3-jun-14created by mr.lafferty maths dept algebra tidying up terms number machine solving simple...
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10 Apr 202310 Apr 2023 Created by Mr.Lafferty Maths DeptCreated by Mr.Lafferty Maths Dept
AlgebraAlgebra
Tidying up terms
Number Machine
Solving Simple Equations
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Working with Expressions
Understanding Inequalities
Solving Harder Equations
Solving Simple Inequalities
MTH 3-14aMTH 3-15aMTH 3-15b
10 Apr 202310 Apr 2023 Created by Mr.Lafferty Maths DeptCreated by Mr.Lafferty Maths Dept
Starter QuestionsStarter Questionsw
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266 % of £ 270
3Q1. Calculate
Q2. Convert 60% to fraction and simplify.
Q3. Convert
Q4. What is the time difference 09:28 and 10:50
45
to a percentage.
Q5. The answer to the question is 90. What is thequestion.
MTH 3-14aMTH 3-15aMTH 3-15b
10 Apr 202310 Apr 2023 Created by Mr.Lafferty Maths DeptCreated by Mr.Lafferty Maths Dept
Aim of the LessonAim of the Lessonw
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1. Tidying up expressions.2. Show steps when tidying up.
a+2b+3a+b
Tidying Terms
MTH 3-14aMTH 3-15aMTH 3-15b
10 Apr 202310 Apr 2023 Created by Mr.Lafferty Maths DeptCreated by Mr.Lafferty Maths Deptww
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2c c 4c+ + = 7c
2nd Row : + + =
2d 2d 3d+ + = 7d
Tidying TermsMTH 3-14aMTH 3-15aMTH 3-15b
10 Apr 202310 Apr 2023 Created by Mr.Lafferty Maths DeptCreated by Mr.Lafferty Maths Deptww
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3f f 2f+ + = 6f
In Total we have
7c + 7d + 6f
CANNOTTIDY UP
ANYMORE
WE CAN ONLY TIDY UP “LIKE TERMS”
Tidying TermsMTH 3-14aMTH 3-15aMTH 3-15b
10 Apr 202310 Apr 2023 Created by Mr.Lafferty Maths DeptCreated by Mr.Lafferty Maths Dept
Tidying Termsw
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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
9a + 2b + 6
MTH 3-14aMTH 3-15aMTH 3-15b
10 Apr 202310 Apr 2023 Created by Mr.Lafferty Maths DeptCreated by Mr.Lafferty Maths Deptww
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Your turn !
Page 46 Exercise 1Q1 and Q2
Tidying TermsMTH 3-14aMTH 3-15aMTH 3-15b
10 Apr 202310 Apr 2023 Created by Mr.Lafferty Maths DeptCreated by Mr.Lafferty Maths Dept
Starter QuestionsStarter Questionsw
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Q2. Calculate
Q3. Round to 1 decimal place.
Q4. 12.5 % as a fraction
2 of 84
3
(a) 2.34 (b) 10.25(c) 3.23
MTH 3-14aMTH 3-15aMTH 3-15b
10 Apr 202310 Apr 2023 Created by Mr.Lafferty Maths DeptCreated by Mr.Lafferty Maths Dept
Aim of the LessonAim of the Lessonw
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1. To build simple expressions.2. To UNDO simple expressions.
Number MachineNumber Machine
MTH 3-14aMTH 3-15aMTH 3-15b
10 Apr 202310 Apr 2023 Created by Mr.Lafferty Maths DeptCreated by Mr.Lafferty Maths Deptww
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.com To build an expression from the number machine
simply follow the rules given:
aMultiply
By 44a+1Add 1
4a
7m7
MultiplyBy m
7m-2Subtract
2
Number MachineNumber MachineMTH 3-14aMTH 3-15aMTH 3-15b
10 Apr 202310 Apr 2023 Created by Mr.Lafferty Maths DeptCreated by Mr.Lafferty Maths Dept
3Multiple
by b?+9
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simply follow the rules given:
4Multiply
By 5?+3
2023
3b3b+9
Number MachineNumber MachineMTH 3-14aMTH 3-15aMTH 3-15b
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Your turn !
Page 93 Exercise 2Q1
Number MachineNumber MachineMTH 3-14aMTH 3-15aMTH 3-15b
10 Apr 202310 Apr 2023 Created by Mr.Lafferty Maths DeptCreated by Mr.Lafferty Maths Deptww
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simply do the opposite of the rules given:
?Divide by
210-8
UNDO+8
1836
UNDOx2
Number MachineNumber MachineMTH 3-14aMTH 3-15aMTH 3-15b
10 Apr 202310 Apr 2023 Created by Mr.Lafferty Maths DeptCreated by Mr.Lafferty Maths Dept
?Divide by
414+9
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simply do the opposite of the rules given:
UNDO-9
520
UNDOx4
Number MachineNumber MachineMTH 3-14aMTH 3-15aMTH 3-15b
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Your turn !
Page 93 Exercise 2Q3 and Q4
Number MachineNumber MachineMTH 3-14aMTH 3-15aMTH 3-15b
10 Apr 202310 Apr 2023 Created by Mr.Lafferty Maths DeptCreated by Mr.Lafferty Maths Dept
Starter QuestionsStarter Questionsw
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2. The ratio of apples to pears is 2:5.
I f there are 28 pieces of f ruit in total.
How many apples are there.
a a d a a d 1. Simplify
3. Find HCF of 8 and 18
MTH 3-14aMTH 3-15aMTH 3-15b
10 Apr 202310 Apr 2023 Created by Mr.Lafferty Maths DeptCreated by Mr.Lafferty Maths Deptww
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2.2. Solving expressions Solving expressions showing working.showing working.
1. To explain the process of working out expressions by substitution method.
1.1. Understand process of Understand process of substitution.substitution.
SubstitutionSubstitutionMTH 3-14aMTH 3-15aMTH 3-15b
10 Apr 202310 Apr 2023 Created by Mr.Lafferty Maths DeptCreated by Mr.Lafferty Maths Dept
1 If a = 3 and b = 9 evaluate
a + b
3 +9=
= 12
Sub in a=3Sub in b=9
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SubstitutionSubstitutionMTH 3-14aMTH 3-15aMTH 3-15b
10 Apr 202310 Apr 2023 Created by Mr.Lafferty Maths DeptCreated by Mr.Lafferty Maths Dept
If a = 3 and b = 9 evaluate
ab
Sub in a=3Sub in b=9
Remember ab means a x b
a x b
3 x 9=
= 27
2
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SubstitutionSubstitutionMTH 3-14aMTH 3-15aMTH 3-15b
10 Apr 202310 Apr 2023 Created by Mr.Lafferty Maths DeptCreated by Mr.Lafferty Maths Dept
3 If a = 3 and b = 9 evaluate
4b
Sub in b=9
Remember 4b means 4 x b
4 x b
4 x 9=
= 36
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SubstitutionSubstitutionMTH 3-14aMTH 3-15aMTH 3-15b
10 Apr 202310 Apr 2023 Created by Mr.Lafferty Maths DeptCreated by Mr.Lafferty Maths Dept
If a = 5 and b = 6 evaluate1. a + b2. ab
3. 3a
4. b - a
5. 4b
6. 3ab
=11=30=15
=1
=24=90w
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SubstitutionSubstitutionMTH 3-14aMTH 3-15aMTH 3-15b
10 Apr 202310 Apr 2023 Created by Mr.Lafferty Maths DeptCreated by Mr.Lafferty Maths Dept
If a = 5 and b = 3 evaluate2a +
4bSub in a=5Sub in b=3
Remember 2a means 2 x a
4
2xa + 4xb2x 5+4x3
=
=
= 10 + 12= 22
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SubstitutionSubstitutionMTH 3-14aMTH 3-15aMTH 3-15b
10 Apr 202310 Apr 2023 Created by Mr.Lafferty Maths DeptCreated by Mr.Lafferty Maths Dept
If a = 5 and b = 3 evaluatea
Sub in a=5
Remember a2 means a x a
5
a x a
5x 5
=
=
= 25
2
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SubstitutionSubstitutionMTH 3-14aMTH 3-15aMTH 3-15b
10 Apr 202310 Apr 2023 Created by Mr.Lafferty Maths DeptCreated by Mr.Lafferty Maths Dept
Remember a means a ÷ b b
If a = 15 and b = 3 evaluate
a
Sub in a=15
6
153
=
= 5
b
Sub in b = 3
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SubstitutionSubstitutionMTH 3-14aMTH 3-15aMTH 3-15b
10 Apr 202310 Apr 2023 Created by Mr.Lafferty Maths DeptCreated by Mr.Lafferty Maths Dept
If a = 2 and b = 6 evaluate1) 4a +
3b2) a2
3) b2
5) 4a2
4) 5b – 3a
6) ba
=26=4=36
=24=16
=3
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SubstitutionSubstitutionMTH 3-14aMTH 3-15aMTH 3-15b
10 Apr 202310 Apr 2023 Created by Mr.Lafferty Maths DeptCreated by Mr.Lafferty Maths Deptww
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Your turn !
Page 94 Exercise 3
SubstitutionSubstitutionMTH 3-14aMTH 3-15aMTH 3-15b
10 Apr 202310 Apr 2023 Created by Mr.Lafferty Maths DeptCreated by Mr.Lafferty Maths Dept
Starter QuestionsStarter Questionsw
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2. The ratio of apples to pears is 3:1.
I f there are 24 pieces of f ruit in total.
How many apples are there.
x x x x 1. Simplify
3. Find LCM of 6 qand 21
MTH 3-14aMTH 3-15aMTH 3-15b
10 Apr 202310 Apr 2023 Created by Mr.Lafferty Maths DeptCreated by Mr.Lafferty Maths Deptww
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2.2. Solving simple algebraic Solving simple algebraic equations.equations.
1. To solve simple equations using the rule ‘‘change side change change side change sign’.sign’.
1.1. Know ruleKnow rule‘‘change side change side
change sign’.change sign’.
EquationsEquationsLevel E Solving Equations
MTH 3-14aMTH 3-15aMTH 3-15b
10 Apr 202310 Apr 2023 Created by Mr.Lafferty Maths DeptCreated by Mr.Lafferty Maths Dept
The rule “change side change sign”
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EquationsEquations
Write down the opposite of the following :
+opposite is
x-÷opposite is
opposite is
opposite is- +÷ x
Level E Solving EquationsMTH 3-14aMTH 3-15aMTH 3-15b
10 Apr 202310 Apr 2023 Created by Mr.Lafferty Maths DeptCreated by Mr.Lafferty Maths Dept
The rule “change side change sign”
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5 11x
16x 11 5x 8 8x
8 8x
0x
Examples
EquationsEquations
-5 opposite
is +5
+8 opposite
is -8
Check to see if correct ! Check to see if correct !
Level E Solving EquationsMTH 3-14aMTH 3-15aMTH 3-15b
10 Apr 202310 Apr 2023 Created by Mr.Lafferty Maths DeptCreated by Mr.Lafferty Maths Dept
The rule “change side change sign”
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3 18y
6y
18
3y 72
8m 8 72m
9m
Examples
EquationsEquations
times by 3 opposite is divide by 3
times by 8 opposite is divide by 8
Check to see if correct ! Check to see if correct !
Level E Solving EquationsMTH 3-14aMTH 3-15aMTH 3-15b
10 Apr 202310 Apr 2023 Created by Mr.Lafferty Maths DeptCreated by Mr.Lafferty Maths Dept
Now try Exercise 4Ch8 (page 96)
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EquationsEquationsLevel E Solving Equations
MTH 3-14aMTH 3-15aMTH 3-15b
10 Apr 202310 Apr 2023 Created by Mr.Lafferty Maths DeptCreated by Mr.Lafferty Maths Dept
Starter QuestionsStarter Questionsw
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2. The ratio of apples to pears is 4:5.
I f there are 72 pieces of f ruit in total.
How many apples are there.
y x x x xy 1. Simplify
3. Find HCF of 15 and 21
MTH 3-14aMTH 3-15aMTH 3-15b
10 Apr 202310 Apr 2023 Created by Mr.Lafferty Maths DeptCreated by Mr.Lafferty Maths Deptww
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2.2. Solving harder algebraic Solving harder algebraic equations by using rule equations by using rule repeatedly.repeatedly.
1. To solve harder equations using the rule ‘‘change side change change side change sign’.sign’.repeatedly.repeatedly.
1.1. Know ruleKnow rule‘‘change side change side
change sign’.change sign’.
EquationsEquationsLevel E Harder Equations
MTH 3-14aMTH 3-15aMTH 3-15b
10 Apr 202310 Apr 2023 Created by Mr.Lafferty Maths DeptCreated by Mr.Lafferty Maths Dept
The rule “change side change sign”
ww
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.com The rule we use to solve equations is
EquationsEquations
Write down the opposite of the following :
+opposite is
x-÷opposite is
opposite is
opposite is- +÷ x
Level E Harder EquationsMTH 3-14aMTH 3-15aMTH 3-15b
10 Apr 202310 Apr 2023 Created by Mr.Lafferty Maths DeptCreated by Mr.Lafferty Maths Dept
The rule “change side change sign”
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2 1 11x
2 10x 2 11 1 10x
Examples
EquationsEquations
+1 opposite
is -1
Check to see if correct !
times by 2 opposite is divide by 2
105
2x
Level E Harder EquationsMTH 3-14aMTH 3-15aMTH 3-15b
10 Apr 202310 Apr 2023 Created by Mr.Lafferty Maths DeptCreated by Mr.Lafferty Maths Dept
The rule “change side change sign”
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4 6 30x
4 36x 4 30 6 36x
Examples
EquationsEquations
-6 opposite
is +6
Check to see if correct !
times by 4 opposite is divide by 4
369
4x
Level E Harder EquationsMTH 3-14aMTH 3-15aMTH 3-15b
10 Apr 202310 Apr 2023 Created by Mr.Lafferty Maths DeptCreated by Mr.Lafferty Maths Dept
Now try Exercise 5Ch8 (page 97)
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EquationsEquationsLevel E Harder Equations
MTH 3-14aMTH 3-15aMTH 3-15b
10 Apr 202310 Apr 2023 Created by Mr.Lafferty Maths DeptCreated by Mr.Lafferty Maths Dept
Starter QuestionsStarter Questionsw
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2. The ratio of apples to pears is 6:7.
I f there are 52 pieces of f ruit in total.
How many apples are there.
a a b b ab 1. Simplify
3. Find LCM of 4 qand 7
MTH 3-14aMTH 3-15aMTH 3-15b
10 Apr 202310 Apr 2023 Created by Mr.Lafferty Maths DeptCreated by Mr.Lafferty Maths Deptww
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2.2. Solving simple Solving simple inequalities equations.inequalities equations.
1. To explain the various symbols for inequalities.
Level E Solving Inequalities
1.1. Know rule the 4 symbols Know rule the 4 symbols forforinequalities.inequalities.
InequalitiesInequalitiesMTH 3-14aMTH 3-15aMTH 3-15b
10 Apr 202310 Apr 2023 Created by Mr.Lafferty Maths DeptCreated by Mr.Lafferty Maths Deptww
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Level E Solving Inequations
The equations you were solving were called equations because they contained an “=“ sign.
InequalitiesInequalities
greater than
less than
greater than or equal to
less than or equal to
There are 4 other Mathematical symbolsThey are called inequalities :
MTH 3-14aMTH 3-15aMTH 3-15b
10 Apr 202310 Apr 2023 Created by Mr.Lafferty Maths DeptCreated by Mr.Lafferty Maths Deptww
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Level E Solving Inequalities
InequalitiesInequalities
Examples : Write in words what each mean.
5 > 3
-7 < -6
y ≤ -5
x ≥ 2
means 5 is greater than 3
means -7 is less than -6
means x can take the value2 or greatermeans y can take the value-5 or less
Arrow ALWAYS points to the
smallest number
MTH 3-14aMTH 3-15aMTH 3-15b
10 Apr 202310 Apr 2023 Created by Mr.Lafferty Maths DeptCreated by Mr.Lafferty Maths Deptww
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Level E Solving Inequalities
Examples : Write out an inequality for the numbers
InequalitiesInequalities
(a) 14 and 6
(b) -2 and 1
(c) -3 and -7
(d) 34 and -35
14 > 6
-2 < 1
-3 > -7
34 > -35
MTH 3-14aMTH 3-15aMTH 3-15b
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Level E Solving Inequalities
Examples : Choosing from -3, -2, -1, 0 , 1, 2, 3
InequalitiesInequalities
(a) y < 0
(b) y > 2
(c) y ≤ -2
(d) y > 3
-3, -2, -1
3
-3, -2
No solution
MTH 3-14aMTH 3-15aMTH 3-15b
10 Apr 202310 Apr 2023 Created by Mr.Lafferty Maths DeptCreated by Mr.Lafferty Maths Dept
Now try Exercise 6Ch8 (page 99)
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InequalitiesInequalitiesLevel E Solving Inequalities
MTH 3-14aMTH 3-15aMTH 3-15b
10 Apr 202310 Apr 2023 Created by Mr.Lafferty Maths DeptCreated by Mr.Lafferty Maths Dept
Starter QuestionsStarter Questionsw
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2. The ratio of apples to pears is 5:14.
I f there are 57 pieces of f ruit in total.
How many pears are there.
y y y y y 1. Simplify
3. Find LCM of 6 and 10
MTH 3-14aMTH 3-15aMTH 3-15b
10 Apr 202310 Apr 2023 Created by Mr.Lafferty Maths DeptCreated by Mr.Lafferty Maths Deptww
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.com Learning IntentionLearning Intention Success CriteriaSuccess Criteria
2.2. Solving simple Solving simple inequalities equations.inequalities equations.
1. To solve simple inequalities using the same rules as for equations ‘‘change side change change side change sign’.sign’.
Level E Inequalities
1.1. Know ruleKnow rule‘‘change side change side
change sign’.change sign’.
InequalitiesInequalitiesMTH 3-14aMTH 3-15aMTH 3-15b
10 Apr 202310 Apr 2023 Created by Mr.Lafferty Maths DeptCreated by Mr.Lafferty Maths Deptww
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Level E Inequalities
InequalitiesInequalities
The Good News
Same rule as solving equations
The rule “change side change sign”
MTH 3-14aMTH 3-15aMTH 3-15b
10 Apr 202310 Apr 2023 Created by Mr.Lafferty Maths DeptCreated by Mr.Lafferty Maths Dept
The rule “change side change sign”
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9 16x
25x 16 9x 19 10x
10 19x
9x
Examples
InequalitiesInequalities
-9 opposite
is +9
+10 opposite
is -10
Check to see if correct ! Check to see if correct !
Level E Solving InequalitiesMTH 3-14aMTH 3-15aMTH 3-15b
10 Apr 202310 Apr 2023 Created by Mr.Lafferty Maths DeptCreated by Mr.Lafferty Maths Dept
The rule “change side change sign”
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7 35y
5y
35
7y 36
9m
9 36m
4m
Examples
InequalitiesInequalities
times by 7 opposite is divide by 7
times by 9 opposite is divide by 9
Check to see if correct ! Check to see if correct !
Level E Solving InequalitiesMTH 3-14aMTH 3-15aMTH 3-15b
10 Apr 202310 Apr 2023 Created by Mr.Lafferty Maths DeptCreated by Mr.Lafferty Maths Dept
Now try Exercise 7Ch8 (page 101)
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Level E Inequalities
InequalitiesInequalitiesMTH 3-14aMTH 3-15aMTH 3-15b