1. 9-Jun-15Created by Mr. Lafferty Maths Dept. Tidying Up Terms Multiplying Terms Algebra www.mathsrevision.com Solving Simple Equations ( x+1=5 ) Removing Brackets & Simplifying Harder Equations ( 2x+1=9 ) Solving Equations ( brackets) Solving Equations (terms either side) Inequalities National 4

2. 9-Jun-15Created by Mr. Lafferty Maths Dept. Starter Questions Starter Questions www.mathsrevision.com 6cm 2cm 3cm National 4 EF 1.1c

3. 9-Jun-15Created by Mr. Lafferty Maths Dept. www.mathsrevision.com Learning Intention Success Criteria 1.Understand the term ‘like terms’. 1. To explain how to gather ‘algebraic like terms’. Algebra 2. Gather like terms for simple expressions. expressions. Multiplying Terms National 4 EF 1.1c

4. 9-Jun-15Created by Mr.Lafferty Maths Dept www.mathsrevision.com First Row : + + = 2cc4c ++ = 7c 2nd Row : + + = 2d 3d ++ = 7d Tidying Terms National 4 EF 1.1c

5. 9-Jun-15Created by Mr.Lafferty Maths Dept www.mathsrevision.com 3rd Row : + + = 3ff2f ++ = 6f In Total we have 7c + 7d + 6f CANNOT TIDY UP ANYMORE WE CAN ONLY TIDY UP “LIKE TERMS” Tidying Terms National 4 EF 1.1c

6. 9-Jun-15Created by Mr.Lafferty Maths Dept Tidying Terms www.mathsrevision.com 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 National 4 EF 1.1c

7. 9-Jun-15Created by Mr. Lafferty Maths Dept. Now try Exercise 1 Ch7 (page 85) www.mathsrevision.com Algebra Simplifying Algebraic Expressions National 4 EF 1.1c

8. 9-Jun-15Created by Mr. Lafferty Maths Dept. Starter Questions Starter Questions www.mathsrevision.com 4d 5d 120 o 40 o National 4 EF 1.1c

9. 9-Jun-15Created by Mr. Lafferty Maths Dept. www.mathsrevision.com Learning Intention Success Criteria 1.Understand the key steps of multiplying terms. 1. To explain how to multiply out algebraic terms. Algebra 2. Apply multiplication rules for simple expressions. Multiplying Terms National 4 EF 1.1c

10. 9-Jun-15Created by Mr. Lafferty Maths Dept. www.mathsrevision.com Algebra Simplifying Algebraic Expressions Reminder ! We can only add and subtract “ like terms “ National 4 EF 1.1c

11. 9-Jun-15Created by Mr. Lafferty Maths Dept. www.mathsrevision.com Algebra Simplifying Algebraic Expressions Reminder ! Multiplying terms ( NOT 2b ) ( NOT 8m ) National 4 EF 1.1c

12. 9-Jun-15Created by Mr. Lafferty Maths Dept. Now try Exercise 2 Ch7 (page 86) www.mathsrevision.com Algebra Simplifying Algebraic Expressions National 4 EF 1.1c

13. 9-Jun-15Created by Mr. Lafferty Maths Dept. Starter Questions Starter Questions www.mathsrevision.com 6h 2a 100 o 60 o National 4 EF 1.1a

14. 9-Jun-15Created by Mr. Lafferty Maths Dept. www.mathsrevision.com Learning Intention Success Criteria 1.Understand the key steps in removing brackets. 1. To explain how to multiply out simply algebraic brackets. Algebra 2. Apply multiplication rules for integers numbers when removing brackets. Removing brackets National 4 EF 1.1a

15. 3(b + 5) =3b + 15 Example 1 4(w - 2) =4w - 8 Example 2 9-Jun-15Created by Mr. Lafferty@mathsrevision.com Removing a Single Bracket www.mathsrevision.com National 4 EF 1.1a

16. 2(y - 1) =2y - 2 Example 3 7(w - 6) =7w - 42 Example 4 9-Jun-15Created by Mr. Lafferty@mathsrevision.com Removing a Single Bracket www.mathsrevision.com National 4 EF 1.1a

17. 8(x + 3) =8x + 24 Example 5 4(3 -2m) =12 - 8m Example 6 9-Jun-15Created by Mr. Lafferty@mathsrevision.com Removing a Single Bracket www.mathsrevision.com National 4 EF 1.1a

18. 7 + 3(4 - y) =7 + 12 Example 7 9 - 3(8 - y) =9 - 24 Example 8 9-Jun-15Created by Mr. Lafferty@mathsrevision.com Removing a Single Bracket - 3y = 19 - 3y Tidy Up + 3y Tidy Up = -15 + 3y www.mathsrevision.com National 4 EF 1.1a

19. 4(m - 3) - (m + 2) =4m - 12 - m - 2 Example 9 Example 10 9-Jun-15Created by Mr. Lafferty@mathsrevision.com = 3m - 14 Tidy Up 7(y - 1) - 2(y + 4) =7y - 7 - 2y - 8 = 5y - 15 Tidy Up Removing Two Single Brackets www.mathsrevision.com National 4 EF 1.1a

20. 9-Jun-15Created by Mr. Lafferty Maths Dept. Now try Exercise 3 Ch7 (page 86) www.mathsrevision.com Algebra Removing brackets National 4 EF 1.1a

21. 9-Jun-15Created by Mr.Lafferty Maths Dept Starter Questions Starter Questions www.mathsrevision.com National 4 REL 1.1b

22. 9-Jun-15Created by Mr.Lafferty Maths Dept www.mathsrevision.com Learning Intention Success Criteria 2.Solving simple algebraic equations. 1.To solve simple equations using the ‘Balancing Method’. 1.Know the process of the ‘Balancing Method’. Equations Solving Equations National 4 REL 1.1b

23. 9-Jun-15 Created by Mr Lafferty Maths Dept Balancing Method www.mathsrevision.com 4 44 4 Kirsty goes to the shops every week to buy some potatoes. She always buys the same total weight. One week she buys 2 large bags and 1 small bag. The following week she buys 1 large bag and 3 small bags. If a small bags weighs 4 kgs. How much does a large bag weigh? What instrument measures balance How can we go about solving this using balance ? National 4 REL 1.1b

24. 9-Jun-15 Created by Mr Lafferty Maths Dept Balancing Method www.mathsrevision.com 4 44 4 Take a small bag away from each side. Take a big bag away from each side. We can see that a big bag is equal to 4 + 4 =8 kg National 4 REL 1.1b

25. 9-Jun-15 Created by Mr Lafferty Maths Dept Balancing Method www.mathsrevision.com PP 4 P 44 4 Let’s solve it using maths. Let P be the weight of a big bag. We know that a small bag = 4 2P + 4P + 12 What symbol should we use for the scales ? = Subtract 4 from each side -4 2P=P + 8 Subtract P from each side -P P=8 National 4 REL 1.1b

26. 9-Jun-15 Created by Mr Lafferty Maths Dept Balancing Method www.mathsrevision.com It would be far too time consuming to draw out the balancing scales each time. We will now learn how to use the rules for solving equations. National 4 REL 1.1b

27. 9-Jun-15Created by Mr.Lafferty Maths Dept The Balancing Method www.mathsrevision.com The method we use to solve equations is Equations Write down the opposite of the following : + opposite is x - ÷ - + ÷ x Solving Equations National 4 REL 1.1b

28. x + 3 = 20 Example 1 9-Jun-15Created by Mr. Lafferty@mathsrevision.com x = 20 - 3 17 (- 3) Simple Equations www.mathsrevision.com National 4 REL 1.1b

29. 24 – 8 = 24 - x = 8 Example 2 9-Jun-15Created by Mr. Lafferty@mathsrevision.com 24 = 8 + x x (+ x) Simple Equations (- 8) 16 = x x = 16 www.mathsrevision.com National 4 REL 1.1b

30. 4x = 20 Example 3 9-Jun-15Created by Mr. Lafferty@mathsrevision.com x = 20 ÷ 4 5 (÷ 4) Simple Equations www.mathsrevision.com National 4 REL 1.1b

31. 8x = 28 Example 4 9-Jun-15Created by Mr. Lafferty@mathsrevision.com x = 20 ÷ 8 3.5 (÷ 8) Simple Equations www.mathsrevision.com National 4 REL 1.1b

32. 9-Jun-15Created by Mr.Lafferty Maths Dept Now try Exercise 4 Ch7 (page 87) www.mathsrevision.com Simple Equations National 4 REL 1.1b

33. 9-Jun-15 Starter Questions www.mathsrevision.com Q1.Solve for x 2x + 3 = 15 Q2.14% of 700 Created by Mr. Lafferty@mathsrevision.com National 4 REL 1.1b

34. 9-Jun-15Created by Mr.Lafferty Maths Dept www.mathsrevision.com Learning Intention Success Criteria 2.Solving harder algebraic equations by using rule repeatedly. 1.To solve harder equations using the rule ‘Balancing Method’. repeatedly. 1.Know the process of ‘Balancing Method’. Equations Harder Equations National 4 REL 1.1b

35. 9-Jun-15 Created by Mr Lafferty Maths Dept Balancing Method www.mathsrevision.com Group of 5 adults and 3 children go to the local swimming. Another group of 3 adults and 8 children also go swimming. The total cost for each group is the same. A child’s ticket costs £2. If a child’s ticket costs £2. How much for an adult ticket ? aa2 a 2 a a 2 Let a be the price of an adult ticket. We know that a child price = £2 2 aa 2a 2 22 2 22 National 4 REL 1.1b

36. 9-Jun-15 Created by Mr Lafferty Maths Dept Balancing Method www.mathsrevision.com For balance we have 5a + 63a + 16 = Subtract 6 from each side -6 5a=3a + 10 Subtract 3a from each side -3a 2a=10 aa a a a 2 2 2 aa a 2 2 2 2 22 2 2 Divide each side by 2 a=5 Adult ticket price is £5 1 National 4 REL 1.1b

37. 9-Jun-15 Created by Mr Lafferty Maths Dept Balancing Method www.mathsrevision.com It would be far too time consuming to draw out the balancing scales each time. We will now learn how to use the rules for solving equations. National 4 REL 1.1b

38. 9-Jun-15Created by Mr.Lafferty Maths Dept The Balancing Method www.mathsrevision.com The rule we use to solve equations is Equations Write down the opposite of the following : + opposite is x - ÷ - + ÷ x Level E Harder Equations National 4 REL 1.1b

39. 2x + 4 = 22 2x Example 1 9-Jun-15Created by Mr. Lafferty@mathsrevision.com = 18 Equations x = 9 (- 4) ( ÷2 ) www.mathsrevision.com National 4 REL 1.1b

40. 9x - 5 = 40 9x Example 2 9-Jun-15Created by Mr. Lafferty@mathsrevision.com = 45 Equations x = 5 (+ 5) ( ÷9 ) www.mathsrevision.com National 4 REL 1.1b

41. 9-Jun-15Created by Mr. Lafferty@mathsrevision.com Now try Exercise 5 Ch7 (page 88) www.mathsrevision.com Equations National 4 REL 1.1b

42. 9-Jun-15 Starter Questions www.mathsrevision.com Q1.Solve for x (a)x + 3 = 8(b)2x – 14 = 50 Q2.Is this statement true (x – 1) – 3(x + 1) = -2x Created by Mr. Lafferty@mathsrevision.com National 4 REL 1.1b

43. 9-Jun-15 www.mathsrevision.com Learning Intention Success Criteria 1.To show how to solve equations that have bracket terms. 1.Be able to multiply out brackets and solve equations. Created by Mr. Lafferty@mathsrevision.com Equations and brackets National 4 REL 1.1b

44. 5(x - 3) = 25 5x Example 1 9-Jun-15Created by Mr. Lafferty@mathsrevision.com - 15 = 25 Multiply out the bracket first and then solve. Equations and brackets 5x = 25 + 15 x = 40 ÷ 5 = 40 = 8 (+15) ( ÷ 5) www.mathsrevision.com National 4 REL 1.1b

45. 3(g - 1) = 9 3g Example 2 9-Jun-15Created by Mr. Lafferty@mathsrevision.com - 3 = 9 Multiply out the bracket first and then solve. Equations and brackets 3g = 9 + 3 g = 12 ÷ 3 = 12 = 4 (+3) ( ÷3 ) www.mathsrevision.com National 4 REL 1.1b

46. 9-Jun-15Created by Mr. Lafferty@mathsrevision.com Now try Exercise 6 Ch7 (page 89) www.mathsrevision.com Equations and brackets National 4 REL 1.1b

47. 9-Jun-15 Starter Questions www.mathsrevision.com Q1.Solve for x (a)x + 7 = 29(b)2x – 5 = 21 Q2.Is this statement true (x + 1) – 2(x + 1) = -x Created by Mr. Lafferty@mathsrevision.com National 4 REL 1.1b

48. 9-Jun-15 www.mathsrevision.com Learning Intention Success Criteria 1.To show how to solve equations with terms on both sides. 1.Be able to solve equations with terms on both sides. Created by Mr. Lafferty@mathsrevision.com Equations and brackets National 4 REL 1.1b

49. 6x - 3 = x + 7 5x Example 1 9-Jun-15Created by Mr. Lafferty@mathsrevision.com - 3 = 7 Equations and brackets 5x = 7 + 3 x = 10 ÷ 5 = 10 2 (- x) ( +3 ) (÷ 5 ) www.mathsrevision.com National 4 REL 1.1b

50. 8y + 1 = 5y + 7 3y Example 2 9-Jun-15Created by Mr. Lafferty@mathsrevision.com + 1 = 7 Equations and brackets 3y = 6 y = 2 (- 5y) ( -1 ) (÷ 2 ) www.mathsrevision.com National 4 REL 1.1b

51. 9-Jun-15Created by Mr. Lafferty@mathsrevision.com Now try Exercise 7 Ch7 (page 89) www.mathsrevision.com Equations and brackets National 4 REL 1.1b

52. 9-Jun-15Created by Mr.Lafferty Maths Dept Starter Questions Starter Questions www.mathsrevision.com National 4 REL 1.1b

53. 9-Jun-15Created by Mr.Lafferty Maths Dept www.mathsrevision.com Learning Intention Success Criteria 2.Solving simple inequalities equations. 1.To explain the various symbols for inequalities. 1.Know rule the 4 symbols for inequalities. Inequalities National 4 REL 1.1b

54. 9-Jun-15Created by Mr.Lafferty Maths Dept www.mathsrevision.com The equations you were solving were called equations because they contained an “=“ sign. Inequalities greater than less than greater than or equal to less than or equal to There are 4 other Mathematical symbols They are called inequalities : National 4 REL 1.1b

55. 9-Jun-15Created by Mr.Lafferty Maths Dept www.mathsrevision.com Inequalities 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 value 2 or greater means y can take the value -5 or less Arrow ALWAYS points to the smallest number National 4 REL 1.1b

56. 9-Jun-15Created by Mr.Lafferty Maths Dept www.mathsrevision.com Examples : Write out an inequality for the numbers Inequalities (a)14 and 6 (b)-2 and 1 (c)-3 and -7 (d)34 and -35 14 > 6 -2 < 1 -3 > -7 34 > -35 National 4 REL 1.1b

57. 9-Jun-15Created by Mr.Lafferty Maths Dept www.mathsrevision.com Examples : Choosing from -3, -2, -1, 0, 1, 2, 3 Inequalities (a)y < 0 (b)y > 2 (c)y ≤ -2 (d)y > 3 -3, -2, -1 3 -3, -2 No solution National 4 REL 1.1b

58. 9-Jun-15Created by Mr.Lafferty Maths Dept www.mathsrevision.com Inequalities The Good News Same rule as solving equations The Balancing Method National 4 REL 1.1b

59. 2x + 4 ≥ 30 2x Example 1 9-Jun-15Created by Mr. Lafferty@mathsrevision.com ≥ 26 x ≥ 13 (- 4) ( ÷2 ) www.mathsrevision.com Inequalities National 4 REL 1.1b

60. 4x - 5 ≤ 19 4x Example 2 9-Jun-15Created by Mr. Lafferty@mathsrevision.com ≤ 24 x ≤ 6 (+ 5) ( ÷6 ) www.mathsrevision.com Inequalities National 4 REL 1.1b

61. 9-Jun-15Created by Mr.Lafferty Maths Dept Now try Extension Booklet 8E (page 27) www.mathsrevision.com Inequalities National 4 REL 1.1b