Integers

1
Integers
S33
Ordering integers
Add / Sub Mathematically
Letters and Numbers
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Multiplying Integers
Dividing Integers
2
Starter Questions
S33
Q1. Explain why
Q2. How many Euros do I get for 20 if exchange
rate is 1 ? 1.5
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Q3. The answer to the question is 90. What is
the question.
3
Integers
S33
Learning Intention
Success Criteria

1. To be put integers in order of size.

1. To understand how to add positive and
negative numbers using the thermometer as an aid.
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4
Sea Level
Temperature
Integers
S33
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
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Write down 3 places where negative numbers are
used
Profit and Loss
Coordinate Grid
5
Integers
S33
Integers can be represented on a thermometer or
number line.
4
3
The further to the top a number is the bigger it
is.
2
Greater than
1
0
-1
12 gt 4
-2
-3
-4
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-2 gt -3
Less than
-4 lt -1
-3.5 lt -2.8
6
Integers
S33
Coordinate Grid
Plot the point
y - axis
(3,2)
3
x-coordinate is 3
2
1
y-coordinate is 2
origin
0
-2
-3
2
4
-1
1
3
-4
x - axis
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-1
(-2,2)
-2
-3
(-4,-2)
Plot the point that makes shape a parallelogram.
7
Integers
S33
Now try Exercise 2.1 Ch2 (page 23)
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8
Starter Questions
S33
Q1. Is 7 6x2 26 or 19
Q2. How many euros do I get for 10 if exchange
rate is 1 ? 1.4
Q3. The answer to the question is 30. What is
the question.
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9
Negative Numbers
S33
Addition Subtraction
Learning Intention
Success Criteria

1. To be able to write down mathematically the
   addition and subtraction of both positive and
   negative integers.

1. To explain how to write down mathematically
addition and subtraction of negative integers.
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10
Negative Numbers
- side by side replace by single -
S33
(a) 12 4
16
4
3
2
Go up 4
Start at 12
1
0
-1
(b) 10 ( - 8)
-2
-3
- - side by side replace by single
-4
2
10 - 8
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(c) -7 (- 10)
3
-7 10
11
Negative Numbers
S33
Examples
Remember - - - -
-4
(1) 3 - 7
(2) 4 (-9)
-5
(3) -7 (- 8)
1
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(4) -2 (-12)
-14
(5) -5 (-25)
20
(6) 8 (-9)
-1
12
Integers
S33
Now try Ex 3.1 to 4.2 Ch2 (page 26)
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Starter Questions
S33
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14
Substitution
S33
Learning Intention
Success Criteria

1. To explain the process of working out expressions
   by substitution method.

1. Understand process of substitution.

2. Solving expressions showing working.
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15
Substitution
S33
1
If a 2 and b 14 evaluate
a b
Sub in a2
2

14

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Sub in b14

16
16
Substitution
S33
2
If a 3 and b -9 evaluate
a - b
3
-
(-9)

Remember - - replace by
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3 9

12
17
Substitution
S33
3
If a 3 and b 9 evaluate
b2 a2
9x9 3x3
Remember b2 means b x b
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-
81
9


72
18
Substitution
S33
If a 5 and b 6 evaluate
1. a b
4. b - a
11
1
2. ab
5. 4b
30
24
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3. 3a
6. 3ab
15
90
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Substitution
S33
Now try Exercise 5.1 Ch2 (page 28) Q1 Q4
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20
Tidying Up Like Terms
S33
Learning Intention
Success Criteria

1. To explain the process of tidying up expressions.

1. Understand the term like terms.

2. Be able to tidy up like terms.
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21
Tidying Terms
S33
WE CAN ONLY TIDY UP LIKE TERMS
1, 3 , 5, -6, 8
are like terms simple numbers
are like terms in x
x, 3x , -2x
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are like terms in x2
x2, 3x2, -2x2
x is NOT the same as x2
22
Tidying Terms
S33
Examples
3a2 2a2
a2
3x 4y x 2y
2x 6y
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10x2 x - y
4x2 x y 6x2
12p2 4q
6p2 q 3q 6p2
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Starter Questions
S33
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24
Integers
S33
Multiplication
Learning Intention
Success Criteria
1. Understand how to multiply positive and
negative integers.
1. Explain how to multiply positive and
negative integers.
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25
Integers
S33
Multiplication
Multiplying Integers
2
1 x (-2)
(-2) x (-1)
-2
-20
(-4) x 5
(- 2) x (-5)
10
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-9
(-3) x 3
(-5) x (-5)
25
-ve x -ve ve ve x ve ve
32
(-4) x (-8)
5 x (-8)
-40
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Remember BODMAS
Integers
S33
Multiplication
Multiplying Integers
1 (-2) x (-10)
21
28
3 (-5)2
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-1
8 (-3)2
-ve x -ve ve ve x ve ve
5 x (-2)2 5 - 19
6
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Integers
S33
Multiplication
Now try MIA Ex 6.1 Ch2 (page 31)
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Starter Questions
S33
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29
Integers
S33
Division
Learning Intention
Success Criteria
1. Understand how to divide positive and
negative integers.
1. Explain how to divide positive and negative
integers.
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30
Integers
S33
Division
Dividing Integers
11
8 (-4)
(-22) (-2)
-2
-4
(-24) 6
(- 56) (-7)
8
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-1
(-3) 3
(-15) (-5)
3
-ve -ve ve ve ve ve
0.5
(-4) (-8)
16 (-2)
-8
31
Remember BODMAS
Integers
S33
Division
Division Integers
1 (-20) (-10)
3
4
100 (-5)2
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96
100 - 36 (-3)2
-ve -ve ve ve ve ve
-48 (6 - 2)2 5
2
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Integers
S33
Division
Now try MIA Ex 8.1 Ch2 (page 31)
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