Calculation Progressions at St Francis CE Primary Welcome to this evenings interactive presentation. Please feel free to have a look through the resources on your table. If you would like to order a Maths Resources Pack for £5, do sign up on the sheets near the entrance.

Aims To understand the progression of calculation for multiplication and division. To see the methods in use and use the calculation strategies that children learn at St Francis.

Outline of the session Multiplication Division Early Years sharing Early Years grouping Arrays Number lines ~ jumping in groups Commutativity The grid method Column Standard Division Early Years sharing Division as repeated grouping on a number line Chunking

Multiplication Early multiplication is groups of or lots of and involves repeated addition of objects. Arrays Times tables begin with 2, 5 and 10. 2s ~ socks, hands, shoes. 5s ~ fingers on gloves. 10s ~ fingers, toes.

Commutativity Multiplication is commutative, 2 x 4 = 4 x 2 Children are encouraged to explore this using objects and by drawing diagrams as well as using a number line.

Grid method This relies on the children understanding multiplication as repeated addition, recalling their times tables quickly and partitioning. 14 x 3 = 10 x 3 and 4 x 3 Task 5 ~ Calculate 27 x 8 using the Grid method

Grid method A two-digit by two-digit number uses the same method, the grid just becomes larger to accommodate for more rows and columns. 14 x 15 = Once this is secure, children move on to multiplying with HTO.

Column multiplication Once the grid method is secure, partitioning is used in the expanded column method. (The grid method vertically)

The standard method Finally this method is used once multiplications are recalled rapidly, place value is clearly understood, exchanging is clear and adding is secure.

Other multiplication tips When a number is multiplied by 10, 100, 1000 etc, you are not simply adding zeros! What is happening is that the number is becoming bigger and is therefore moving into the appropriate place value position. The numbers always stay together and any spaces remaining are filled with zeros i.e. 156 x 10= Th H T O …otherwise it would be 1 5 6 ( x 10) 156.0! 1 5 6 0

Multiplication ~ reminders Times tables are key Place value columns must be checked You don’t just add zeros when multiplying by multiples of ten

Division Early years start with ‘sharing’. 6 sweets are shared between 2 people. How many do they have each?   You might hear children say, “One for me, one for you.” and so on. Eventually pictures are replaced with dots. It is important for children to know how to count on and back in multiples of 1,2,5 and 10 so they can derive the multiples of 2, 5 and 10.

Structured number lines Early division is seen as repeated subtraction. Here is a calculation for 15 ÷ 3 The answer is 5 groups of / lots of / sets of 3.

Unstructured number lines e.g. 18 ÷ 6 = 3 The children are also given examples whereby there is a remainder. e.g. 16 ÷ 3 = 5 r 1

Chunking on a number line and vertically 38 / 3 = 12 r 2 38 / 3 = 3| 38 30 (10 x 3) 8 6 (2 x 3) 2 10 lots of a number is a great starting point. Knowing how to subtract when digits are presented vertically is key.

Chunking vertically by 2 digits 840 ÷ 15 = 56 Task 6 ~ calculate 742 / 14 using this method. When you know 10 lots of a number it’s easy to calculate 20 lots ~ double it!

Standard method of division Finding out how many of the divisor go into each digit as a separate number. The next step is to find remainders. This involves the children having to apply their knowledge of decimals.

Division ~ reminders Place value is key Times tables knowledge must be secure Use multiplication to check as an inverse calculation

To conclude Using objects and number lines helps the size of numbers to be recognised. Number bonds help quick recall of addition and can be multiplied and divided by base 10. Times tables are key. Place value keeps the numbers where they should be for what they are worth.

Thank you so much for participating 7 years of learning multiplication and division calculation progression in one evening!