How we teach calculations at Town Farm Primary School (+ and -) Town Farm Primary School and Nursery

Aims: To explain how we teach + and – To explain why we use these written methods. This will give you some idea of how you can support your child at home.

Common problems when approaching Mathematics “We weren’t taught these strange methods and our maths is ok!” “I want to help with Maths homework, but they do things differently now!”

Why is Maths taught differently now? When I was at school, maths lessons involved teaching rules of how to do things. We didn't question and often we didn't understand why we were "carrying ten" or “taking one". This meant that I was fine as long as I remembered the rules and as long as the type of question didn’t change, but I had no clear understanding of what I was doing and why it worked. Activities like this were probably okay for the children who ‘got’ maths, but not for those who struggled or were uninspired by the work on offer. A new emphasis on understanding before writing.

Overall outcomes The overall aim is that when children leave primary school they: have a secure knowledge of number facts and be fluent in the four operations; can carry out mental calculations and apply appropriate strategies when working with bigger numbers use notes and diagrams to help record steps when solving more complex problems have efficient, reliable written methods for each operation that they can confidently apply to calculations that they cannot carry out mentally.

Overview of progression in addition

Nursery - working with numbers to 10 Children should be counting and reciting number rhymes. They should also be using practical work to find one more. They should begin to recognise the numbers 1-10 and begin to represent in written form, they should also recognise sets of objects (1,2,3)

Reception - working with numbers to 20 Lessons are practical with lots of verbal counting forwards and backwards. Children should be able to count and order numbers from 1 to 20 and say which is one more and one less. Using quantities and objects children should be able to add and subtract two single digit numbers by counting on or counting back. (addition to 10) Children should be able to solve problems involving doubling, halving and sharing and solving number bonds to 5 Children should be able to record using marks that they can interpret and explain.

Year 1: Add with numbers up to 20 Children should be able to write + and = symbols and use a variety of counting equipment e.g a number lines and everyday objects. It is important that children know that: = means “is the same as” Children should then count on without a number line so 6+3 becomes 6, 7,8,9

Bead strings or bead bars can be used to illustrate addition. The colours of the beads on the bead string make it clear how many more need to be added to make ten. 8+5 Other representations can include:

Year 2: Add with 2-digit numbers Use empty number lines, concrete equipment, hundred squares etc. to build confidence and fluency in mental addition skills. Money should also be used. Add 2-digit numbers and ones:Add 2-digit numbers and tens: Add pairs of 2-digit numbers, Children may take these jottings to support their calculation = = 60 or = = = = 72 Or = = 72

Partitioning numbers  Add the tens and then the ones to form partial sums and then add these partial sums  Partitioning both numbers into tens and ones mirrors the column method where ones are placed under ones and tens under tens. This also links to mental methods.  This method can be extended for 2-digit + 3-digit and 3-digit + 3-digit and beyond = = = = 86

Year 3: Add numbers with up to 3-digits When the tens barrier is crossed in the ‘ones’ then exchange takes place Because of the exchange we can now see that this ten belongs in the tens column and is carried there to be included in the total of that column. Start adding with the ‘least significant digit’ on the right.

Year 4: Add numbers with up to 4-digits Reinforce correct place value by reminding them the actual value is 5 hundreds add 3 hundreds, not 5 add 3, for example. ‘Carry’ numbers underneath the bottom line. Add ones first. Continue with the column method. e.g = 3913

Year 5: Add numbers with more than 4-digits Include money, measures and decimals The decimal point should be aligned in the same way as the place value columns, and must be in the same place in each row. Numbers should exceed 4 digits. Pupils should be able to add more than two values, carefully aligning place value columns. O Reinforce correct place value by reminding them the actual value is 1 hundredths add 5 hundredths, not 1 add 5 for example.

Year 6: Add several numbers of increasing difficulty OO O O Empty decimal places can be filled with zero to show the place value in each column. Adding several numbers with more than 4 digits.

Overview of progression in subtraction

Nursery Working with numbers up to 10 and finding one less. Working with numbers up to 20 Lots of counting backwards Problems using objects and sharing. Reception

Year 1: Subtract numbers up to 20 Count back in ones on a numbered number line to take away, with numbers up to 20: ‘Seven is 3 more than four’ Find the ‘difference between’

Year 2: Subtract with 2-digit numbers Subtract on a number line by counting back, aiming to develop mental subtraction skills = 24 Partition the second number and subtract it in tens and units, as below: Subtracting pairs of 2-digit numbers on a number line: Subtract tens first. Then subtract ones. Move towards more efficient jumps block, as below: Combine methods with use of a hundred square to reinforce understanding of number value and order.

Year 3: Subtract with 2 and 3-digit numbers Introduce ‘exchanging’ through practical subtraction. Make the larger number with Base 10, then subtract 47 from it Before subtracting ‘7’ from the 72 blocks, they will need to exchange a row of 10 for ten ones. Then subtract 7, and subtract 4 tens.

Counting on as mental strategy for subtraction: Continue to reinforce as a strategy for close-together numbers (e.g ) and also for numbers that are ’nearly’ multiples of 10, 100, 1000 or £s, which make it easier to count on (e.g , , or calculating change from £1 etc.).  Start at the smaller number and count on in tens first, then count on in units to find the rest of the difference: 102 – 89 = – 47 = 35

Year 4: Subtract with up to 4-digit numbers column subtraction with ‘exchanging’ Always encourage children to consider the best method for the numbers involved - mental, counting on, counting back or written method. Give plenty of opportunities to apply this to money and measures.

Year 5: Subtract with at least 4-digit numbers including money, measures, decimals Column subtraction (with ‘exchanging’). Subtract with decimal values, including mixtures of integers and decimals, aligning the decimal point.

Year 6: Subtracting with increasingly large and more complex numbers Using the column method to subtract money and measures, including decimals with different numbers of decimal places.

More information: Visit the TFPS website to access the calculations policy

Any Questions?