1. fa http://www.mathsisfun.com/fraction s.html Year 8 Mathematics Directed Numbers

2. Learning Intentions Understand the meaning of negative whole numbers Calculate with negatives in context of – temperature – height above sea level Add and subtract positive and negative numbers Multiply and divide positive and negative numbers

3. Contour Lines Contour lines are used on maps to indicate the height you are above sea level. Negative numbers are used to indicate depths under water.

4. Temperatures Temperature is recorded on a thermometer. There are three different temperature scales – Celsius (Centigrade) – Fahrenheit – Kelvin Our normal body temperature is 36.9 O C The freezing point of water is 0 O C The boiling point of water is 100 O C

5. Thermometer Temperatures above the freezing point of water are positive Temperatures below the freezing point of water are negative

6. Reading Temperature What temperature is showing on these thermometers?

7. Increasing Temperature Increase the following temperatures by 20 O C. Write this increase as a calculation.

8. Decreasing Temperature Decrease the following temperatures by 15 O C. Write this decrease as a calculation.

9. Difference In Temperature What is the difference between these temperatures? Write this as a calculation.

10. Difference In Temperature What is the difference between these temperatures? Write this as a calculation.

11. Difference In Temperature What is the difference between these temperatures? Write this as a calculation.

12. The Number Line We use the number line to help with adding and subtracting directed numbers. When adding numbers we move up the number line. When subtracting numbers we move down the number line.

13. Using the Number Line Use the number line to do the following calculations. Always start the first number and then move up to add or down to subtract.  2 + 3 =  – 2 + 4 =  3 – 5 =  – 1 – 3 =

14. Doubling Up Remember that a number that does not have a sign is always ___________. For example, the sum 6 – 2 means + 6 – 2 This means start with positive 6 and take away a positive 2. We could also write this as (+ 6) – (+2)

15. Adding a Sign Add extra signs to each of the following:  3 – 4  3 + 3  – 3 + 4  – 1 – 2

16. Simplifying Write these calculations in a simplifier form by removing the signs:  (+3) + (+2)  (– 4) + (+2)  (+5) – (+3)  (– 5) – (– 3)

17. Calculations! Calculate the following:  5 + (– 10) =  7 – (– 11) =  – 8 + (– 9) =  16 – (– 4) + (– 6) = SAME signs make a PLUS – DIFFERENT signs make a MINUS

18. Multiplying and Dividing The sign rules also apply for multiplying and dividing When two numbers have the same sign, the answer is _______________. When two numbers have different signs, the answer is _______________.

19. Calculations! Calculate the following:  3 x (– 10) =  – 7 x 4 =  – 8 x (– 9) =  15 ÷ (– 3) =  (– 77) ÷ ( – 11) =