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Created by Mr.Lafferty Maths Dept Algebra MTH 3-14a MTH 3-15a MTH 3-15b Tidying up terms Number Machine Working with Expressions Solving Simple Equations www.mathsrevision.com Solving Harder Equations Understanding Inequalities Solving Simple Inequalities 1-Apr-17 Created by Mr.Lafferty Maths Dept

Created by Mr.Lafferty Maths Dept Starter Questions MTH 3-14a MTH 3-15a MTH 3-15b Q1. Calculate Q2. Convert 60% to fraction and simplify. Q3. Convert to a percentage. www.mathsrevision.com Q4. What is the time difference 09:28 and 10:50 Q5. The answer to the question is 90. What is the question. 1-Apr-17 Created by Mr.Lafferty Maths Dept

Created by Mr.Lafferty Maths Dept Aim of the Lesson MTH 3-14a MTH 3-15a MTH 3-15b Tidying Terms a+2b+3a+b Tidying up expressions. Show steps when tidying up. www.mathsrevision.com 1-Apr-17 Created by Mr.Lafferty Maths Dept

Created by Mr.Lafferty Maths Dept Tidying Terms MTH 3-14a MTH 3-15a MTH 3-15b + + = First Row : + + 2c c 4c = 7c www.mathsrevision.com + + = 2nd Row : + + 2d 2d 3d = 7d 1-Apr-17 Created by Mr.Lafferty Maths Dept

Created by Mr.Lafferty Maths Dept Tidying Terms MTH 3-14a MTH 3-15a MTH 3-15b + + = 3rd Row : + + 3f f 2f = 6f CANNOT TIDY UP ANYMORE www.mathsrevision.com In Total we have 7c + 7d + 6f WE CAN ONLY TIDY UP “LIKE TERMS” 1-Apr-17 Created by Mr.Lafferty Maths Dept

Created by Mr.Lafferty Maths Dept 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 www.mathsrevision.com 9a + 2b + 6 1-Apr-17 Created by Mr.Lafferty Maths Dept

Created by Mr.Lafferty Maths Dept Tidying Terms MTH 3-14a MTH 3-15a MTH 3-15b Your turn ! Page 46 Exercise 1 Q1 and Q2 www.mathsrevision.com 1-Apr-17 Created by Mr.Lafferty Maths Dept

Created by Mr.Lafferty Maths Dept Starter Questions MTH 3-14a MTH 3-15a MTH 3-15b Q1. Tidy up the expression Q2. Calculate Q3. Round to 1 decimal place. www.mathsrevision.com (a) 2.34 (b) 10.25 (c) 3.23 Q4. 12.5 % as a fraction 1-Apr-17 Created by Mr.Lafferty Maths Dept

Created by Mr.Lafferty Maths Dept Aim of the Lesson MTH 3-14a MTH 3-15a MTH 3-15b Number Machine To build simple expressions. To UNDO simple expressions. www.mathsrevision.com 1-Apr-17 Created by Mr.Lafferty Maths Dept

Number Machine 4a 7m www.mathsrevision.com MTH 3-14a MTH 3-15a MTH 3-15b To build an expression from the number machine simply follow the rules given: 4a www.mathsrevision.com 7m 1-Apr-17 Created by Mr.Lafferty Maths Dept

Number Machine 20 www.mathsrevision.com 23 3b MTH 3-14a MTH 3-15a MTH 3-15b To build an expression from the number machine simply follow the rules given: 20 23 www.mathsrevision.com 3b 3b+9 1-Apr-17 Created by Mr.Lafferty Maths Dept

Created by Mr.Lafferty Maths Dept Number Machine MTH 3-14a MTH 3-15a MTH 3-15b Your turn ! Page 93 Exercise 2 Q1 www.mathsrevision.com 1-Apr-17 Created by Mr.Lafferty Maths Dept

Number Machine www.mathsrevision.com 18 36 To UNDO the number machine MTH 3-14a MTH 3-15a MTH 3-15b To UNDO the number machine simply do the opposite of the rules given: x2 UNDO +8 UNDO 18 36 www.mathsrevision.com 1-Apr-17 Created by Mr.Lafferty Maths Dept

Number Machine www.mathsrevision.com 5 20 To UNDO the number machine MTH 3-14a MTH 3-15a MTH 3-15b To UNDO the number machine simply do the opposite of the rules given: x4 UNDO -9 UNDO 5 www.mathsrevision.com 20 1-Apr-17 Created by Mr.Lafferty Maths Dept

Created by Mr.Lafferty Maths Dept Number Machine MTH 3-14a MTH 3-15a MTH 3-15b Your turn ! Page 93 Exercise 2 Q3 and Q4 www.mathsrevision.com 1-Apr-17 Created by Mr.Lafferty Maths Dept

Created by Mr.Lafferty Maths Dept Starter Questions MTH 3-14a MTH 3-15a MTH 3-15b www.mathsrevision.com 1-Apr-17 Created by Mr.Lafferty Maths Dept

Created by Mr.Lafferty Maths Dept 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 1-Apr-17 Created by Mr.Lafferty Maths Dept

Created by Mr.Lafferty Maths Dept Substitution MTH 3-14a MTH 3-15a MTH 3-15b 1 If a = 3 and b = 9 evaluate a + b www.mathsrevision.com Sub in a=3 = 3 + 9 Sub in b=9 = 12 1-Apr-17 Created by Mr.Lafferty Maths Dept

Created by Mr.Lafferty Maths Dept Substitution MTH 3-14a MTH 3-15a MTH 3-15b 2 If a = 3 and b = 9 evaluate ab a x b www.mathsrevision.com Remember ab means a x b Sub in a=3 = 3 x 9 Sub in b=9 = 27 1-Apr-17 Created by Mr.Lafferty Maths Dept

Created by Mr.Lafferty Maths Dept 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 www.mathsrevision.com = 4 x 9 Sub in b=9 = 36 1-Apr-17 Created by Mr.Lafferty Maths Dept

Created by Mr.Lafferty Maths Dept 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 www.mathsrevision.com 3. 3a =15 6. 3ab =90 1-Apr-17 Created by Mr.Lafferty Maths Dept

Created by Mr.Lafferty Maths Dept Substitution MTH 3-14a MTH 3-15a MTH 3-15b 4 If a = 5 and b = 3 evaluate 2a + 4b 2xa + 4xb = Remember 2a means 2 x a Sub in a=5 4x 3 www.mathsrevision.com = 2x 5 + Sub in b=3 = 10 12 + = 22 1-Apr-17 Created by Mr.Lafferty Maths Dept

Created by Mr.Lafferty Maths Dept 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 www.mathsrevision.com Sub in a=5 = 5 x 5 = 25 1-Apr-17 Created by Mr.Lafferty Maths Dept

Created by Mr.Lafferty Maths Dept Substitution MTH 3-14a MTH 3-15a MTH 3-15b 6 If a = 15 and b = 3 evaluate a 15 Remember a means a ÷ b b = b 3 www.mathsrevision.com Sub in a=15 = 5 Sub in b = 3 1-Apr-17 Created by Mr.Lafferty Maths Dept

Created by Mr.Lafferty Maths Dept 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 www.mathsrevision.com 3) b2 =36 6) b a =3 1-Apr-17 Created by Mr.Lafferty Maths Dept

Created by Mr.Lafferty Maths Dept Substitution MTH 3-14a MTH 3-15a MTH 3-15b Your turn ! Page 94 Exercise 3 www.mathsrevision.com 1-Apr-17 Created by Mr.Lafferty Maths Dept

Created by Mr.Lafferty Maths Dept Starter Questions MTH 3-14a MTH 3-15a MTH 3-15b www.mathsrevision.com 1-Apr-17 Created by Mr.Lafferty Maths Dept

Created by Mr.Lafferty Maths Dept 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. www.mathsrevision.com 1-Apr-17 Created by Mr.Lafferty Maths Dept

Created by Mr.Lafferty Maths Dept 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 : + + - - www.mathsrevision.com opposite is opposite is x x ÷ ÷ opposite is opposite is 1-Apr-17 Created by Mr.Lafferty Maths Dept

Created by Mr.Lafferty Maths Dept 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 www.mathsrevision.com Check to see if correct ! Check to see if correct ! 1-Apr-17 Created by Mr.Lafferty Maths Dept

The rule “change side change sign” 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 www.mathsrevision.com Check to see if correct ! Check to see if correct ! 1-Apr-17 Created by Mr.Lafferty Maths Dept

Created by Mr.Lafferty Maths Dept Equations MTH 3-14a MTH 3-15a MTH 3-15b Level E Solving Equations Now try Exercise 4 Ch8 (page 96) www.mathsrevision.com 1-Apr-17 Created by Mr.Lafferty Maths Dept

Created by Mr.Lafferty Maths Dept Starter Questions MTH 3-14a MTH 3-15a MTH 3-15b www.mathsrevision.com 1-Apr-17 Created by Mr.Lafferty Maths Dept

Created by Mr.Lafferty Maths Dept 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. www.mathsrevision.com 1-Apr-17 Created by Mr.Lafferty Maths Dept

Created by Mr.Lafferty Maths Dept 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 1-Apr-17 Created by Mr.Lafferty Maths Dept

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 Check to see if correct ! times by 2 opposite is divide by 2 www.mathsrevision.com 1-Apr-17 Created by Mr.Lafferty Maths Dept

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 Check to see if correct ! times by 4 opposite is divide by 4 www.mathsrevision.com 1-Apr-17 Created by Mr.Lafferty Maths Dept

Created by Mr.Lafferty Maths Dept Equations MTH 3-14a MTH 3-15a MTH 3-15b Level E Harder Equations Now try Exercise 5 Ch8 (page 97) www.mathsrevision.com 1-Apr-17 Created by Mr.Lafferty Maths Dept

Created by Mr.Lafferty Maths Dept Starter Questions MTH 3-14a MTH 3-15a MTH 3-15b www.mathsrevision.com 1-Apr-17 Created by Mr.Lafferty Maths Dept

Created by Mr.Lafferty Maths Dept Inequalities MTH 3-14a MTH 3-15a MTH 3-15b Level E Solving 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 1-Apr-17 Created by Mr.Lafferty Maths Dept

Created by Mr.Lafferty Maths Dept 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 : www.mathsrevision.com greater than greater than or equal to less than less than or equal to 1-Apr-17 Created by Mr.Lafferty Maths Dept

x ≥ 2 Inequalities 5 > 3 -7 < -6 y ≤ -5 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 www.mathsrevision.com y ≤ -5 means y can take the value -5 or less 1-Apr-17 Created by Mr.Lafferty Maths Dept

Created by Mr.Lafferty Maths Dept 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 www.mathsrevision.com (c) -3 and -7 -3 > -7 (d) 34 and -35 34 > -35 1-Apr-17 Created by Mr.Lafferty Maths Dept

Created by Mr.Lafferty Maths Dept 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 www.mathsrevision.com (c) y ≤ -2 -3, -2 (d) y > 3 No solution 1-Apr-17 Created by Mr.Lafferty Maths Dept

Created by Mr.Lafferty Maths Dept Inequalities MTH 3-14a MTH 3-15a MTH 3-15b Level E Solving Inequalities Now try Exercise 6 Ch8 (page 99) www.mathsrevision.com 1-Apr-17 Created by Mr.Lafferty Maths Dept

Created by Mr.Lafferty Maths Dept Starter Questions MTH 3-14a MTH 3-15a MTH 3-15b www.mathsrevision.com 1-Apr-17 Created by Mr.Lafferty Maths Dept

Created by Mr.Lafferty Maths Dept 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. www.mathsrevision.com 1-Apr-17 Created by Mr.Lafferty Maths Dept

Created by Mr.Lafferty Maths Dept Inequalities MTH 3-14a MTH 3-15a MTH 3-15b Level E Inequalities The Good News Same rule as solving equations www.mathsrevision.com The rule “change side change sign” 1-Apr-17 Created by Mr.Lafferty Maths Dept

Created by Mr.Lafferty Maths Dept 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 Check to see if correct ! Check to see if correct ! 1-Apr-17 Created by Mr.Lafferty Maths Dept

The rule “change side change sign” 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 www.mathsrevision.com Check to see if correct ! Check to see if correct ! 1-Apr-17 Created by Mr.Lafferty Maths Dept

Created by Mr.Lafferty Maths Dept Inequalities MTH 3-14a MTH 3-15a MTH 3-15b Level E Inequalities Now try Exercise 7 Ch8 (page 101) www.mathsrevision.com 1-Apr-17 Created by Mr.Lafferty Maths Dept

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