Vectors – Substitution – Bingo – Method Students should choose nine answers from the grid and place them randomly into a 3x3 square in their book. You may want to pause your display and choose questions according to difficulty during the game. Depending on time, students could win with a line, an X, or a ‘full house’ (all).

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BINGO! 45 54 23 82 37 12 76 25 91 Substituting Vectors

Choose your numbers… 4 9 −9 −4 7 −2 −3 2 5 13 3 3 6 4 −5 6 4 8 −2 3 0 −4 −6 2 2 0 4 −1 1 3 3 −5 Draw a 3x3 grid in your book.

Work out a + b as a column vector. = 6 4

Work out a − b as a column vector. = 4 −1

Work out b − a as a column vector. = −3 2

Work out 2a + b as a column vector. × 2 2a = 4 8 Work out 2a + b as a column vector. 2a + b = 4+1 8+5 = 5 13

Work out 2a − b as a column vector. × 2 2a = 10 2 Work out 2a − b as a column vector. 2a − b = 10−3 2−4 = 7 −2

Work out a + 2b as a column vector. × 2 2b = 2 4 Work out a + 2b as a column vector. a + 2b = 2+2 5+4 = 4 9

Work out b − 2a as a column vector. × 2 2a = 10 −4 Work out b − 2a as a column vector. b − 2a = 4−10 −2−−4 = −6 2

Work out a + b as a column vector. = 2 0

Work out 2a + b as a column vector. × 2 2a = −2 6 Work out 2a + b as a column vector. 2a + b = −2+5 6+−3 = 3 3

Work out a − b as a column vector. = 1 3

Work out 2a + 2b as a column vector. × 2 × 2 2a = 8 −2 2b = −4 10 Work out 2a + 2b as a column vector. 2a + 2b = 8+−4 −2+10 = 4 8

Work out 2a − b as a column vector. × 2 2a = −4 −8 Work out 2a − b as a column vector. 2a − b = −4−5 −8−−4 = −9 −4

Work out a + 2b as a column vector. × 2 2b = −2 6 Work out a + 2b as a column vector. a + 2b = −3+−2 0+6 = −5 6

Work out a − 2b as a column vector. × 2 2b = 8 0 Work out a − 2b as a column vector. a − 2b = 6−8 3−0 = −2 3

Work out 2b − a as a column vector. × 2 2b = 8 −6 Work out 2b − a as a column vector. 2b − a = 8−5 −6−−1 = 3 −5

Work out a − 2b as a column vector. × 2 2b = −4 2 Work out a − 2b as a column vector. a − 2b = −4−−4 −2−2 = 0 −4

tom@goteachmaths.co.uk Questions? Comments? Suggestions? …or have you found a mistake!? Any feedback would be appreciated . Please feel free to email: tom@goteachmaths.co.uk