Algebra

1
Algebra
Tidying up terms
Number Machine
Working with Expressions
Solving Simple Equations
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Solving Harder Equations
Understanding Inequalities
Solving Simple Inequalities
2
Starter Questions
Q1. Calculate
Q2. Convert 60 to fraction and simplify.
to a percentage.
Q3. Convert
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Q4. What is the time difference 0928 and 1050
Q5. The answer to the question is 90. What is
the question.
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We are Learning to
a 2b 3a b

1. Tidying up expressions.
2. Show steps when tidying up.

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Tidying Terms



First Row


2c
c
4c
7c
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2nd Row


2d
2d
3d
7d
5
Tidying Terms



3rd Row


3f
f
2f
6f
CANNOT TIDY UP ANYMORE
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In Total we have
7c 7d 6f
WE CAN ONLY TIDY UP LIKE TERMS
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Tidying Terms
WE CAN ONLY TIDY UP LIKE TERMS
Tidy up the following Q1. 2x4x5y-3y18 Q2. 4a
3b5a6-b
6x5y-3y18
6x2y18
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9a3b-b6
9a2b6
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Tidying Terms
Your turn ! Page 46 Exercise 1 Q1 and Q2
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Starter Questions
Q1. Tidy up the expression
Q2. Calculate
Q3. Round to 1 decimal place.
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(a) 2.34 (b) 10.25 (c) 3.23
Q4. 12.5 as a fraction
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We are learning
Number Machine

1. To build simple expressions.
2. To UNDO simple expressions.

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Number Machine
To build an expression from the number machine
simply follow the rules given
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Number Machine
To build an expression from the number machine
simply follow the rules given
20
23
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3b
3b9
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Number Machine
Your turn ! Page 93 Exercise 2 Q1
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Number Machine
To UNDO the number machine simply do the
opposite of the rules given
8
x2
18
36
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Number Machine
To UNDO the number machine simply do the
opposite of the rules given
-9
x4
5
20
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Number Machine
Your turn ! Page 93 Exercise 2 Q3 and Q4
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Starter Questions
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Substitution
Learning Intention
Success Criteria

1. We are learning the process of working out
   expressions by substitution method.

1. Understand process of substitution.

2. Solving expressions showing working.
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Substitution
If a 3 and b 9 evaluate
a b
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3

9


12
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Substitution
If a 3 and b 9 evaluate
ab
Remember ab means a x b
a x b
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3
9

x

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20
Substitution
If a 3 and b 9 evaluate
4b
Remember 4b means 4 x b
4 x b
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4
9

x

36
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Substitution
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
If a 5 and b 3 evaluate
2a 4b
2xa 4xb

4x
3
2x
5


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12
10


22
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Substitution
If a 5 and b 3 evaluate
a
2
Remember a2 means a x a
a x a

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5
5

x

25
24
Substitution
If a 15 and b 3 evaluate
a
15

b
3
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5
25
Substitution
If a 2 and b 6 evaluate
1) 4a 3b
4) 5b 3a
26
24
2) a2
5) 4a2
4
16
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3) b2
36
3
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Substitution
Your turn ! Page 94 Exercise 3
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Starter Questions
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Equations
Solving Equations
Learning Intention
Success Criteria

1. We are learning to solve simple equations.

1. Understand the process of the Balancing
Method.
2. Solving simple algebraic equations.
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Balancing Method
Kirsty goes to the shops every week to buy some
potatoes. She always buys the same total weight.
One week she buys 2 large bags and 1 small bag.
The following week she buys 1 large bag and 3
small bags.
If a small bags weighs 4 kgs. How much does a
large bag weigh?
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What instrument measures balance
How can we go about solving this using balance ?
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Balancing Method
Take a small bag away from each side.
4
4
4
4
Take a big bag away from each side.
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We can see that a big bag is equal to
4 4
8 kg
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Balancing Method
What symbol should we use for the scales ?
Lets solve it using maths.
4
P
P
P
Let P be the weight of a big bag.
4
4
4
We know that a small bag 4
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Subtract 4 from each side
2P 4
P 12

-4
-4
Subtract P from each side
2P

P 8
-P
-P
P

8
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Balancing Method
Group of 5 adults and 3 children go to the local
swimming. Another group of 3 adults and 8
children also go swimming. The total cost for
each group is the same. A childs ticket costs
2.
If a childs ticket costs 2. How much for an
adult ticket ?
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Let a be the price of an adult ticket.
We know that a child price 2
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Balancing Method
Subtract 6 from each side
Subtract 3a from each side
For balance we have
5a 6
3a 16

-6
-6
2
2
1
a
5a

3a 10
a
-3a
-3a
Divide each side by 2
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2a

10
a

5
Adult ticket price is 5
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Balancing Method
It would be far too time consuming to draw
out the balancing scales each time. We will now
learn how to use the rules for solving equations.
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Equations
Solving Equations
The method we use to solve equations is
The Balancing Method
Write down the opposite of the following


-
-
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opposite is
opposite is
x
x


opposite is
opposite is
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Simple Equations
Type 1
20
x 3
- 3
- 3
17
x
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Simple Equations
Type 1
72
x - 5
5
5
77
x
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Simple Equations
Type 2
8
24 - x
x
x
Swap
24
8 x
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x 8
24
- 8
- 8
x
16
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Simple Equations
Type 2
10
13 - x
x
x
Swap
13
10 x
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x 10
13
- 10
- 10
x
3
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Simple Equations
Type 3
4x
20
x
20 4
( 4)
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5
x
41
Simple Equations
Type 3
8x
28
x
28 8
( 8)
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3.5
x
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Equations
Solving Equations
Now try Exercise 4 Ch8 (page 96)
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Starter Questions
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Equations
Harder Equations
Learning Intention
Success Criteria

1. We are learning to solve harder equations.

1. Understand the process of the Balancing
Method.
2. Solving harder algebraic equations by using
rule repeatedly.
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Equations
Harder Equations
The rule we use to solve equations is
The Balancing Method
Write down the opposite of the following


-
-
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opposite is
opposite is
x
x


opposite is
opposite is
46
Equations
Type 4
22
2x 4
- 4
- 4
2x
18
(2)
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Do a Check !
x
9
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Equations
Type 4
40
9x - 5
5
5
9x
45
(9)
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Do a Check !
x
5
48
Equations
Harder Equations
Now try Exercise 5 Ch8 (page 97)
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Starter Questions
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Inequalities
Solving Inequalities
Learning Intention
Success Criteria

1. We are learning the various symbols for
   inequalities.

• Remember the 4 symbols for
• inequalities.

2. Solving simple inequalities equations.
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Inequalities
Solving Inequations
The equations you were solving were called
equations because they contained an sign.
There are 4 other Mathematical symbols They are
called inequalities
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greater than or equal to
greater than
less than or equal to
less than
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Inequalities
Arrow ALWAYS points to the smallest number
Solving Inequalities
Examples Write in words what each mean.
5 gt 3
means 5 is greater than 3
-7 lt -6
means -7 is less than -6
means x can take the value 2 or greater
x 2
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y -5
means y can take the value -5 or less
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Inequalities
Solving Inequalities
Examples Write out an inequality for the
numbers
(a) 14 and 6
14 gt 6
(b) -2 and 1
-2 lt 1
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(c) -3 and -7
-3 gt -7
(d) 34 and -35
34 gt -35
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Inequalities
Solving Inequalities
Examples Choosing from -3, -2, -1, 0 , 1, 2, 3
(a) y lt 0
-3, -2, -1
(b) y gt 2
3
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(c) y -2
-3, -2
(d) y gt 3
No solution
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Inequalities
Solving Inequalities
Now try Exercise 6 Ch8 (page 99)
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Starter Questions
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Inequalities
Inequalities
Learning Intention
Success Criteria

1. We are learning to solve simple inequalities.

• Understand the
• Balancing Method

2. Solving simple inequalities equations.
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Inequalities
Inequalities
The Good News
Same rule as solving equations
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The Balancing Method
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Inequalities
Solving Inequalities
The Balancing Method
Subtract 10 from each side
Add 9 to each side
Examples
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Inequalities
Solving Inequalities
The Balancing Method
Divide by 9 each side
Divide by 7 each side
Examples
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Inequalities
Inequalities
Now try Exercise 7 Ch8 (page 101)
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