double times multiple Multiplication factor multiply Find the product of double

Where do we start? Repeated addition Arrays Visualisation

Arrays 3 X 4

Repeated addition 4 x 3 = 12 + 3 + 3 + 3 + 3 6 9 3 12

I have four friends and I want to give them two sweets each, how many sweets will I need? 4 lots of 2 is 8 4 x 2 = 8

inverse The inverse of multiplication is division 23 x 7 = 161 161 ÷ 7 = 23 161 ÷ 23 = 7

Multiplying by 10 H T U 3

H T U 2 7

H T U . t h 1 . 6 7

3 x 70 = 210 40 x 60 = 2400

…and powers of 10 100 = 10 x 10 Move 2 places to the left Move 3 places to the left 1 000 = 10 x 10 x 10

a × b = b × a Example: Commutative Laws The "Commutative Laws" say we can swap numbers over and still get the same answer ... a × b  =  b × a Example:

Associative Laws The "Associative Laws" say that it doesn't matter how we group the numbers (i.e. which we calculate first) ... (a × b) × c  =  a × (b × c)

a × (b + c) = a × b + a × c Distributive Law This is what it lets us do: 3 lots of (2+4) is the same as 3 lots of 2 plus 3 lots of 4 So, the 3× can be "distributed" across the 2+4, into 3×2 and 3×4 a × (b + c)  =  a × b  +  a × c

Try the calculations yourself: 3 × (2 + 4)  =  3 × 6  =  18 3×2 + 3×4  =  6 + 12  = 18

We get the same answer when we: multiply a number by a group of numbers added together, or multiply each separately then add them

"Factors" are the numbers you can multiply together to get another number: 2 and 3 are factors of 6

A number can have many factors. 1 x 12 =12 2 x 6 = 12 3 x 4 = 12

Finding the area of a rectangle l x w = A 6 m 12 m² 2 m

SQUARE NUMBERS

Jottings Crossing the tens boundary 17x5= (10x5=50, 7x5=35, 50+35=85)

Doubling

Written Methods x 10 3   4 40 12

x 30 8 5 150 40 190

36x4= 36 X 4 1 4 4 2