Programme 8: Difference
Developing knowledge of number bonds as subtraction facts
- Recognising subtraction as the inverse of addition
- Finding small differences by counting on from the smaller number
- Understanding complementary sums to work out the difference between two numbers
- Subtracting single digit numbers from multiples of ten
Vocabulary: counting on, difference between, change, pairs
Resources: 10p and 1p coins, shopping area, cubes, difference between puzzles
Some children may have difficulty with the concept of 'the difference between', possibly due to confusion in the vocabulary used. They may consider the difference between to relate to the physical attributes rather than a numerical value. It is important to explicitly discuss what is meant by the difference between two numbers. Recording this concept can also cause confusion. When we talk about the difference between two numbers, it does not matter which way it is stated e.g. the difference between 3 and 5 is the same as the difference between 5 and 3. However, when recording this as a number sentence, the largest number is always put first. This does not apply to other subtraction calculations e.g. 3 -5 is not the same as 5 - 3.
When discussing the difference between and subtraction, negative numbers may arise spontaneously. Teachers may find it useful to discuss and extend the number line to include numbers less than zero. It can be helpful to make analogies with owing money or marbles, lifts going down below 0 (usually ground floor) or the temperature.
Some children may need concrete examples to reinforce the concept. Encourage them to count on to find the difference and relate this to the numberline. Children need to recognize that you can count on or count back to find the difference between two numbers and can use the alternative method to check answers. Many people seem to find counting on an easier strategy to use.
Introduction through role play whole class or group
Role play situations that relate to the class can provide a useful introduction. For example giving two children different numbers of marbles (e.g. 18 and 21) and asking questions e.g. Who has more marbles? What is the difference between the number of marbles? Ask the children to find the numbers on the numberline and count on to find the difference.
Using a shop and giving change provides many opportunities for finding the difference between two amounts. Initially use 10p and 1p coins only to encourage children to count on in ones and tens.
The Bill and Bernie sketch with snack machines can provide a useful context for finding the difference between two amounts. Ask the children to select items for an outing that will cost 16p, 14p and 10p and work out what they can buy with 40p (two 20p coins). This can be extended by changing the prices, increasing the range of goods for sale and giving children 50p coins.