Calculation strategies and challenge. Cannon Lane Primary School KS1 Supporting your child with Mathematics Calculation strategies and challenge.

Agenda Outline of the strategies used to teach each of the four rules. What the National Curriculum says. Practical session. Any questions.

Addition Y1 Counting and Combining sets of Objects Combining two sets of objects (aggregation) , which will progress onto adding on to a set (augmentation). Understanding of counting on with a number track. Counting on from the largest number supports adding on to a set. Understanding of counting on with a numberline (supported by models and images). Counting on in ones on a number line with a finger or object, moving on to drawing the jumps. 7+ 4

Addition Y2 47+25 Leading to exchanging: 72 Add by partitioning in different ways and recombining. Continue to use number lines and concrete materials to develop an understanding of: Counting on in ones from a two-digit number Counting on in tens from a two-digit number Partitioning and bridging through 10. The steps in addition often bridge through a multiple of 10. Children should be able to partition the 7 to relate adding the 2 and then the 5. 8 + 7 = 15 Counting on in tens and ones from a two-digit number 47+25 Leading to exchanging: 72 Adding 9 or 11 by adding 10 and adjusting by 1 35 + 9 = 44

Subtraction Year 1 Understand subtraction as take-away: Use concrete objects and pictorial representations. As with addition children can move onto counting back on a hundred square when their understanding of numbers up to 100 is more secure. Showing or making subtraction facts with different apparatus such as Numicon. Understand subtraction as finding the difference: Counting back in ones on a number line moving onto drawing the jumps on it. The above model would be introduced with concrete objects which children can move (including cards with pictures) before progressing to pictorial representation. The use of other images is also valuable for modelling subtraction e.g. Numicon, bundles of straws, Dienes apparatus, multi-link cubes, bead strings.

Subtraction Year 2 Move on to taking away a number with more than Using concrete materials to take away in multiples of ten and then one. Continue to use number lines to model subtraction as finding the difference. Using a hundred square or a number line to count back, by counting back in tens and ones if subtracting a 2-digit number. Showing on a number line that subtraction is the inverse of addition. Drawing their own number line and counting back in tens and ones (as with addition). Start with subtracting a teen number. Move on to taking away a number with more than one ten.

Multiplication Year 1 Understand multiplication is related to doubling and combing groups of the same size (repeated addition). Use practical objects such as Numicon and bundles of as well as real life objects such as a washing line. Count objects in groups of 2, 5 and 10. Problem solving with concrete objects and pictorial representations. (including money and measures). Ben had five football stickers, his friend gave him five more how many does he have altogether? Read and solve simple multiplication sums using concrete objects. 2 x 5 = Introduce arrays to show that multiplication can be done in any order. 5 x 2 = 10 2 x 5 = 10 Use concrete objects to develop vocabulary related to ‘times’ eg. pick up five, four times.

Multiplication Year 2 Use jottings such as number lines and concrete materials to solve problems (including measures). I have four sweets. My sister has five times as many. How many sweets does my sister have? Build upon the commutative law learned introduced in Year 1. Use learned x facts to derive new ones eg. If 2 x 7 = 14 then 7 x 2 = 14. Solve a multiplication by drawing groups or arrays. Move on to drawing their own number line. Doubling numbers up to 10 + 10 Using known doubles to work out doubles of 2-digit numbers (double 15 = double 10 + double 5). Use partitioning to develop an understanding of how to double 2-digit numbers. 15 x 2 = 30 10 x 2 = 20 5 x 2 = 10

Division Year 1 Sharing This develops 1:1 correspondence. Arrays can also be used to give a pictorial representation of grouping. Sharing This develops 1:1 correspondence. I have 15 eggs and I share them between 5 of my friends. They get 3 eggs each. In 15 there are five groups of 3. (15 ÷ 3 = 5) In 15 there are three groups of 5. ( 15 ÷ 5 = 3) Grouping Understand grouping as putting a set of objects into equal groups. How many groups of 2 are there in 10?

Division Year 2 Grouping using apparatus. Understand that division is the inverse of multiplication. Find the division facts related to the multiplication facts that they know. If 6 x 2 = 12 then 2 x 6 = 12 and 12 ÷ 6 = 2. There are 10 lollies in a bag. Charlie needs 30 lollies for his party. How many bags does he need to buy? Show how you worked this out. Use their knowledge of x and ÷ facts to solve missing number problems. Recording their groupings. Calculate a division as repeated subtraction on a number line.

What does the National Curriculum say What does the National Curriculum say.. It aims to ensure that all pupils : Become fluent in the fundamentals of mathematics. Can reason mathematically. Can solve problems by applying their mathematics to a variety of problems. Pupils who grasp concepts rapidly should be challenged through being offered rich and sophisticated problems before acceleration through new content. –

Mastery and Greater Depth All children need a deep understanding of the maths they are learning . This allows the children to gain greater depth of proficiency and understanding. They need to be able to use knowledge appropriately, flexibly, creatively and to apply it in new and unfamiliar situations.

Now it is your turn … Put yourself in your child's shoes Can you solve some of the calculations as a Year 1 or 2 child would ? Have a go at using some of the strategies and concrete materials provided . Then try out some of the Mastery and Greater Depth activities .