zero

1. 4 3 2 1 We are going to look at the flight of a hot air balloon. The pilot always measures her height from level with the top of the tower. The balloon starts at a height of 1metre above the top of the tower zero Every puff of a air added makes the balloon rise by 1 metre. This is the way to work out 1 + 2 = 3

2. -2 -3 -4 4 What happens if the balloon starts below the top of the tower? 3 What sum does this show? Where will the balloon end up? This shows that -4 + 6 = 2 2 Say the balloon started at -4 1 This shows that -4 + 3 = -1 What happens if I had added 6 puffs of air instead of three? zero -1

3. summary • Heights above the top of the tower are positive. • Heights below the top of the tower are negative. • The first number tells you where the balloon starts. • Each puff of air makes the balloon rise by 1m. • This represents adding a positive number

4. Exercise - adding air 1) -2 + 5 = 3 -5 • 2) -12 + 7 = • 3) 5 + 8 = 13 • 4) -5 + 21 = 16 -7.2 • 5) -14.2 + 7 = -7 11 • 6) -18 + =

5. 4 3 2 -1 -1 1 zero -1 -2 -3 -4 But what happens if we want the balloon to go down? Where will the balloon end up if we attach the sand bags? What happens if I had added 5 sand bags instead of two? Each sandbag will send the balloon down by 1 metre This shows that 2 + -5 = -3 This shows that 2 + -2 = 0

6. 4 3 2 -1 -1 -1 -1 -1 1 zero -1 -2 -3 -4 What sum does this show? How many sand bags have been added? This shows 1 + -5 = -4

7. summary • The first number still tells you where the balloon starts. • Each bag of sand added makes the balloon sink by 1m. • This represents adding a negative number

8. Exercise - adding sand bags 1) -2 + -5 = -7 • 2) 12 + -7 = 5 • 3) 5 + -8 = -3 16 • 4) 21 + -5 = -21.2 • 5) -14.2 + -7 = -11 • 6) 18 + = 7

9. Now for the clever bit……… • We can make the balloon go down not only by putting on more sand bags but also by……….

10. -2 -3 -4 4 3 2 This shows that 2 - 6 = - 4 1 zero -1 What happens if I let out 6 puffs of air?

11. How many puffs of air have been taken out? 4 3 2 1 zero -1 -2 -3 -4 This shows 1 - 5 = -4

12. summary • The first number still tells you where the balloon starts. • Each puff of air taken out makes the balloon sink by 1m. • This represents subtracting a positive number

13. Exercise – subtracting air 1) -2 - 5 = -7 • 2) -12 - 7 = -19 • 3) 5 - 8 = -3 • 4) -5 - 21 = -26 7.2 • 5) 14.2 - 7 = = -19 - 1 • 6) -18

14. Now for the real clever bit……… • What would happen to the balloon if I took off sand bags?

15. 4 3 2 -1 -1 -1 -1 -1 -1 1 zero -1 -2 -3 -4 Where will the balloon end up if we remove the sand bags? This shows that -1- -4 = -1+4 = 3 Each sandbag subtracted will send the balloon up by 1 metre What happens if I had more sand bags I could throw off, how many would I need to subtract to make the balloon go up to 3? This shows that -3- -2 = -3+2 = -1

16. Exercise - subtracting sand bags 1) -2 - -5 = -2 + 5 = 3 • 2) 12 - -7 = 12 + 7 = 19 • 3) 5 - -8 = 5 + 8 = 13 21 + 5 = 26 • 4) 21 - -5 = -14.2 + 7 = -7.2 • 5) -14.2 - -7 = 29 -11 • 6) 18 - = 18 + 11 =

17. Exercise - mixture 1) -2 + -5 = -7 • 2) -12 - 7 = -19 • 3) 5 - - 8 = 13 • 4) -5 + 21 = 16 -7.2 • 5) -14.2 - -7 = 7 25 • 6) -18 + =