Maths Methodology: Subtraction and Division

Why Subtraction & Division?

AIMS Secure understanding of subtraction and division Review the use of models, images and language in the teaching of subtraction and division Review progression – calculation policy Share practical ideas and resources

Subtraction

A good mathematician is one who understands the problem and then chooses an appropriate method to solve it!

2000 – 1902 = A museum opened in 1902 and closed in How long was it open for?

Examples of Early Problems Combining (putting two groups together): I have a bag of 3 green apples and another bag of 5 red apples. I put them all together in a bowl to get 8 apples. Adding on: I have 5 apples in the bowl. I add three more apples, and that makes 8 apples now in the bowl. Taking away: I have 8 apples in the bowl, and I take 5 out to eat them. That leaves 3 apples in the bowl. Comparing (finding how many more or less): I have a bag of 5 green apples and another bag of 8 red apples. That means I have 3 more red apples than green apples (and 3 fewer green apples than red apples).

The Must Haves … Recognise number Understand number order Know number bonds – to and within a given number Good understanding of addition Solid understanding of place value

Early Subtraction Physical Actions Taking Away Find the Difference

Taking Away: A shepherd has nine sheep in the pen and takes five away. How many are left in the pen?

Finding the difference: A shepherd has two pens of sheep: one pen has four sheep and the other pen has nine sheep. How many more are in the pen with nine?

Subtraction using a 100 square: 37 – 12 = 37 – 2 – 10 = The number (12) is partitioned and then taken away from 37.

Finding the difference using a number line: 15 – 7 = 8 = 3 + 5

Larger numbers using partitioning: 563 – 241 = = 322

Larger numbers without partitioning:

Larger numbers using decomposition:

Larger numbers using decomposition, different units of measure and decimals:

Division

Sharing Sharing objects out equally into groups Lots of practical activities - activities at home: sharing out portions at dinner, sweets, etc.

Sharing / Dividing Introducing the division sign: ÷ Still using sharing as a strategy for problem solving but using ‘division’ vocabulary. What could this number sentence be?

Number lines for Division Start to use more formal methods of division. Children find ‘counting on’ easier than counting back so we would introduce the strategy as counting in 3s until you get to How many jumps did you make?

Now try: 15 ÷ 3 = _____________________

126 ÷ 6 = Using what they know....

Now try ÷ 4 = _______________________________________

Bus Stop At this stage, short division (bus stop) is introduced to the children. They need to have a sound knowledge of times tables before this can be used. More difficult numbers with remainders would then be introduced :

Numbers requiring exchange:

Finally: Remainders as decimals Only some children will reach this strategy if they are ready for the challenge. ster/busstopdivision.html