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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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Algebra l.jpg

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

Created by Mr.Lafferty Maths Dept


Starter questions l.jpg

MTH 3-14a

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


Aim of the lesson l.jpg

MTH 3-14a

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


Slide4 l.jpg

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

Created by Mr.Lafferty Maths Dept


Slide5 l.jpg

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”

Created by Mr.Lafferty Maths Dept


Slide6 l.jpg

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

Created by Mr.Lafferty Maths Dept


Slide7 l.jpg

Tidying Terms

MTH 3-14a

MTH 3-15a

MTH 3-15b

Your turn !

Page 46 Exercise 1

Q1 and Q2

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Created by Mr.Lafferty Maths Dept


Starter questions8 l.jpg

MTH 3-14a

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


Aim of the lesson9 l.jpg

MTH 3-14a

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


Slide10 l.jpg

4a

7m

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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Created by Mr.Lafferty Maths Dept


Slide11 l.jpg

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

3b+9

Created by Mr.Lafferty Maths Dept


Slide12 l.jpg

Number Machine

MTH 3-14a

MTH 3-15a

MTH 3-15b

Your turn !

Page 93 Exercise 2

Q1

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Created by Mr.Lafferty Maths Dept


Slide13 l.jpg

UNDO

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


Slide14 l.jpg

UNDO

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


Slide15 l.jpg

Number Machine

MTH 3-14a

MTH 3-15a

MTH 3-15b

Your turn !

Page 93 Exercise 2

Q3 and Q4

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Created by Mr.Lafferty Maths Dept


Starter questions16 l.jpg

MTH 3-14a

MTH 3-15a

MTH 3-15b

Starter Questions

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Created by Mr.Lafferty Maths Dept


Slide17 l.jpg

Substitution

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.

www.mathsrevision.com

Created by Mr.Lafferty Maths Dept


Slide18 l.jpg

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 a=3

=

3

+

9

Sub in b=9

=

12

Created by Mr.Lafferty Maths Dept


Slide19 l.jpg

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 a=3

=

3

x

9

Sub in b=9

=

27

Created by Mr.Lafferty Maths Dept


Slide20 l.jpg

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 b=9

=

36

Created by Mr.Lafferty Maths Dept


Slide21 l.jpg

Substitution

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


Slide22 l.jpg

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 a=5

4x

3

=

2x

5

+

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Sub in b=3

=

10

12

+

=

22

Created by Mr.Lafferty Maths Dept


Slide23 l.jpg

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 a=5

=

5

x

5

=

25

Created by Mr.Lafferty Maths Dept


Slide24 l.jpg

Remember a means a ÷ b

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


Slide25 l.jpg

6) b

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


Slide26 l.jpg

Substitution

MTH 3-14a

MTH 3-15a

MTH 3-15b

Your turn !

Page 94 Exercise 3

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Created by Mr.Lafferty Maths Dept


Starter questions27 l.jpg

MTH 3-14a

MTH 3-15a

MTH 3-15b

Starter Questions

www.mathsrevision.com

Created by Mr.Lafferty Maths Dept


Equations l.jpg

MTH 3-14a

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


Slide29 l.jpg

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

Created by Mr.Lafferty Maths Dept


Slide30 l.jpg

Check to see if correct !

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


Slide31 l.jpg

Check to see if correct !

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


Slide32 l.jpg

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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Created by Mr.Lafferty Maths Dept


Starter questions33 l.jpg

MTH 3-14a

MTH 3-15a

MTH 3-15b

Starter Questions

www.mathsrevision.com

Created by Mr.Lafferty Maths Dept


Equations34 l.jpg

MTH 3-14a

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


Slide35 l.jpg

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 :

+

+

-

-

www.mathsrevision.com

opposite is

opposite is

x

x

÷

÷

opposite is

opposite is

Created by Mr.Lafferty Maths Dept


Slide36 l.jpg

Check to see if correct !

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


Slide37 l.jpg

Check to see if correct !

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


Slide38 l.jpg

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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Created by Mr.Lafferty Maths Dept


Starter questions39 l.jpg

MTH 3-14a

MTH 3-15a

MTH 3-15b

Starter Questions

www.mathsrevision.com

Created by Mr.Lafferty Maths Dept


Inequalities l.jpg

MTH 3-14a

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


Slide41 l.jpg

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

Created by Mr.Lafferty Maths Dept


Slide42 l.jpg

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 > 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


Slide43 l.jpg

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 > 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


Slide44 l.jpg

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 < 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


Slide45 l.jpg

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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Created by Mr.Lafferty Maths Dept


Starter questions46 l.jpg

MTH 3-14a

MTH 3-15a

MTH 3-15b

Starter Questions

www.mathsrevision.com

Created by Mr.Lafferty Maths Dept


Inequalities47 l.jpg

MTH 3-14a

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


Slide48 l.jpg

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”

Created by Mr.Lafferty Maths Dept


Slide49 l.jpg

Check to see if correct !

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

www.mathsrevision.com

Created by Mr.Lafferty Maths Dept


Slide50 l.jpg

Check to see if correct !

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


Slide51 l.jpg

Inequalities

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


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