a number by 10, and then divide the result by 10. The answer is 0.3.
- What number did I start with? How do you know?
- How would you explain to someone how to multiply a decimal by 10 … , how to divide a decimal by 100? …

## What if pupils find this a barrier?

Use units that pupils are confident with, for example conversions between cm and m.

Encourage pupils to use common sense, e.g. $0.67\times 100$. Is the answer larger or smaller?

- Targeting level 4 lesson: Multiplying and dividing decimals by 10 or 100
- Example questions: Multiplication and ordering of decimals (DOC-76 KB) Attachments

Download Mathematics ITP: Moving digits (SWF-32 KB) Attachments to show that it is the digits that 'move' and not the decimal point.

Use Partitioning loop cards (PDF-89 KB) Attachments , set 10 to practise.

- Round positive whole numbers to the nearest 10, 100 or 1000, and decimals to the nearest whole number or one decimal place
## Examples of what pupils should know and be able to do

- Secondary mathematics exemplification: Round numbers, including to a given number of decimal places

## Probing questions

- How do you go about rounding a number to the nearest 100? What do you look for?
- Is 230 rounded to the nearest 10, 100 or 1000? How do you know?
- Is 500 rounded to the nearest 10, 100 or 1000? How do you know?
- What is the largest/smallest number to one decimal place that would be rounded to 7?
- What is the largest/smallest number to two decimal places that would be rounded to 7?
- What is the largest/smallest number altogether that would be rounded to 7?

## What if pupils find this a barrier?

Refer back to Step 3 and possibly Step 2.

Expand the number-line image to include tenths and hundredths.

Encourage pupils to see the equivalence between rounding to one decimal place and rounding to the nearest tenth.

- Find the difference between a positive and a negative integer, or two negative integers, in a context such as temperature or the number line
## Examples of what pupils should know and be able to do

- Secondary mathematics exemplification: Order, add, subtract, multiply and divide positive and negative numbers

## Probing questions

- Talk me through the picture in your mind when you calculate the answer to the following question:
- The temperature is
^{-}5° C. If it falls by 6 degrees, what will the temperature be?

## What if pupils find this a barrier?

Build on understanding of difference, using a number line to count forwards or back.

Use vertical and horizontal number lines.

- Targeting level 4 lesson: Positive and negative numbers
- Mathematics ITP: Thermometer (SWF-52 KB) Attachments
- Mathematics ITP: Difference (SWF-32 KB) Attachments

### Attachments

### Related downloads

- Place value (space invaders): Aba [ pdf : 775 KB ]
- Multiplication and ordering of decimals [ doc : 76 KB ]
- Mathematics ITP: Moving digits
- [Windows executable] - [ exe : 4.1 MB ]
- [Flash] - [ swf : 32 KB ]
- Mathematics ITP: Thermometer
- [Windows executable] - [ exe : 4.1 MB ]
- [Flash] - [ swf : 52 KB ]
- Mathematics ITP: Difference
- [Windows executable] - [ exe : 4.1 MB ]
- [Flash] - [ swf : 32 KB ]
- Partitioning loop cards [ pdf : 89 KB ]
- Download all [ 959 KB ]