1. Calculating with Negatives THE FOUR RULES AND NEGATIVE NUMBERS

2. Calculations cards You have 5 cards, each with a sequence of two operations. They are as follows: You will be shown a slide with a number to use in the calculations. Perform the calculations, and then place your cards in order: smallest to largest, from left to right on your desk. multiply by -2 then add 3 subtract -2 then multiply by -3 add -2 then multiply by 3 subtract 3 then multiply by -2 multiply by 3 then add -2

3. Your number is … 1 Order your cards on your desk, smallest to largest.

4. Solution 1 multiply by -2 then add 3 1 subtract -2 then multiply by -3 -9 add -2 then multiply by 3 -3 subtract 3 then multiply by -2 4 multiply by 3 then add -2 1

5. Your number is … Order your cards on your desk, smallest to largest.

6. Solution multiply by -2 then add 3 5 subtract -2 then multiply by -3 -3 add -2 then multiply by 3 -9 subtract 3 then multiply by -2 8 multiply by 3 then add -2 -5

7. Your number is … 0 Order your cards on your desk, smallest to largest.

8. Solution 0 multiply by -2 then add 3 3 subtract -2 then multiply by -3 -6 add -2 then multiply by 3 -6 subtract 3 then multiply by -2 -6 multiply by 3 then add -2 -2

9. Your number is … -5 Order your cards on your desk, smallest to largest.

10. Solution -5 multiply by -2 then add 3 13 subtract -2 then multiply by -3 9 add -2 then multiply by 3 -21 subtract 3 then multiply by -2 16 multiply by 3 then add -2 -17

11. Your number is … -10 Order your cards on your desk, smallest to largest.

12. Solution -10 multiply by -2 then add 3 23 subtract -2 then multiply by -3 24 add -2 then multiply by 3 -36 subtract 3 then multiply by -2 26 multiply by 3 then add -2 -32

13. Your number is … 6 Order your cards on your desk, smallest to largest.

14. Solution 6 multiply by -2 then add 3 -9 subtract -2 then multiply by -3 -24 add -2 then multiply by 3 12 subtract 3 then multiply by -2 -6 multiply by 3 then add -2 16

15. Your number is … 3.5 Order your cards on your desk, smallest to largest.

16. Solution 3.5 multiply by -2 then add 3 -4 subtract -2 then multiply by -3 -16.5 add -2 then multiply by 3 4.5 subtract 3 then multiply by -2 multiply by 3 then add -2 8.5

17. Your number is … -2.5 Order your cards on your desk, smallest to largest.

18. Solution -2.5 multiply by -2 then add 3 8 subtract -2 then multiply by -3 1.5 add -2 then multiply by 3 -13.5 subtract 3 then multiply by -2 11 multiply by 3 then add -2 -9.5

19. Your number is … -½ Order your cards on your desk, smallest to largest.

20. Solution -½ multiply by -2 then add 3 4 subtract -2 then multiply by -3 -4½ add -2 then multiply by 3 -7½ subtract 3 then multiply by -2 7 multiply by 3 then add -2 -3½

21. Calculating with negatives: further reasoning There are certain sets of numbers for which the final order of these cards is the same. E.g. for 3.5 and 6, and separately for -1, -2.5 and -5. However, other numbers do not fit into these sets. Investigate! multiply by -2 then add 3 subtract -2 then multiply by -3 add -2 then multiply by 3 subtract 3 then multiply by -2 multiply by 3 then add -2