- Understand and use decimal notation and place value
## Examples of what pupils should know and be able to do

Know, for example:

- In 5.239 the digit 9 represents nine thousandths, which is written as 0.009.
- The number 5.239 in words is 'five point two three nine'.
- The fraction $5\frac{239}{1000}$ is read as 'five and two hundred and thirty-nine thousandths'.
- Secondary mathematics exemplification: Understand and use decimal notation and place value; multiply and divide integers and decimals by powers of 10

## Probing questions

- What is the purpose of the decimal point?
- What is a 'decimal'?
- Why is 0 so useful when it is worth nothing?
- How would you explain to someone that 0.35 is greater than 0.035?

## What if pupils find this a barrier?

Use number lines to show that 0.1 is equivalent to $\frac{1}{10}$ (one tenth) or 10 hundredths and that 0.01 is equivalent to one hundredth.

A common mistake is for pupils to read the number 5.239 as 'five point two hundred and thirty-nine'.

Download Mathematics ITP: Moving digits (SWF-32 KB) Attachments and use it to change between fractions, decimals, and place value to make appropriate links.

- Targeting level 4 lesson: Decimal notation and place value

- Order a given set of positive and negative integers
## Examples of what pupils should know and be able to do

Pupils should be able to order a set of positive and negative integers on a number line and on a temperature scale.

- Primary mathematics exemplification: Negative numbers
- Assessment example: Temperatures: Vinay and Sam (PDF-254 KB) Attachments

## Probing questions

- What do you look for first when you are asked to order a set of positive and negative integers?
- Which part of each number do you look at to help you?
- Which is larger,
^{-}4 or 2? - Give me a number that is between these two integers, e.g.
^{-}10 and 3? - Which of the two integers is it closer to?
- Give me two temperatures between 0° C and
^{-}10° C. Which is the lower? How can you tell?

## What if pupils find this a barrier?

The number line is an important visual image.

Extend from the thermometer to use and display a vertical number line.

Count on and back using a counting stick (holding horizontally and vertically).

A common misconception is to think that

^{-}8 is greater than^{-}2.Pupils often ignore the negative sign when ordering negative numbers.

- Mathematics ITP: Thermometer (SWF-52 KB) Attachments
- Mathematics ITP: Number line (SWF-39 KB) Attachments
- Targeting level 4 lesson: Positive and negative numbers.

- Compare and order a mixed set of numbers or measurements with up to three decimal places
## Examples of what pupils should know and be able to do

Put these in order, largest/smallest first:

5.25, 15.3, 5.78, 5.87, 5.2

7.765, 7.675, 6.765, 7.756, 6.776.

- Primary mathematics exemplification: Decimal notation
- Assessment example: Long jump: Wendy and James (PDF-1.6 MB) Attachments
- Assessment example: Ordering decimals: Julie (PDF-638 KB) Attachments

## Probing questions

- What do you look for first when you are ordering numbers with decimals?
- Which part of each number do you look at to help you?
- Which numbers are the hardest to put in order? Why?
- Give me a number between 3.12 and 3.17. Which of the two numbers is it closer to? How do you know?
- What do you do when numbers have the same digit in the same place?

## What if pupils find this a barrier?

Encourage pupils to look at the value of the digit on the left.

Pupils may find it helps to read the numbers in words including the place value, e.g. reading 6.25 as six units, two tenths and five hundredths, which is smaller than 6.3 (6 units and 3 tenths).

Practise with situations that pupils are comfortable with, e.g. metres or money. Extend from two decimal places to three decimal places.

Write numbers on cards so that they can sort them, move them around, compare and discuss.

- Targeting level 4 lesson: Positioning decimals on a number line
- Targeting level 4 lesson: Ordering decimals

### Attachments

### Related downloads

- Temperatures: Vinay and Sam [ pdf : 254 KB ]
- Long jump: Wendy and James [ pdf : 1.6 MB ]
- Ordering decimals: Julie [ pdf : 638 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: Number line
- [Windows executable] - [ exe : 4.1 MB ]
- [Flash] - [ swf : 39 KB ]
- Download all [ 2.5 MB ]