Algebra

1
Algebra
MTH 3-14a MTH 3-15a MTH 3-15b
Tidying up terms
Number Machine
Working with Expressions
Solving Simple Equations
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Solving Harder Equations
Understanding Inequalities
Solving Simple Inequalities
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Starter Questions
MTH 3-14a MTH 3-15a MTH 3-15b
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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Aim of the Lesson
MTH 3-14a MTH 3-15a MTH 3-15b
Tidying Terms
a2b3ab

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

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Tidying Terms
MTH 3-14a MTH 3-15a MTH 3-15b



First Row


2c
c
4c
7c
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2nd Row


2d
2d
3d
7d
5
Tidying Terms
MTH 3-14a MTH 3-15a MTH 3-15b



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
MTH 3-14a MTH 3-15a MTH 3-15b
WE CAN ONLY TIDY UP LIKE TERMS
Tidy up the following Q1. 2x 4x 5y -3y 18
Q2. 4a 3b 5a 6 b
6x 2y 18
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9a 2b 6
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Tidying Terms
MTH 3-14a MTH 3-15a MTH 3-15b
Your turn ! Page 46 Exercise 1 Q1 and Q2
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Starter Questions
MTH 3-14a MTH 3-15a MTH 3-15b
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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Aim of the Lesson
MTH 3-14a MTH 3-15a MTH 3-15b
Number Machine

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

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Number Machine
MTH 3-14a MTH 3-15a MTH 3-15b
To build an expression from the number machine
simply follow the rules given
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Number Machine
MTH 3-14a MTH 3-15a MTH 3-15b
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
MTH 3-14a MTH 3-15a MTH 3-15b
Your turn ! Page 93 Exercise 2 Q1
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Number Machine
MTH 3-14a MTH 3-15a MTH 3-15b
To UNDO the number machine simply do the
opposite of the rules given
8
x2
18
36
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Number Machine
MTH 3-14a MTH 3-15a MTH 3-15b
To UNDO the number machine simply do the
opposite of the rules given
-9
x4
5
20
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Number Machine
MTH 3-14a MTH 3-15a MTH 3-15b
Your turn ! Page 93 Exercise 2 Q3 and Q4
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Starter Questions
MTH 3-14a MTH 3-15a MTH 3-15b
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Substitution
MTH 3-14a MTH 3-15a MTH 3-15b
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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Substitution
MTH 3-14a MTH 3-15a MTH 3-15b
1
If a 3 and b 9 evaluate
a b
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Sub in a3
3

9

Sub in b9

12
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Substitution
MTH 3-14a MTH 3-15a MTH 3-15b
2
If a 3 and b 9 evaluate
ab
a x b
Remember ab means a x b
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Sub in a3
3
x
9

Sub in b9

27
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Substitution
MTH 3-14a MTH 3-15a MTH 3-15b
3
If a 3 and b 9 evaluate
4b
4 x b
Remember 4b means 4 x b
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4
x
9

Sub in b9

36
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Substitution
MTH 3-14a MTH 3-15a MTH 3-15b
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
MTH 3-14a MTH 3-15a MTH 3-15b
If a 5 and b 3 evaluate
4
2a 4b
2xa 4xb

Remember 2a means 2 x a
Sub in a5
4x
3
2x
5


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Sub in b3

10
12


22
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Substitution
MTH 3-14a MTH 3-15a MTH 3-15b
5
If a 5 and b 3 evaluate
a
2
a x a

Remember a2 means a x a
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Sub in a5
5
x
5


25
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Substitution
MTH 3-14a MTH 3-15a MTH 3-15b
6
If a 15 and b 3 evaluate
a
15

b
3
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Sub in a15

5
Sub in b 3
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Substitution
MTH 3-14a MTH 3-15a MTH 3-15b
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
MTH 3-14a MTH 3-15a MTH 3-15b
Your turn ! Page 94 Exercise 3
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Starter Questions
MTH 3-14a MTH 3-15a MTH 3-15b
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Equations
MTH 3-14a MTH 3-15a MTH 3-15b
Level E Solving Equations
Learning Intention
Success Criteria

• To solve simple equations using the rule
• change side change sign.

1. Know rule change side change sign.
2. Solving simple algebraic equations.
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Equations
MTH 3-14a MTH 3-15a MTH 3-15b
Level E Solving Equations
The rule we use to solve equations is
The rule change side change sign
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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Equations
MTH 3-14a MTH 3-15a MTH 3-15b
Level E Solving Equations
The rule change side change sign
8 opposite is -8
-5 opposite is 5
Examples
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Equations
MTH 3-14a MTH 3-15a MTH 3-15b
Level E Solving Equations
The rule change side change sign
times by 8 opposite is divide by 8
times by 3 opposite is divide by 3
Examples
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Equations
MTH 3-14a MTH 3-15a MTH 3-15b
Level E Solving Equations
Now try Exercise 4 Ch8 (page 96)
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Starter Questions
MTH 3-14a MTH 3-15a MTH 3-15b
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Equations
MTH 3-14a MTH 3-15a MTH 3-15b
Level E Harder Equations
Learning Intention
Success Criteria

• To solve harder equations using the rule
• change side change sign.
• repeatedly.

1. Know rule change side change sign.
2. Solving harder algebraic equations by using
rule repeatedly.
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35
Equations
MTH 3-14a MTH 3-15a MTH 3-15b
Level E Harder Equations
The rule we use to solve equations is
The rule change side change sign
Write down the opposite of the following


-
-
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opposite is
opposite is
x
x


opposite is
opposite is
36
Equations
MTH 3-14a MTH 3-15a MTH 3-15b
Level E Harder Equations
The rule change side change sign
1 opposite is -1
Examples
times by 2 opposite is divide by 2
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Equations
MTH 3-14a MTH 3-15a MTH 3-15b
Level E Harder Equations
The rule change side change sign
-6 opposite is 6
Examples
times by 4 opposite is divide by 4
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38
Equations
MTH 3-14a MTH 3-15a MTH 3-15b
Level E Harder Equations
Now try Exercise 5 Ch8 (page 97)
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Starter Questions
MTH 3-14a MTH 3-15a MTH 3-15b
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Inequalities
MTH 3-14a MTH 3-15a MTH 3-15b
Level E Solving Inequalities
Learning Intention
Success Criteria

1. To explain the various symbols for inequalities.

• Know rule the 4 symbols for
• inequalities.

2. Solving simple inequalities equations.
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Inequalities
MTH 3-14a MTH 3-15a MTH 3-15b
Level E 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
MTH 3-14a MTH 3-15a MTH 3-15b
Arrow ALWAYS points to the smallest number
Level E 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
MTH 3-14a MTH 3-15a MTH 3-15b
Level E 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
MTH 3-14a MTH 3-15a MTH 3-15b
Level E 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
MTH 3-14a MTH 3-15a MTH 3-15b
Level E Solving Inequalities
Now try Exercise 6 Ch8 (page 99)
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Starter Questions
MTH 3-14a MTH 3-15a MTH 3-15b
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Inequalities
MTH 3-14a MTH 3-15a MTH 3-15b
Level E Inequalities
Learning Intention
Success Criteria

• To solve simple inequalities using the same rules
  as for equations
• change side change sign.

1. Know rule change side change sign.
2. Solving simple inequalities equations.
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48
Inequalities
MTH 3-14a MTH 3-15a MTH 3-15b
Level E Inequalities
The Good News
Same rule as solving equations
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The rule change side change sign
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Inequalities
MTH 3-14a MTH 3-15a MTH 3-15b
Level E Solving Inequalities
The rule change side change sign
10 opposite is -10
-9 opposite is 9
Examples
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Inequalities
MTH 3-14a MTH 3-15a MTH 3-15b
Level E Solving Inequalities
The rule change side change sign
times by 9 opposite is divide by 9
times by 7 opposite is divide by 7
Examples
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Inequalities
MTH 3-14a MTH 3-15a MTH 3-15b
Level E Inequalities
Now try Exercise 7 Ch8 (page 101)
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