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Year 8 Mathematics

Directed Numbers

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

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.

Temperatures

• Temperature is recorded on a thermometer.• There are three different temperature scales– Celsius (Centigrade)– Fahrenheit– Kelvin

• Our normal body temperature is 36.9OC• The freezing point of water is 0OC• The boiling point of water is 100OC

Thermometer

• Temperatures above the freezing point of water are positive

• Temperatures below the freezing point of water are negative

Reading Temperature

• What temperature is showing on these thermometers?

Increasing Temperature

• Increase the following temperatures by 20OC.

• Write this increase as a calculation.

Decreasing Temperature

• Decrease the following temperatures by 15OC.

• Write this decrease as a calculation.

Difference In Temperature

• What is the difference between these temperatures?

• Write this as a calculation.

Difference In Temperature

• What is the difference between these temperatures?

• Write this as a calculation.

Difference In Temperature

• What is the difference between these temperatures?

• Write this as a calculation.

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.

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 =

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)

Adding a Sign

• Add extra signs to each of the following: 3 – 4 3 + 3 – 3 + 4 – 1 – 2

Simplifying

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

Calculations!

• Calculate the following: 5 + (– 10) =

7 – (– 11) =

– 8 + (– 9) =

16 – (– 4) + (– 6) =

SAME signs make a PLUS – DIFFERENT signs make a MINUS

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 _______________ .

Calculations!

• Calculate the following: 3 x (– 10) =

– 7 x 4 =

– 8 x (– 9) =

15 ÷ (– 3) =

(– 77) ÷ (– 11) =