Algebra MTH 3 14 a MTH 3 15
Algebra MTH 3 -14 a MTH 3 -15 b www. mathsrevision. com Tidying up terms Number Machine Working with Expressions Solving Simple Equations Solving Harder Equations Understanding Inequalities Solving Simple Inequalities 05 -Jun-21 Created by Mr. Lafferty Maths Dept
Starter Questions www. mathsrevision. com MTH 3 -14 a MTH 3 -15 b Q 1. Calculate Q 2. Convert 60% to fraction and simplify. Q 3. Convert Q 4. What is the time difference 09: 28 and 10: 50 Q 5. The answer to the question is 90. What is the question. 05 -Jun-21 to a percentage. Created by Mr. Lafferty Maths Dept
Aim of the Lesson www. mathsrevision. com MTH 3 -14 a MTH 3 -15 b Tidying Terms a+2 b+3 a+b 1. Tidying up expressions. 2. Show steps when tidying up. 05 -Jun-21 Created by Mr. Lafferty Maths Dept
Tidying Terms www. mathsrevision. com MTH 3 -14 a MTH 3 -15 b First Row : 2 c c 2 d + + + = 4 c = 7 c + + 2 nd Row : 05 -Jun-21 + + 2 d + Created by Mr. Lafferty Maths Dept = 3 d = 7 d
Tidying Terms www. mathsrevision. com MTH 3 -14 a MTH 3 -15 b + 3 rd Row : 3 f + = + 2 f = 6 f In Total we have 7 c + 7 d + 6 f CANNOT TIDY UP ANYMORE WE CAN ONLY TIDY UP “LIKE TERMS” 05 -Jun-21 Created by Mr. Lafferty Maths Dept
Tidying Terms MTH 3 -14 a MTH 3 -15 b www. mathsrevision. com WE CAN ONLY TIDY UP “LIKE TERMS” Tidy up the following: Q 1. 2 x + 4 x + 5 y -3 y + 18 = 6 x + 2 y + 18 Q 2. 4 a + 3 b + 5 a + 6 – b = 9 a + 2 b + 6 05 -Jun-21 Created by Mr. Lafferty Maths Dept
Tidying Terms www. mathsrevision. com MTH 3 -14 a MTH 3 -15 b Your turn ! Page 46 Exercise 1 Q 1 and Q 2 05 -Jun-21 Created by Mr. Lafferty Maths Dept
Starter Questions www. mathsrevision. com MTH 3 -14 a MTH 3 -15 b Q 1. Tidy up the expression Q 2. Calculate Q 3. Round to 1 decimal place. (a) Q 4. 05 -Jun-21 2. 34 (b) 10. 25 (c) 12. 5 % as a fraction Created by Mr. Lafferty Maths Dept 3. 23
Aim of the Lesson www. mathsrevision. com MTH 3 -14 a MTH 3 -15 b Number Machine 1. To build simple expressions. 2. To UNDO simple expressions. 05 -Jun-21 Created by Mr. Lafferty Maths Dept
Number Machine www. mathsrevision. com MTH 3 -14 a MTH 3 -15 b To build an expression from the number machine simply follow the rules given: 4 a 7 m 05 -Jun-21 Created by Mr. Lafferty Maths Dept
Number Machine www. mathsrevision. com MTH 3 -14 a MTH 3 -15 b To build an expression from the number machine simply follow the rules given: 20 3 b 05 -Jun-21 Created by Mr. Lafferty Maths Dept 23 3 b+9
Number Machine www. mathsrevision. com MTH 3 -14 a MTH 3 -15 b Your turn ! Page 93 Exercise 2 Q 1 05 -Jun-21 Created by Mr. Lafferty Maths Dept
Number Machine www. mathsrevision. com MTH 3 -14 a MTH 3 -15 b To UNDO the number machine simply do the opposite of the rules given: x 2 36 05 -Jun-21 UNDO 18 +8 Created by Mr. Lafferty Maths Dept UNDO
Number Machine www. mathsrevision. com MTH 3 -14 a MTH 3 -15 b To UNDO the number machine simply do the opposite of the rules given: x 4 20 05 -Jun-21 UNDO 5 -9 Created by Mr. Lafferty Maths Dept UNDO
Number Machine www. mathsrevision. com MTH 3 -14 a MTH 3 -15 b Your turn ! Page 93 Exercise 2 Q 3 and Q 4 05 -Jun-21 Created by Mr. Lafferty Maths Dept
Starter Questions www. mathsrevision. com MTH 3 -14 a MTH 3 -15 b 05 -Jun-21 Created by Mr. Lafferty Maths Dept
Substitution www. mathsrevision. com MTH 3 -14 a MTH 3 -15 b 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. 05 -Jun-21 Created by Mr. Lafferty Maths Dept
Substitution www. mathsrevision. com MTH 3 -14 a MTH 3 -15 b 1 If a = 3 and b = 9 evaluate a+b = 3+ 9 Sub in a=3 Sub in b=9 = 12 05 -Jun-21 Created by Mr. Lafferty Maths Dept
Substitution www. mathsrevision. com MTH 3 -14 a MTH 3 -15 b 2 If a = 3 and b = 9 evaluate ab axb = 3 x 9 05 -Jun-21 = 27 Remember ab means a x b Sub in a=3 Sub in b=9 Created by Mr. Lafferty Maths Dept
Substitution www. mathsrevision. com MTH 3 -14 a MTH 3 -15 b 3 If a = 3 and b = 9 evaluate 4 b 4 xb = 4 x 9 Remember 4 b means 4 x b Sub in b=9 = 36 05 -Jun-21 Created by Mr. Lafferty Maths Dept
Substitution www. mathsrevision. com MTH 3 -14 a MTH 3 -15 b If a = 5 and b = 6 evaluate 1. a + b =11 4. b - a =1 2. ab =30 5. 4 b =24 3. 3 a =15 6. 3 ab =90 05 -Jun-21 Created by Mr. Lafferty Maths Dept
www. mathsrevision. com MTH 3 -14 a MTH 3 -15 b Substitution 4 If a = 5 and b = 3 evaluate 2 a + 4 b = 2 xa + 4 xb = 2 x 5 + 4 x 3 = 10 = 22 05 -Jun-21 Remember 2 a means 2 x a Sub in a=5 Sub in b=3 + 12 Created by Mr. Lafferty Maths Dept
Substitution www. mathsrevision. com MTH 3 -14 a MTH 3 -15 b 5 If a = 5 and b = 3 evaluate a 2 = a x a = 5 x 5 = 25 05 -Jun-21 Remember a 2 means a x a Sub in a=5 Created by Mr. Lafferty Maths Dept
Substitution www. mathsrevision. com MTH 3 -14 a MTH 3 -15 b 6 If a = 15 and b = 3 evaluate a 15 = b 3 = 5 05 -Jun-21 Remember a means a ÷ b b Sub in a=15 Sub in b = 3 Created by Mr. Lafferty Maths Dept
Substitution www. mathsrevision. com MTH 3 -14 a MTH 3 -15 b If a = 2 and b = 6 evaluate 1) 4 a + 3 b =26 4) 5 b – 3 a =24 2) a 2 =4 5) 4 a 2 3) b 2 =36 6) b =3 a 05 -Jun-21 Created by Mr. Lafferty Maths Dept =16
Substitution www. mathsrevision. com MTH 3 -14 a MTH 3 -15 b Your turn ! Page 94 Exercise 3 05 -Jun-21 Created by Mr. Lafferty Maths Dept
Starter Questions www. mathsrevision. com MTH 3 -14 a MTH 3 -15 b 05 -Jun-21 Created by Mr. Lafferty Maths Dept
Equations www. mathsrevision. com MTH 3 -14 a MTH 3 -15 b Level E Solving Equations Learning Intention Success Criteria 1. To solve simple equations using the rule ‘change side change sign’. 1. Know rule ‘change side change sign’. 2. Solving simple algebraic equations. 05 -Jun-21 Created by Mr. Lafferty Maths Dept
Equations www. mathsrevision. com MTH 3 -14 a MTH 3 -15 b 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 : + x opposite is ÷ opposite is 05 -Jun-21 - opposite is + ÷ opposite is x Created by Mr. Lafferty Maths Dept
Equations www. mathsrevision. com MTH 3 -14 a MTH 3 -15 b Level E Solving Equations The rule “change side change sign” Examples Check to see if correct ! 05 -Jun-21 +8 opposite is -8 -5 opposite is +5 Check to see if correct ! Created by Mr. Lafferty Maths Dept
Equations www. mathsrevision. com MTH 3 -14 a MTH 3 -15 b Level E Solving Equations The rule “change side change sign” Examples Check to see if correct ! 05 -Jun-21 times by 8 opposite is divide by 8 times by 3 opposite is divide by 3 Check to see if correct ! Created by Mr. Lafferty Maths Dept
Equations www. mathsrevision. com MTH 3 -14 a MTH 3 -15 b Level E Solving Equations Now try Exercise 4 Ch 8 (page 96) 05 -Jun-21 Created by Mr. Lafferty Maths Dept
Starter Questions www. mathsrevision. com MTH 3 -14 a MTH 3 -15 b 05 -Jun-21 Created by Mr. Lafferty Maths Dept
Equations www. mathsrevision. com MTH 3 -14 a MTH 3 -15 b Level E Harder Equations Learning Intention Success Criteria 1. To solve harder equations using the rule ‘change side change sign’. repeatedly. 05 -Jun-21 1. Know rule ‘change side change sign’. 2. Solving harder algebraic equations by using rule repeatedly. Created by Mr. Lafferty Maths Dept
Equations www. mathsrevision. com MTH 3 -14 a MTH 3 -15 b 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 : + x opposite is ÷ opposite is 05 -Jun-21 - opposite is + ÷ opposite is x Created by Mr. Lafferty Maths Dept
Equations www. mathsrevision. com MTH 3 -14 a MTH 3 -15 b Level E Harder Equations The rule “change side change sign” Examples +1 opposite is -1 times by 2 opposite is divide by 2 Check to see if correct ! 05 -Jun-21 Created by Mr. Lafferty Maths Dept
Equations www. mathsrevision. com MTH 3 -14 a MTH 3 -15 b Level E Harder Equations The rule “change side change sign” Examples -6 opposite is +6 times by 4 opposite is divide by 4 Check to see if correct ! 05 -Jun-21 Created by Mr. Lafferty Maths Dept
Equations www. mathsrevision. com MTH 3 -14 a MTH 3 -15 b Level E Harder Equations Now try Exercise 5 Ch 8 (page 97) 05 -Jun-21 Created by Mr. Lafferty Maths Dept
Starter Questions www. mathsrevision. com MTH 3 -14 a MTH 3 -15 b 05 -Jun-21 Created by Mr. Lafferty Maths Dept
Inequalities www. mathsrevision. com MTH 3 -14 a MTH 3 -15 b Level E Solving Inequalities Learning Intention Success Criteria 1. To explain the various symbols for inequalities. 1. Know rule the 4 symbols for inequalities. 2. Solving simple inequalities equations. 05 -Jun-21 Created by Mr. Lafferty Maths Dept
Inequalities www. mathsrevision. com MTH 3 -14 a MTH 3 -15 b 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 : greater than or equal to less than or equal to 05 -Jun-21 Created by Mr. Lafferty Maths Dept
www. mathsrevision. com MTH 3 -14 a MTH 3 -15 b Inequalities Level E Solving Inequalities Arrow ALWAYS pointsmean. to the Examples : Write in words what each smallest number 5>3 -7 < -6 x≥ 2 y ≤ -5 05 -Jun-21 means 5 is greater than 3 means -7 is less than -6 means x can take the value 2 or greater means y can take the value -5 or less Created by Mr. Lafferty Maths Dept
Inequalities www. mathsrevision. com MTH 3 -14 a MTH 3 -15 b Level E Solving Inequalities Examples : Write out an inequality for the numbers (a) 14 and 6 14 > 6 (b) -2 and 1 -2 < 1 (c) -3 and -7 -3 > -7 (d) 34 and -35 05 -Jun-21 34 > -35 Created by Mr. Lafferty Maths Dept
Inequalities www. mathsrevision. com MTH 3 -14 a MTH 3 -15 b Level E Solving Inequalities Examples : Choosing from -3, -2, -1, 0 , 1, 2, 3 (a) y<0 -3, -2, -1 (b) y>2 3 (c) y ≤ -2 -3, -2 (d) y>3 05 -Jun-21 No solution Created by Mr. Lafferty Maths Dept
Inequalities www. mathsrevision. com MTH 3 -14 a MTH 3 -15 b Level E Solving Inequalities Now try Exercise 6 Ch 8 (page 99) 05 -Jun-21 Created by Mr. Lafferty Maths Dept
Starter Questions www. mathsrevision. com MTH 3 -14 a MTH 3 -15 b 05 -Jun-21 Created by Mr. Lafferty Maths Dept
Inequalities www. mathsrevision. com MTH 3 -14 a MTH 3 -15 b Level E Inequalities Learning Intention Success Criteria 1. To solve simple inequalities using the same rules as for equations ‘change side change sign’. 05 -Jun-21 1. Know rule ‘change side change sign’. 2. Solving simple inequalities equations. Created by Mr. Lafferty Maths Dept
Inequalities www. mathsrevision. com MTH 3 -14 a MTH 3 -15 b Level E Inequalities The Good News Same rule as solving equations The rule “change side change sign” 05 -Jun-21 Created by Mr. Lafferty Maths Dept
Inequalities www. mathsrevision. com MTH 3 -14 a MTH 3 -15 b Level E Solving Inequalities The rule “change side change sign” Examples Check to see if correct ! 05 -Jun-21 +10 opposite is -10 -9 opposite is +9 Check to see if correct ! Created by Mr. Lafferty Maths Dept
Inequalities www. mathsrevision. com MTH 3 -14 a MTH 3 -15 b Level E Solving Inequalities The rule “change side change sign” Examples times by 7 opposite is divide by 7 Check to see if correct ! 05 -Jun-21 times by 9 opposite is divide by 9 Check to see if correct ! Created by Mr. Lafferty Maths Dept
Inequalities www. mathsrevision. com MTH 3 -14 a MTH 3 -15 b Level E Inequalities Now try Exercise 7 Ch 8 (page 101) 05 -Jun-21 Created by Mr. Lafferty Maths Dept
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