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# algebra - PowerPoint PPT Presentation

MTH 3-14a MTH 3-15a MTH 3-15b. Algebra. Tidying up terms. Number Machine. Working with Expressions. Solving Simple Equations. www.mathsrevision.com. Solving Harder Equations. Understanding Inequalities. Solving Simple Inequalities. MTH 3-14a MTH 3-15a MTH 3-15b. Starter Questions.

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MTH 3-15a

MTH 3-15b

### Algebra

Tidying up terms

Number Machine

Working with Expressions

Solving Simple Equations

www.mathsrevision.com

Solving Harder Equations

Understanding Inequalities

Solving Simple Inequalities

Created by Mr.Lafferty Maths Dept

MTH 3-15a

MTH 3-15b

### 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 09:28 and 10:50

Q5. The answer to the question is 90. What is the

question.

Created by Mr.Lafferty Maths Dept

MTH 3-15a

MTH 3-15b

### Aim of the Lesson

Tidying Terms

a+2b+3a+b

• Tidying up expressions.

• Show steps when tidying up.

www.mathsrevision.com

Created by Mr.Lafferty Maths Dept

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

Created by Mr.Lafferty Maths Dept

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”

Created by Mr.Lafferty Maths Dept

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

Created by Mr.Lafferty Maths Dept

MTH 3-14a

MTH 3-15a

MTH 3-15b

Page 46 Exercise 1

Q1 and Q2

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Created by Mr.Lafferty Maths Dept

MTH 3-15a

MTH 3-15b

### 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

Created by Mr.Lafferty Maths Dept

MTH 3-15a

MTH 3-15b

### Aim of the Lesson

Number Machine

• To build simple expressions.

• To UNDO simple expressions.

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Created by Mr.Lafferty Maths Dept

7m

Number Machine

MTH 3-14a

MTH 3-15a

MTH 3-15b

To build an expression from the number machine

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Created by Mr.Lafferty Maths Dept

MTH 3-14a

MTH 3-15a

MTH 3-15b

To build an expression from the number machine

20

23

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3b

3b+9

Created by Mr.Lafferty Maths Dept

MTH 3-14a

MTH 3-15a

MTH 3-15b

Page 93 Exercise 2

Q1

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Created by Mr.Lafferty Maths Dept

UNDO

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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Created by Mr.Lafferty Maths Dept

UNDO

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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Created by Mr.Lafferty Maths Dept

MTH 3-14a

MTH 3-15a

MTH 3-15b

Page 93 Exercise 2

Q3 and Q4

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Created by Mr.Lafferty Maths Dept

MTH 3-15a

MTH 3-15b

### Starter Questions

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Created by Mr.Lafferty Maths Dept

MTH 3-14a

MTH 3-15a

MTH 3-15b

Learning Intention

Success Criteria

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

• Understand process of substitution.

• 2. Solving expressions showing working.

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Created by Mr.Lafferty Maths Dept

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 a=3

=

3

+

9

Sub in b=9

=

12

Created by Mr.Lafferty Maths Dept

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 a=3

=

3

x

9

Sub in b=9

=

27

Created by Mr.Lafferty Maths Dept

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 b=9

=

36

Created by Mr.Lafferty Maths Dept

MTH 3-14a

MTH 3-15a

MTH 3-15b

If a = 5 and b = 6 evaluate

1. a + b

=11

4. b - a

=1

2. ab

=30

5. 4b

=24

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3. 3a

=15

6. 3ab

=90

Created by Mr.Lafferty Maths Dept

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 a=5

4x

3

=

2x

5

+

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Sub in b=3

=

10

12

+

=

22

Created by Mr.Lafferty Maths Dept

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 a=5

=

5

x

5

=

25

Created by Mr.Lafferty Maths Dept

b

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 a=15

=

5

Sub in b = 3

Created by Mr.Lafferty Maths Dept

a

Substitution

MTH 3-14a

MTH 3-15a

MTH 3-15b

If a = 2 and b = 6 evaluate

1) 4a + 3b

=26

4) 5b – 3a

=24

2) a2

=4

5) 4a2

=16

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3) b2

=36

=3

Created by Mr.Lafferty Maths Dept

MTH 3-14a

MTH 3-15a

MTH 3-15b

Page 94 Exercise 3

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Created by Mr.Lafferty Maths Dept

MTH 3-15a

MTH 3-15b

### Starter Questions

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Created by Mr.Lafferty Maths Dept

MTH 3-15a

MTH 3-15b

Level E Solving Equations

### 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.

www.mathsrevision.com

Created by Mr.Lafferty Maths Dept

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

Created by Mr.Lafferty Maths Dept

Check to see if correct !

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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Created by Mr.Lafferty Maths Dept

Check to see if correct !

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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Created by Mr.Lafferty Maths Dept

MTH 3-14a

MTH 3-15a

MTH 3-15b

Level E Solving Equations

Now try Exercise 4

Ch8 (page 96)

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Created by Mr.Lafferty Maths Dept

MTH 3-15a

MTH 3-15b

### Starter Questions

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Created by Mr.Lafferty Maths Dept

MTH 3-15a

MTH 3-15b

Level E Harder Equations

### 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.

www.mathsrevision.com

Created by Mr.Lafferty Maths Dept

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 :

+

+

-

-

www.mathsrevision.com

opposite is

opposite is

x

x

÷

÷

opposite is

opposite is

Created by Mr.Lafferty Maths Dept

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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Created by Mr.Lafferty Maths Dept

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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Created by Mr.Lafferty Maths Dept

MTH 3-14a

MTH 3-15a

MTH 3-15b

Level E Harder Equations

Now try Exercise 5

Ch8 (page 97)

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Created by Mr.Lafferty Maths Dept

MTH 3-15a

MTH 3-15b

### Starter Questions

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Created by Mr.Lafferty Maths Dept

MTH 3-15a

MTH 3-15b

Level E Solving Inequalities

### Inequalities

Learning Intention

Success Criteria

• To explain the various symbols for inequalities.

• Know rule the 4 symbols for

• inequalities.

• 2. Solving simple inequalities equations.

www.mathsrevision.com

Created by Mr.Lafferty Maths Dept

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

Created by Mr.Lafferty Maths Dept

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 > 3

means 5 is greater than 3

-7 < -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

Created by Mr.Lafferty Maths Dept

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 > 6

(b) -2 and 1

-2 < 1

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(c) -3 and -7

-3 > -7

(d) 34 and -35

34 > -35

Created by Mr.Lafferty Maths Dept

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 < 0

-3, -2, -1

(b) y > 2

3

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(c) y ≤ -2

-3, -2

(d) y > 3

No solution

Created by Mr.Lafferty Maths Dept

MTH 3-14a

MTH 3-15a

MTH 3-15b

Level E Solving Inequalities

Now try Exercise 6

Ch8 (page 99)

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Created by Mr.Lafferty Maths Dept

MTH 3-15a

MTH 3-15b

### Starter Questions

www.mathsrevision.com

Created by Mr.Lafferty Maths Dept

MTH 3-15a

MTH 3-15b

Level E Inequalities

### 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.

www.mathsrevision.com

Created by Mr.Lafferty Maths Dept

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”

Created by Mr.Lafferty Maths Dept

Check to see if correct !

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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Created by Mr.Lafferty Maths Dept

Check to see if correct !

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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Created by Mr.Lafferty Maths Dept

MTH 3-14a

MTH 3-15a

MTH 3-15b

Level E Inequalities

Now try Exercise 7

Ch8 (page 101)

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Created by Mr.Lafferty Maths Dept