Making expressions and gathering terms

Sweeties s = number of sweets in the box If I add 2 how many? s + 2 If I add 4 more, how many? s = s + 6 If I then eat 10, how many? s + 6 – 10 = s – 4 How many in 2 boxes? s + s = 2 x s = 2s How many in 11 boxes? 11 x s = 11s How many in 3 boxes, then I eat 7? 3s -7

Rich Tea h = number of biscuits in a packet of HobNobs r = number of biscuits in a packet of Rich Tea Hobnobs h + h r = “6 lots of h” = 6 x h = 6h Rich Tea + r Rich Tea + r Rich Tea + r = 4 x r = 4r Algebra - the basics : “Collecting Like Terms”

h + 2r Biscuits Hobnobs Rich Tea Biscuits Rich Tea Hobnobs 3h + r Big tin of biscuits Hobnobs Rich Tea h + 2r + 3h + r = 4h + 3r 4h 3r

Big tin of biscuits Hobnobs Rich Tea B = 4h + 3r How many biscuits if : - 20 in a pack of Hobnobs - 25 in a pack of Rich Tea? h = 20 r = 25 B = 4 x x 25 = = 155 Biscuits Yum

Hobnobs Rich Tea Algebra - the basics : “Collecting Like Terms - with loose biscuits” 3h + 2r + 5 Hobnobs Rich Tea h + 2r + 3 Hobnobs Rich Tea Hobnobs Rich Tea 3h + 2r h + 2r + 3 = 4h + 4r + 8 Gather number separately Altogether

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2h + 2r 5h 7h + 2r 5h + 5r8a + 10b 3x + 4y 12h + 4r a + 5b -4 12x + 6y + 4 6h + 3r a + 10b 11x + 4y 14h - 13r 14a - 12b + 3 2x + 11y + 2z

Algebra - the basics : “Working With Powers” w w Area = w x w = w x w x w x w = w2w2 w4w4 The power tells us how many are multiplied together a 8 = a x a x a x a x a x a x a x a

Algebra - the basics : “Products” Recall, 4h = 4 x h Similarly, gh = g x h When letters are multiplied together, in algebra, you don’t need to put the multiplication (x) sign E.g. f x g = fg g x 3h = g x 3 x h = 3gh 4r x 2s = 4 x r x 2 x s = 8rs (2p) 2 = 2p x 2p = 2 x p x 2 x p = 4p 2 Note: always write the number first, then the letters in alphabetical order Pg.153 ex 8:2 and 8:3

Biscuits b b b (b + 5) = b b b + 5 = 3b + 15 = b + b + b Algebra - “Brackets” 3 lots of : ‘a tin of biscuits and 5 loose ones’ b + 5

h + 2r h + 2r h + 2r (h + 2r + 3) = h + 2r h + 2r h + 2r + 3 = = h + h + h + 2r + 2r + 2r = 3h + 6r + 9 Algebra - “Brackets” Hobnobs Rich Tea Hobnobs Rich Tea Hobnobs Rich Tea 3h+ 6r+ 9

Pg ex 8:5 and 8:6 Everything inside the bracket must be multiplied by the number outside Algebra - “Brackets” 3(4x - 6) “3 times” “3 times 4x - 3 times 6” = 3 x 4x - 3 x 6 = 12x - 18 As a multiplication table: 3 4x -6 12x -18

Pg ex 8:5 and 8:6 Everything inside the bracket must be multiplied by the number outside Algebra - “Brackets” m(4n - 6) “m times” “m times 4n - m times 6” = m x 4n - m x 6 = 4mn – 6m As a multiplication table: m 4n -6 4mn -6m

Pg ex 8:5 and 8:6 Everything inside the bracket must be multiplied by the number outside Algebra - “Brackets” 3(4x - 6) – 4(x – 1) = (3 x 4x - 3 x 6) – (4 x x – 4 x 1) = (12x – 18) – (4x -4) = 12x – 18 -4x equals + = 12x – 18 – 4x + 4 Gather like terms = 8x - 14