Maths in Key Stage 2 (Years 3 and 4)
Maths in Years 3 to 6 at primary school encompasses shape, space, data handling, money and measures, in addition to numeracy.
Children in Year 3 are likely to be using numbers up to 1,000. They are reading, writing and ordering numbers on a number line (some children will be using smaller numbers until they are both confident and competent).
'Hands-on' learning is still important and teachers provide appropriate equipment for children to manipulate and use. Teachers encourage children to use number lines, place value cards and bead strings and so on. They learn to visualise, describe and represent what is in front of them.
Counting on and back in tens is a basic skill. Children learn that a number such as 459 can be split into 4 hundreds, 5 tens and 9 units. They may well do a lot of work on this. They learn combinations that make 100, work out calculations and explain what they have done.
During Year 3, children's mathematical language is extended (eg fractions, factor, digit, zero and inverse). They begin to understand 25 ÷ 5 = 5 and 5 × 5 = 25.
This knowledge helps them to work out division calculations from multiplication facts (6 × 9 = 54; 54 ÷ 9 = 6 and 54 ÷ 6 = 9).
They learn 3, 4 and 6 times tables and work on multiples of 2, 5, 10 up to 1000 (eg which of the following numbers is a multiple of 5: 100, 102, 75, 90 and 27?)
There will be work on multiplying one-digit and two-digit numbers by 10 and work with specific fractions such as ½, ¼, and ¾.
Most of the work relates to 'real' situations:
- My dad runs for 25 minutes a day. How many minutes does he run in three days? In a week? Can you explain how you did this?
- There are 30 children in a class and 2/3 are girls. How many are boys and how many are girls? How did you work that out?
Children are given puzzles, problems and investigations to practise, consolidate and extend their understanding. They might be asked to play a game such as Back to One: a child chooses any number up to 500 (the number will depend on the level of the child's confidence). They must divide an even number by 2 and if the resultant number is odd, add 1 etc.
For example: 60 ÷ 2 = 30; 30 ÷ 2 = 15; as 15 is odd, add 1; 15 + 1 = 16; 16 ÷ 2 = 8; 8 ÷ 2 = 4; 4 ÷ 2 = 2; 2 ÷ 2 = 1.
How long can you make your chain?
Can you repeat with a different number?
Who has the longest chain?
In Year 4, children are introduced to decimals, particularly with money and measurement.
By this stage of primary, they have a good understanding of place value, and they will continue ordering and reading numbers. For example: what is the larger number: 1300 or 1302, 762 or 726? Can you explain why?
They are shown four-digit numbers and asked to say what each digit represents: 2345 = 2 thousands, 3 hundreds, 4 tens and 5 ones (units). They become more confident about using mental and informal written methods of calculation in all four operations. They also use written methods of calculation to add and subtract two-digit and three-digit numbers.
To solve increasingly difficult problems, children may use a calculator. So they're introduced to calculations involving the four operations ie addition, subtraction, multiplication and division.
They also use language such as multiple, decimal, factor, fractions, ratio and proportion.
In multiplication, they will be doubling two-digit numbers and will have been taught tables up to 10 times 10 and place value to 1 or 2 decimal places.
The idea of equivalent fractions is introduced, often using diagrams. They also use a number line to put whole numbers and fractions on. They may be asked to write 5/10 ,6/12 and 4/8. Or which is the smallest out of ½, ¾ and ¼?
They will be asked to place decimals on a number line:
They could place these numbers on the line: 0.5, 1.5, 1.2 and 0.9. Or they might be asked to put the following decimals in order - 5.6, 3.2, 7.5, 7.03 and 1.9.
Some children recognise the equivalence between decimals and fractions, while others may need more help and may be working towards goals set for them by their teacher. Some other children may be given work to broaden and deepen their learning.
As at earlier levels, teachers give children the opportunity to practise, reinforce and apply their learning, ensuring that children become more confident and competent in their work and are ready to move on to Year 5.