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11 Apr 202311 Apr 2023 Created by Mr. Lafferty Maths DeptCreated by Mr. Lafferty Maths Dept
Integers – Positive and Negative
Add /Sub using Thermometer
IntegersIntegersw
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Add / Sub Integers Mathematically
Negative Coordinate Grid
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Multiplying & dividing Integers
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11 Apr 202311 Apr 2023 Created by Mr. Lafferty Maths DeptCreated by Mr. Lafferty Maths Dept
Starter QuestionsStarter Questionsw
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10% of £270Q1. Calculate
Q2. How many euros do I get for £20 if exchange rate is £1 1.5 €
Q3. What is the time difference 09:28 and 10:50
Q4. The answer to the question is 90. What is thequestion.
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11 Apr 202311 Apr 2023 Created by Mr. Lafferty Maths DeptCreated by Mr. Lafferty Maths Deptww
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1.1. To be able to do add To be able to do add and subtract both and subtract both positive and negative positive and negative integers using a integers using a thermometer.thermometer.
1. To understand how to add positive and negative numbers using the thermometer as an aid.
IntegersIntegersS4
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IntegersIntegersS4
Definition : An INTEGER is a negative or positive whole number, including 0.
e.g. -2, -1, 0, 5, 100
Note : -2.5, -1.2, 23.5 Are NOT INTEGERS
Ex1 Page 16 Round ClassInterpreting negative numbers
Write down 3 places where negative numbers are used
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Created by Mr. Lafferty Maths DeptCreated by Mr. Lafferty Maths Dept
Integersw
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2
8
2422
20
14
1816
1210
64
0-2
-8
-24
-22-20
-14
-18-16
-12-10
-6-4
(a) 4oC up from 12
o C
(b) 8oC down from 10
o C
(c) 3oC up from -2
o C
(d) 6oC down from 2
o C
Down -
UP +12 + 4 = 16
10 - 8 = 2
-2 + 3 = 1
2 - 6 = -4
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11 Apr 202311 Apr 2023 Created by Mr. Lafferty Maths DeptCreated by Mr. Lafferty Maths Dept
Now try Ex 2Ch1 (page 19)
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IntegersIntegersS4
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11 Apr 202311 Apr 2023 Created by Mr. Lafferty Maths DeptCreated by Mr. Lafferty Maths Dept
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50% of £300Q1. Calculate
Q2. How many euros do I get for £10 if exchange rate is £1 1.4 €
Q3. What is the time difference 09:45 and 20:30
Q4. The answer to the question is 30. What is thequestion.
![Page 8: 15-Jan-15Created by Mr. Lafferty Maths Dept Integers – Positive and Negative Add /Sub using Thermometer Integers Add / Sub Integers](https://reader036.vdocuments.us/reader036/viewer/2022062511/551c4af0550346a5458b4a2f/html5/thumbnails/8.jpg)
11 Apr 202311 Apr 2023 Created by Mr. Lafferty Maths DeptCreated by Mr. Lafferty Maths Deptww
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1.1. To be able to write down To be able to write down mathematically the mathematically the addition and subtraction addition and subtraction of both positive and of both positive and negative integers.negative integers.
1. To explain how to write down mathematically addition and subtraction of negative integers.
IntegersIntegersAddition & Subtraction
S4
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11 Apr 202311 Apr 2023 Created by Mr. Lafferty Maths DeptCreated by Mr. Lafferty Maths Dept
Integersw
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2
8
2422
20
14
1816
1210
64
0-2
-8
-24
-22-20
-14
-18-16
-12-10
-6-4
(a) 12 + 4 =
(b) 10 +(-8) =
(c) 7 - 10 =
Down -
UP +
2
-3
16
Start at 12
Go up 4
Start at 10
Go down 8
Start at 7
Go down
10
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= -4
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(1) 3 - 7
(2) 4 + (-9)
(3) -7 - 8
(4) -2 + (-12)
(5) -5 - 25
(6) 8 + (-9)
Examples
= -5
= -15
= -14
= -30
= -1
IntegersIntegersS4
Remember
“+ -” = -
“- +” = -
![Page 11: 15-Jan-15Created by Mr. Lafferty Maths Dept Integers – Positive and Negative Add /Sub using Thermometer Integers Add / Sub Integers](https://reader036.vdocuments.us/reader036/viewer/2022062511/551c4af0550346a5458b4a2f/html5/thumbnails/11.jpg)
11 Apr 202311 Apr 2023 Created by Mr. Lafferty Maths DeptCreated by Mr. Lafferty Maths Dept
Now try Ex 3Ch1 (page 20)
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IntegersIntegersS4
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11 Apr 202311 Apr 2023 Created by Mr. Lafferty Maths Dept.Created by Mr. Lafferty Maths Dept.
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Calculate 3
2. x + 5 = - 3 Find the value of x
3. Put in order, smallest first.
0.25, 0.19, 0.01, 0.026
5. Find the missing angle in the triangle.
% of 4001.
20o
xoxo
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11 Apr 202311 Apr 2023 Created by Mr. Lafferty Maths Dept.Created by Mr. Lafferty Maths Dept.ww
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1. Explain how to multiply and divide positive and negative integers.
1. Understand how to multiply and divide positive and negative integers.
IntegersIntegersMultiplication & Division
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Multiplication & Division
11 Apr 202311 Apr 2023 Created by Mr. Lafferty Maths Dept.Created by Mr. Lafferty Maths Dept.ww
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IntegersIntegers
1 1 xx (-2) = (-2) =
Multiplying Integers
5 5 x x (-8) =(-8) =
(-3) (-3) xx 3 = 3 =
(-4) (-4) xx 5 = 5 =
(-2) (-2) xx (-1) = (-1) =
(- 2) (- 2) xx (-5) = (-5) =
(-5) (-5) x x (-5) =(-5) =
(-4) (-4) xx (-8) = (-8) =
-2-2
-20-20
-9-9
-40-40
22
1010
2525
3232
With your partner can try and come
up with the rules for multiplying integers
(+ve) x (+ve) = (+ve)
(-ve) x (–ve) = (+ve)
(-ve) x (+ve) = (-ve)(+ve) x (–ve) = (-
ve)
Same signs = positive answer
Different signs = negative answer
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Multiplication & Division
11 Apr 202311 Apr 2023 Created by Mr. Lafferty Maths Dept.Created by Mr. Lafferty Maths Dept.ww
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IntegersIntegers
(-2) ÷ 1 =(-2) ÷ 1 =
(-25) ÷(-25) ÷ 55 = =
(-9) ÷ 3 =(-9) ÷ 3 =
20 ÷ (-5) =20 ÷ (-5) =
(-2) (-2) ÷÷ (-1) = (-1) =
(- 20) (- 20) ÷ ÷ (-(-5) =5) =
(-9) (-9) ÷ ÷ (-3) =(-3) =
(-40) (-40) ÷ ÷ (-8) =(-8) =
-2-2
-4-4
-3-3
-5-5
22
44
33
55
With your partner can try and come
up with the rules for multiplying integers
(+ve) ÷ (+ve) = (+ve)
(-ve) ÷ (–ve) = (+ve)
(-ve) ÷ (+ve) = (-ve)
(+ve) ÷ (–ve) = (-ve)
Same signs = positive answer
Different signs = negative answer
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11 Apr 202311 Apr 2023 Created by Mr. Lafferty Maths Dept.Created by Mr. Lafferty Maths Dept.ww
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IntegersIntegers
1 1 ++ (-2) (-2) xx (-10) = (-10) =
Multiplying Integers
5 5 x x (-2)(-2)22 + 5 – 19 = + 5 – 19 =
8 – (-3)8 – (-3)22 = =
3 + (-5)3 + (-5)22 = =
Multiplication
2121
2828
-1-1
66
Remember BODMAS
S33
Same signs = positive answer
Different signs = negative answer
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11 Apr 202311 Apr 2023 Created by Mr. Lafferty Maths Dept.Created by Mr. Lafferty Maths Dept.ww
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IntegersIntegers
1 1 ++ (-20) (-20) ÷÷ (-10) = (-10) =
Division Integers
-48 -48 ÷ ÷ (6 - 2)(6 - 2)22 + 5 = + 5 =
100 - 36 100 - 36 ÷÷ (-3) (-3)22 = =
100 100 ÷÷ (-5) (-5)22 = =
Division
33
44
9696
22
Remember BODMAS
S33
Same signs = positive answer
Different signs = negative answer
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11 Apr 202311 Apr 2023 Created by Mr. Lafferty Maths Dept.Created by Mr. Lafferty Maths Dept.
Now try MIA Ex 4Ch1 (page 21)
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IntegersIntegersMultiplication & Division
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11 Apr 202311 Apr 2023 Created by Mr. Lafferty Maths DeptCreated by Mr. Lafferty Maths Dept
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1. I f 25% of £ 300
2. Calculate the f ollowing :
(a) 3.45 x 10 (b) 7.5 100
(c) 5789 1000
3. How long between half past eight
in the moring to 14:20 hrs
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11 Apr 202311 Apr 2023 Created by Mr. Lafferty Maths DeptCreated by Mr. Lafferty Maths Deptww
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1. To show how we can extend the coordinate grid to include negative numbers.
1. Identify main parts of coordinate grid.
CoordinatesCoordinates
2. Understand the negative grid both in y-axis direction and x-axis direction.
Extending the Grid – Negative NumbersS4
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CoordinatesCoordinates
We can further extend the negative grid
1 32 540
1
3
2
5
4
1 32 40
-2
1
-1
32
Plot the point(-2,2)
(-4,-2)x - axis
y - axis
x-coordinate is -2
y-coordinate is 2
x-coordinate is -4
y-coordinate is -2
origin
-3
-4 -2-3 -1
Write down coordinatesof the other points
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Extending the Grid – Negative Numbers
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11 Apr 202311 Apr 2023 Created by Mr. Lafferty Maths DeptCreated by Mr. Lafferty Maths Dept
Now try Ex 5Ch1 (page 23)
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CoordinatesCoordinatesExtending the Grid
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