Multiplication

Mental multiplication Continue to learn the times tables – multiplication and division facts Class 2 order: 10, 5, 2, 4, 8, 3, 6, 9, 7, 11, 12 National Curriculum: all tables need to be learnt by the end of year 4 Discuss links between times tables.

Resources Counting stick with post-it notes Physical activity e.g. skipping, jumping, whilst saying them Online resources – Maths Zone

Doubling Find doubles to double 50 using partitioning Use doubling as a strategy in multiplying by 2 e.g. 18 x 2 is double 18 Resources – numicon, dienes

Doubling Find doubles to double 100 and beyond using partitioning Begin to double amounts of money, e.g. £3.50 doubled is £7 Use doubling as a strategy in multiplying by 2, 4 and 8 i.e. doubling twice for 4x and doubling three times for 8x.

Doubling Double amounts of money using partitioning, e.g. £6.73 Use doubling as a strategy in multiplying by 2, 4, 8, 5 and 20 (x 5 = ½ of a x 10)

Doubling Double decimal numbers with up to 2 places using partitioning. Use doubling and halving as strategies in mental multiplication

Grouping Know that multiplication is commutative e.g. 4 x 6 = 24 and 6 x 4 = 24

Grouping Multiply multiples of 10 by a single digit numbers, e.g. 40 x 20 Show wallpaper

Grouping Use partitioning to multiply 2 digit numbers by single digit numbers 15 x 6 = 10 x 6 = 60 5 x 6 = 30 Multiply multiples of 100 by a single digit numbers using times tables facts, e.g. 300 x 4 = 1200 Multiply using near multiples by rounding, e.g. 24 x 19 as (24 x 20) – 24 90 Wallpaper

Grouping Multiplying decimals by 10, 100, 1000 e.g. 3.4 x 100 = 340 Use partitioning to multiply friendly 2 digit and 3 digit numbers by single digit numbers e.g. 402 x 6 as 400 x 6 and 2 x 6. Using partitioning to multiply decimal numbers by single digit numbers e.g. 4.5 x 3 as (4 x 3) + (4 x 0.5) Demonstrate place value grid- no adding 0

Grouping Use partitioning as a strategy in mental multiplication e.g. 3060 x 4 as (3000 x 4) + (60 x 4) or 8.4 x 8 as 8 x 8 (64) and 0.4 x 8 (3.2) Use factors in mental multiplication, e.g. 421 x 6 as 421 x 3 (1263) doubled (2526) or 3.42 x 5 as half of (3.42 x 10) Multiply decimal numbers using near multiples by rounding, e.g. 4.3 x 19 as (4.3 x 20) – 4.3

Written Multiplication As with written addition and subtraction, written multiplication shouldn’t be introduced too early, otherwise they depend on using these methods only. Essential to know their multiplication and division facts to do written multiplication with accuracy

Partitioning to Grid Method TO x O

Grid Method to Expanded Method 3 digit x 1 digit 2 x 2 digit 3 x 1 expanded method

Short multiplication 2,3 and 4 digit by 1 digit Then

Long multiplication Long multiplication of 2 digit, 3 digit and 4 digit numbers by teen numbers, moving onto any 2 digit number

Multiplication Essentials Know their multiplication and division facts Have a good understanding of place value Know that it is repeated addition and commutative

Halving Find half of even numbers to 100 using partitioning Use halving as a strategy in dividing by 2 e.g. 36 ÷ 2 is half of 36 Odd digits can be more tricky – so we can look at 10 and the rest e.g. 50 is = 10 + 40 (5 + 20) = 25

Halving Find halves of even numbers to 200 using partitioning Begin to half amounts of money, e.g. £9 halved is £4.50 doubled Use halving as a strategy in dividing by 2, 4 and 8 i.e. halving twice for ÷ 4 and halving three times for ÷ 8.

Halving Halve amounts of money using partitioning, e.g. £6.74 Use halving as a strategy in dividing by 2, 4, 8, 5 and 20, e.g. 115 ÷ 5 as double 115 ÷ 10

Halving Halve amounts of money using partitioning, e.g. £6.74 Use halving as a strategy in dividing.

Grouping Recognise that division is not commutative. Relate division to multiplications e.g.  x 5 = 30 is the same calculation as 30 ÷ 5 =  Divide multiples of 10 by single digit numbers, e.g. 240 ÷ 8 = 30 Use a numberline to support

Grouping Use multiples of 10 times the divisor to divide by numbers ≤9 above the tables facts, e.g. 100 ÷ 7 Divide multiples of 100 by single digit numbers using division facts, e.g. 3200 ÷ 8 = 400

Grouping Divide numbers by 10, 100, 1000 to obtain decimal answers with up to 3 places, e.g. 340 ÷ 100 = 3.4 Use the 10th, 20th, 30th, … multiple of the divisor to divide friendly 2 digit and 3 digit numbers by single digit numbers, e.g. 186 ÷ 6, as 30 x 6 and 1 x 6

Grouping Use the 10th, 20th, 30th, … or 100th, 200th, 300th…. multiples of the divisor to divide large numbers, e.g. 378 ÷ 9 40 x 9 = 360 2 x 9 = 18 so 378 ÷ 9 = 42 Use tests of divisibility, e.g. 135 divides by 3, as the sum of the digits in 9.

Written Division Written version of a mental method – grouping.

Written Division  Short division of 3 digit and 4 digit numbers by single digit numbers

Written Division Long division of 3 digit and 4 digit numbers by 2 digit numbers giving answers with remainders, simple fractions or decimals. or 150 21/24 simplified to 150 7/8

Written Division

Vocabulary Multiples - Multiples are really just extended times tables. e.g. The multiples of 2 are all the numbers in the 2 times table: 2, 4, 6, 8, 10 and so on. Factors - Factors are numbers that divide exactly into another number e.g. factors of 12 are 1, 12, 2, 6, 3, 4, Prime number – any number that is only divisible by 1 and itself, e.g. 2, 5, 7, 11, 13, 17 etc. Prime factor – a factor of a number that is also a prime number Composite number – a number than can be divided by more numbers than just itself and one (e.g. the opposite of a prime number) Product of 2 numbers – you multiply the 2 numbers together.

Vocabulary Square number: The number we get after multiplying an integer (not a fraction) by itself. Example: 4 × 4 = 16, so 16 is a square number. Here are the first few square numbers: 0 (=0×0) 1 (=1×1) 4 (=2×2) 9 (=3×3) 16 (=4×4) 25 (=5×5) ...

Vocabulary Cube number: The result of multiplying a whole number by itself twice. Example: 3 × 3 × 3 = 27, so 27 is a cube number. Here are the first few cube numbers: 1 (=1×1×1) 8 (=2×2×2) 27 (=3×3×3) 64 (=4×4×4) 125 (=5×5×5)

BODMAS Order of the operations:

Useful websites www.mathletics.co.uk - each pupil has a login and password for this – this website will be used for homework tasks, revision and some assessments –teachers have access to this and can use it to monitor progress www.bbc.co.uk/bitesize/ - follow the links to thecorrect Key stage: Years 5 and 6 are KS2, www.woodlands-junior.kent.sch.uk/maths/ - Useful website for KS2 pupils to practise some key skills in maths www.mathszone.co.uk - Useful website with hundreds of links to other websites – most resources are for KS2 www.supermathsworld.com - Maths games website aimed at mostly KS2 pupils – pupils can log in as a guest or create an account www.coolmath.com - Maths games website for pupils with links to lots of other sister websites such as coolmaths4kids.com www.crickweb.co.uk/ks2numeracy.html - Free online maths games resources for KS2 pupils http://www.free-training-tutorial.com/ordering-numbersgames.html - A maths games website (with some links to typing practice as well) mostly suitable for KS2 pupils www.mathisfun – lots of useful mathematics definitions www.sumdog.com – lots of games and sometimes competitions to help with all 4 operations