Methods for Addition

Place value To help children as they progress through Key Stage 2 children need to develop the habit of putting one digit in each box in their maths book and so develop correct place value habits to help them when dealing with aspects in the upper part of the Key Stage.

Place value T U H T U Th H T U Recognising Thousand H T U H T U Development into decimals (often through work on money) H T U . hundredths tenths

Background Pupils need to have various mental strategies at their disposal to develop their pencil and paper methods of recording.

Number Bonds Do you know your number bonds to 10 in its different forms? 7 + 3 = 10 10 = 3 + 7 10 - 7 = 3 etc. Do you know your number bonds to 20? Do you know your number bonds to 100? Can you answer the number bonds correctly and quickly?

Rounding Pupils need to be able to round to the nearest 10. 42 to the nearest 10 is 40 47 to the nearest 10 is 50 45 to the nearest 10 is 50 (5 always rounds up) Following through the school, rounding to the nearest 100, 1000 etc..

Adding Tens Add 10, 20, 30 etc. to numbers. 50 + 20 = 70 Counting on and back in tens from any integer (whole number). (Recognising the unit digit does not change). 23 + 30 = 53 Then crossing the hundred boundary. 46 + 60 = 106

Partitioning Splitting the numbers into parts 87 = 80 + 7 345 = 300 + 40 + 5 Your turn! (colours not needed) 634 = 600 + 30 + 4 2698 = 2000 + 600 + 90 + 8 206 = 200 + 6

Addition using place value on a number square + 35 = ? Find 35 on the number square. Partition 26 = 2 tens + 6 Move down to 45 55 Then add 6 more. Pupils will use 100 squares Also 51 to 250 squares (to help cross the hundred boundary)

Addition Addition words and sum increase plus add + together total more

Written Methods for Addition Key Stage 2

Explaining our mental thoughts. Children need to develop pencil and paper methods to support, record and explain calculations.

Adding 9 and 11 Adding 9 and 11 by compensating/adjusting. 25 + 9 = +10 -1 25 35 34 44 + 11 = +10 +1 44 54 55

Adding: using a number line. 26 + 8 = 34 Start with the largest number on the number line. +8 26 34 (Some children will count on in ones/units using fingers or a ruler.)

Adding: using a number line. 36 + 57 =

Adding: using a number line. 36 + 57 = Remember start with the largest number first on your number line.

Adding: using a number line. 36 + 57 = Remember start with the largest number first on your number line. 57

Adding: using a number line. 36 + 57 = Remember start with the largest number first on your number line. +30 57 87

Adding: using a number line. 36 + 57 = 93 Remember start with the largest number first on your number line. +30 +6 57 87 93

Adding: using a number line. 257 + 385 = 642 Remember to start with the largest number first on your number line. +200 +50 +7 385 585 635 642

Adding: using a number line. 783 + 652 = 1435 Remember to start with the largest number first. +600 +50 +2 783 1383 1433 1435

Adding: using a number line. 36 + 57 = 57 Compensating/adjusting (using the skill of rounding)

Adding: using a number line. 36 + 57 = +40 57 97 Compensating/adjusting (using the skill of rounding)

Adding: using a number line. 36 + 57 = +40 - 4 57 97 93 Compensating/adjusting (using the skill of rounding)

Adding: using a number line. 36 + 57 = 93 +40 - 4 57 97 93 Compensating/adjusting (using the skill of rounding)

Adding: mental strategy Knowing the place value we add the largest values of the numbers together first. Pencil and paper recordings of what we are doing in our head are developed. Your turn! Q1. 57 + 64 Q2. 46 + 53 57 + 32 = (50 + 30) = 80 + 7 + 2 = 89 0r = (50 + 30) + (7 + 2) = 80 + 9 = 89

Pencil and paper recording of mental thoughts Q1. 57 + 64 = (60 + 50) = 110 + 7 + 4 = 121 (60 + 50) + (7 + 4) 110 + 11 110 + 10 + 1 = 121 Q1. Some children might think (rounding and compensate) 64 + 60 = 124 – 3 = 121 Q2. 46 + 53 = (50 + 40) = 90 + 6 + 3 = 99 (50 + 40) + (6 + 3) 90 + 9 = 99 Q2. Some children might Double 50 = 100 100 - 4 + 3 = 99

Addition: column (extended) without carrying Always start with the units first for column method. HTU HTU 83 267 + 42 + 85 5 12 120 140 125 200 352

Addition: column (compact) Initially sums without carrying to develop appropriate setting out. (T U to start with.) H T U H T U 6 2 5 3 6 7 + 4 4 + 3 2 6 6 9 3 9 9

Addition: column with carrying Then move on to carrying. H T U H T U 6 2 5 3 6 7 + 4 8 + 8 5 6 7 3 4 5 2 1 1 1

Addition: column with carrying An example of the carrying method. The numbers underneath the bottom line should have a line to cross them out once they are added in. H T U 3 6 7 + 8 5 4 / 5 1 / 2 1

Addition: development Using similar methods begin to add two or more three digit sums of money, with or without adjustment from the pence to the pounds. Know that decimal points should line up under each other, particularly when adding or subtracting mixed amounts such as £3.59 + or – 78p.

Addition: development Continue with the standard written methods using carrying with three, four, five digit numbers and beyond. Extend with decimals.

How you can support your child Look for and talk about numbers in the environment Play games Shopping Counting on/back Number bonds Doubles/Halves Time tables Division facts