CONTENTS – Click to go to… 06/12/2018 CONTENTS – Click to go to… ORDERING NUMBERS INCLUDING NEGATIVES ADDING AND SUBTRACTING WITH NEGATIVES MULTIPLYING AND DIVIDING WITH NEGATIVES NEGATIVES IN REAL LIFE

ORDERING NUMBERS INCLUDING NEGATIVES 06/12/2018 ORDERING NUMBERS INCLUDING NEGATIVES

- + 06/12/2018 Integers ( whole numbers ) Getting: Lower, Colder, - 5 - 4 - 3 - 2 - 1 0 1 2 3 4 5 Integers ( whole numbers ) Getting: Lower, Colder, Poorer, Younger, Smaller Getting: Higher, Hotter, Richer, Older, Bigger

06/12/2018 We can also use a number line to help us write integers in order. Write the integers –2, 8, 2, –6, –9 and 5 in order from smallest to largest. Look at the position of the integers on the number line: –9 –6 –2 2 5 8 So, the integers in order are: –9, –6, –2, 2, 5, and 8

06/12/2018 Put these in order of size, smallest to biggest 1) 5 °C, 3 °C, -5 °C, 0 °C, -8 °C 2) -34 m, 12m, -15m, 1m, -3m 3) 2.5, -0.5, -1, 4, -2, -1.5, 0 -8°C, -5°C, 0°C, 3°C, 5°C -34m, -15m, -3m, 1m, 12m -2, -1.5, -1, -0.5, 0, 2.5, 4

ADDING AND SUBTRACTING WITH NEGATIVES 06/12/2018 ADDING AND SUBTRACTING WITH NEGATIVES

4 and – 8 3 and -1 6 and -7 10 and -1 6 and -2 5 and -9 3 and -3 06/12/2018 Positive numbers Negative numbers What is the difference between: 4 and – 8 3 and -1 6 and -7 10 and -1 6 and -2 5 and -9 3 and -3

06/12/2018 Worded questions

06/12/2018

Which direction we move 06/12/2018 When we add and subtract negative numbers, we imagine a number line Where we start 3 + 2 How far we move = 5 Which direction we move + 1 2 3 4 5 6 7 8 9 -1 -2 -3 -4 -5 -6 -7 -8 -9

06/12/2018 -3 + 2 = -1 + -9 -8 -7 -6 -5 -4 -3 -2 -1 1 2 3 4 5 6 7 8 9

06/12/2018 –2 + 5 = = 3 -2 3

06/12/2018 Try these! - 1 + 3 = 1 2 - 8 + 8 = 6 - 4 + 5 = 2 1 - 9 + 6 = 7 -3 - 6 + 9 = 3 3 - 5 + 4 = 8 -1 - 7 + 12 = 4 5 - 10 + 20 = 9 10 - 6 + 10 = 5 4 - 15 + 8 = 10 -7

06/12/2018 = -5 -2 - 3 - -9 -8 -7 -6 -5 -4 -3 -2 -1 1 2 3 4 5 6 7 8 9

06/12/2018 5 – 8 = = –3 5 -3

06/12/2018 Try these! 7 - 3 = 1 4 - 1 - 1 = 6 -2 4 - 4 = 2 - 2 - 3 = 7 - 2 - 3 = 7 -5 3 - 5 = 3 - 2 - 5 - 3 = 8 -8 1 - 8 = 4 - 7 - 7 - 3 = 9 -10 0 - 6 = 5 - 6 - 3 - 12 = 10 -15

06/12/2018 1) 5 – 7 2) 3 – 5 3) 1 – 4 4) 2 – 6 5) 5 – 10 6) -1 – 2 7) -2 – 3 8) -3 – 1 9) 0 – 3 10) -2 + 5 11) -1 + 6 12) -5 + 7 13) -4 + 7 14) -4 + 4 15) -3 + 8 16) -5 + 2 17) -3 + 1 18) -2 + 2 19) 12 – 20 20) -15 – 10 21) -8 + 20 22) -14 + 7 23) -30 – 20 24) 15 – 20 25) 12 – 20 + 10 26) -10 + 4 – 10 27) -1 + 2 – 3 + 4 – 5 + 6 – 7 + 8 – 9 + 10 - 2 - 2 - 3 - 4 - 5 - 3 - 5 - 4 - 3 3 5 2 3 5 - 3 - 2 - 8 - 25 12 - 7 - 50 - 5 2 - 16 5

06/12/2018 Discussion - how do we solve problems like these? 4 + -2 -3 + -1 2 - -3 -5 - -7

General rule for signs between the numbers: 06/12/2018 General rule for signs between the numbers: + - - - + -

06/12/2018 4 + -2 = 2 - - -9 -8 -7 -6 -5 -4 -3 -2 -1 1 2 3 4 5 6 7 8 9

06/12/2018 = -4 -3 + -1 - -9 -8 -7 -6 -5 -4 -3 -2 -1 1 2 3 4 5 6 7 8 9

06/12/2018 2 - -3 = 5 + + -9 -8 -7 -6 -5 -4 -3 -2 -1 1 2 3 4 5 6 7 8 9

06/12/2018 = 2 -5 - -7 + -9 -8 -7 -6 -5 -4 -3 -2 -1 1 2 3 4 5 6 7 8 9

06/12/2018 1) 5 + -2 2) 3 - -3 3) -5 + -1 4) -6 - 3 5) 8 + 4 6) 9 - -9 1) 5 + -2 2) 3 - -3 3) -5 + -1 4) -6 - 3 5) 8 + 4 6) 9 - -9 7) 0 + -7 8) -8 - -10 9) 6 - 6 10) 6 - -7 + -3 11) 6 + 5 - -1 12) -2 - 5 - -1 13) 0 - - 4 - - 4 + 4 14) -1 - 1 - - 1- -1 3 6 -6 -9 12 18 -7 2 10 12 -6 12

06/12/2018

MULTIPLYING AND DIVIDING WITH NEGATIVES 06/12/2018 MULTIPLYING AND DIVIDING WITH NEGATIVES

DIFFERENT signs make a – 06/12/2018 Multiplying and dividing with negatives Ignore the signs Complete the calculation without them Decide whether the result will be positive or negative using the rules below SAME signs make a + DIFFERENT signs make a – 1st Number 2nd Number Answer + -

a) -5 x -3 b) -4 x 8 c) -20 ÷ -5 d) 39 ÷ -3 e) -11 x -7 f) 12 ÷ -1 06/12/2018 Try these! a) -5 x -3 b) -4 x 8 c) -20 ÷ -5 d) 39 ÷ -3 e) -11 x -7 f) 12 ÷ -1 g) -9 ÷ -9 h) -3 x -4 ÷ -2 = -15 = -32 = 4 = -13 = 77 = -12 = 1 = -6

06/12/2018 1) 4 × -3 2) 6 ( 4 ) 3) -5 × 4 4) -3 ( -8 ) 5) -6 ( 10 ) 6) -7 × -2 7) -1 × 1 8) 3 ( -6 ) 9) -7 ( 7 ) 10) -2 × -3 × -4 11) 5 × -2 × -3 12) 4 × 2 × -2 13) -1 × 2 × -3 × 4 14) ( -2 )2 15) ( 3 )2 16) ( -2 )3 17) 3 ( -2 )2 18) -5 ( -3 )2 19) -2 ( -1 )3 20) ( 2 × -3 )2 21) -2 ( -1 × -3 )3 - 12 24 - 20 24 - 60 14 - 1 - 18 - 49 - 24 30 - 16 24 4 9 - 8 12 - 45 2 36 - 54

06/12/2018 Complete the following: –3 × 8 = –24 –36 ÷ = –4 9 42 ÷ = –6 –36 ÷ = –4 9 42 ÷ = –6 –7 ÷ –90 = –6 540 × –8 = 96 –12 –7 × = 175 –25 47 × = 141 3 –4 × –5 × –8 = –160 –72 ÷ –6 = 12 3 × –8 ÷ = 1.5 –16

06/12/2018 Mixed Questions

06/12/2018 –2 –10 –8 ×2 ÷ –5 –4 2 –11 –7 + 4 × –1 – 5 –15 3 Work towards the centre of the spiral to reveal the picture of a snail blinking. –16 –2 + 16 × 5 + 8 –3 6 ÷ –2

06/12/2018 2 - 14 - 4 1) -2 + 4 2) -7 × 2 3) 12 ÷ -3 4) -3 - -5 5) -5 × 3 6) -6 ÷ 3 7) 8 - +4 8) 7 ×-2 9) -9 ( -2 ) 10) 6 – 8 11) -1 + -5 12) 3 ( -5 ) 13) -8 - +3 14) ( -3 )2 15) -3 – 5 16) 4 × -1 × -2 17) ( 3 – 5 )2 18) -1 × -1 × -1 19) -20 - + 20 20) -30 21) 15 2 - 15 - 2 4 - 14 18 - 2 - 6 - 15 - 11 9 - 8 8 4 - 1 - 40 3 - 5 -10 -3

On your mini whiteboards… 06/12/2018 QUICK CALCULATIONS! On your mini whiteboards… Choose R, B, G, Y!

06/12/2018 1) -2 + 7 -9 5 -5 9

06/12/2018 2) 6 - -5 1 11 -1 -11

06/12/2018 3) -12 + -3 -9 15 -15 9

06/12/2018 4) -24 - 13 -37 -27 27 -11

06/12/2018 5) 9 + -10 19 -19 1 -1

06/12/2018 6) -3 x 7 21 -21 -10 10

06/12/2018 7) -7 x -8 -13 1 -56 56

06/12/2018 8) -2 x 6 x -3 -24 36 -36 24

06/12/2018 9) (-4)2 16 -8 -16 8

06/12/2018 10) (-8)2 16 -64 -16 64

Now lets have a go at the booklet 06/12/2018 Now lets have a go at the booklet