Algebra

1
Algebra
Collecting Like Terms
Removing Brackets
Removing Brackets Simplifying
Solving Simple Equations
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Solving Equations with Brackets
Evaluating Expressions Formulae
Constructing Formulae
2
Starter Questions
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2cm
3cm
6cm
2cm
3
Algebra
Simplifying Algebraic Expressions
Learning Intention
Success Criteria

1. Understand the techniques for simplifying terms.

1. We are learning to simplify terms.

2. Be able too simplify algebraic expressions.
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4
Algebra
Simplifying Algebraic Expressions
Collecting LIKE terms
- m a
1 4g
(NOT 5g )
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7 k2
(NOT 7k6)
5
Algebra
Simplifying Algebraic Expressions
Multiplying Terms
6 d
4 h
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(NOT 2e )
e2
8
(NOT 8a)
a2
6
Algebra
Simplifying Algebraic Expressions
Dividing Terms
4
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e
3
7
What is the total area of the downstairs house?
Algebra
Simplifying Algebraic Expressions
Below is a floor plan of the down stairs of a
house.
y
5
Living Room
y
y2
5y
Tidy up !
Bedroom
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3y
15
3
Kitchen
Bathroom
y2
8y
15
8
Algebra
Removing Brackets
Now try TJ3a Ex 1 Ch7 (page 54)
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9
Starter Questions
2a
6h
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10
Algebra
Removing brackets
Learning Intention
Success Criteria

1. Understand the key steps in removing brackets.

1. We are learning how to multiply out simply
algebraic brackets.
2. Apply multiplication rules for positive and
negative numbers when removing brackets.
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11
Removing a Single Bracket
Example
15
3(b 5)
3b
Example
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- 8
4(w - 2)
4w
12
Removing a Single Bracket
Example
24
8(x 3)
8x
Example
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- 8m
4(3 -2m)
12
13
Removing a Single Bracket
Example Write down an expression for the
amount indicate below in two difference ways.
y-2
y-2
y-2
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- 10
5(y - 2)
5y
y-2
y-2
17-Aug-19
Created by Mr. Lafferty_at_mathsrevision.com
14
Removing a Single Bracket
Example
5a
a(b 5)
ab
Example
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- 2p
p(w - 2)
pw
15
Removing a Single Bracket
Example
- y
y(y - 1)
y2
Example
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- 21w
7w(w - 3)
7w2
16
Removing a Single Bracket
Example
3ab
a(a2 3b)
a3
Example
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- 2cy2
y2(3y -2c)
3y3
17
Removing a Single Bracket
Example
- y
-(x y)
-x
Example
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35
-5(a - 7)
-5a
18
Algebra
Removing brackets
Question Find the area of the rectangle (i)
With brackets (ii) Without brackets.
y 5
(i) A L x B
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4
4(y 5)
(ii) 4(y 5)
4y
20
19
Algebra
Removing Brackets
Now try TJ3a Ex 2 Ch7 (page 56)
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20
Starter Questions
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(x-6)cm
3cm
21
Algebra
Removing brackets
Learning Intention
Success Criteria

1. Understand the key steps in removing brackets and
   simplifying.

1. We are learning how to multiply out simply
algebraic brackets and collecting like terms.
2. Apply multiplication rules for positive and
negative numbers when removing brackets.
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22
Removing a Single Bracket
Tidy Up
Example
- 3y
12
7 3(4 - y)
7
19 - 3y
Tidy Up
Example
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- 24
3y
9 - 3(8 - y)
9
-15 3y
23
Removing a Single Bracket
Example
12
10
Find my Area
Find my Area
x
(x - 2)
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A L x B
A L x B
A 10(x 2)
A 12x
24
Removing Two Single Brackets
Tidy Up
Example
- m - 2
4(m - 3) - (m 2)
4m - 12
3m - 14
Tidy Up
Example
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- 2y - 8
7(y - 1) - 2(y 4)
7y - 7
5y - 15
25
Removing a Single Bracket
Example Find area of the orange border
12
Area Big Rec Small Rec
10
x
(x - 2)
12x 10(x - 2)
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12x
-10x
20
2x 20
26
Removing Two Single Brackets
Example Find an expression for the difference
in the areas.
(y - 5)
A 4(y 5)
4
7
A 7(y - 4)
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(y - 4)
Calculate difference if y 14
Diff 3 x 14 8 34
Difference 7(y - 4) - 4(y 5)
7y - 28
- 4y 20
3y - 8
27
Removing Two Single Brackets
Example Find an expression for the difference
in the areas.
(x 1)
A 7(x 1)
7
9
A 9(x 3)
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x 3
Calculate difference if x 4
Diff 2 x 4 20 28
Difference 9(x 3) - 7(x 1)
9x 27
7x - 7
2x 20
28
Algebra
Removing Brackets Simplifying
Question Find the area of the large rectangle,
then the small rectangle and
hence find the area of the red section.
x
x-3
4
Ab 6x
6
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As 4(x - 3)
4x
- 12
As 6x - 4(x - 3)
6x
2x 12
- 4x
12
29
Algebra
Removing Brackets
Now try TJ3a Ex 3 Ch7 (page 57)
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30
Starter Questions
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31
Equations
Revision of Level 2
Learning Intention
Success Criteria

• To revise Level 2
• using the rule
• Balancing Method

1. Understand the process of the Balancing
Method
2. Solving simple algebraic equations.
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32
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 ?
33
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
34
Balancing Method
What symbol should we use for the scales ?
Lets solve it using maths.
4
P
P
P
Let P be the weigh 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
35
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
36
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
37
Balancing Method
It would be far too time consuming to draw
out the balancing scales each time. We will now
review how to use the rules for solving equations.
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38
Equations
Revision of Level 2
Examples
x 5 11
x 8 37
5
5
- 8
- 8
x 16
x 29
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39
Equations
Revision of Level 2
Examples
6x 72
2x 11
x 12
x 5.5
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40
Equations
Revision of Level 2
Examples
¾x 9
½x 5
(x 2)
(x 4)
x 10
3x 36
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x 12
41
Equations
Revision of Level 2
Examples
4x 2 34
2x 9 31
2
2
- 9
- 9
4x 36
2x 22
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x 11
x 9
42
Algebra
Removing Brackets
Now try TJ3a Ex 4 Ch7 (page 58)
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43
Starter Questions
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44
Equations
Equations with Brackets
Learning Intention
Success Criteria
1. Remember rule for Multiply out brackets.
1. We are learning how to solve equations with
brackets and fractions .
2. Apply Balancing Method to solve fractional
equations.
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45
Each group has 2 minutes come up with a method
for solving this type of equation
Equations
Equations with Brackets
Example
3(x 2) 33
3x - 6 33
6
6
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3x 39
x 13
46
Equations
Equations with Brackets
Example
5(3x 2) 2(4x - 3) 2x 36
15x
10
8x
6
2x 36
Tidy up terms !
7x 16 2x 36
- 16
- 16
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7x 2x 20
- 2x
- 2x
5x 20
x 4
47
Each group has 2 minutes come up with a method
for solving this type of equation
Equations
Equations with Fractions
Example
(x 2)
x 6 14
- 6
- 6
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x 8
48
Equations
Equations with Fractions
Example
(x 4)
3x - 2 16
2
2
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3x 18
x 6
49
Algebra
Removing Brackets
Now try TJ3a Ex 5 Ch7 (page 59)
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50
Starter Questions
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(x2)cm
7cm
51
Algebra
Evaluating Expressions number for letter
Learning Intention
Success Criteria
1. Be able to substitute numbers for letters
in an expression.
1. We are learning how to evaluate an
expression.
2. Use previous knowledge of Number to evaluate
a expression.
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52
Algebra
Evaluating Expressions number for letter
BODMAS
Given the following information find the values
of -
a 3 b 4 and c -1
2a c
b2 a2
2b2
42 32
2x3 (-1)
2x(4)2
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16 9
2x3 - 1
2x16
6 - 1
7
32
5
53
Algebra
Evaluating Expressions number for letter
Given the following information find the values
of -
a 3 b 4 and c -1
2a2 3b 30c
2x(3)2 3x4 30x(-1)
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18 12 - 30
0
54
Algebra
Evaluating Expressions number for letter
BODMAS
Given the following information find the values
of -
d 3 e 4 and f -1
2(d - f)
¾(d f2)
v(16e)
¾(3 (-12))
2(3 -(-1))
v(16x4)
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¾(4)
2 x 4
v64
8
3
8
55
Algebra
Removing Brackets
Now try TJ3a Ex 6 Ch7 (page 60)
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56
Starter Questions
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57
Formulae
Learning Intention
Success Criteria

1. To explain how to work with formulae expressed in
   words.

1. Understand formulae expressed in words.

2. Solve problems given formulae in words.
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58
Formulae
Sometimes formulae are expressed in words.
A tile fitter charges 20 per hour. How much
will he charge for 8 hours of work.
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C
20xh
For h 8
C 20 x 8
160
59
Formulae
The cost for hiring a carpet cleaner is 30 plus
3 a day How much will it cost to hire for a week.
C
30

3d
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For d 7
51
C 30 3 x 7
60
Formulae
Profit Subtract how much you paid for goods in
the first place from the amount you actually sold
them for. How much profit did Daniel make if he
bought a CD for 9.99 and sold it for 12
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p s - b
2.01
Profit 12 9.99
61
Algebra
Removing Brackets
Now try TJ3a Ex 7 Ch7 (page 62)
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Are you on Target ? I can ?