1 / 51

Algebra

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.

paul
Download Presentation

Algebra

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript


  1. 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

  2. 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 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. Created by Mr.Lafferty Maths Dept

  3. 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

  4. 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 Created by Mr.Lafferty Maths Dept

  5. 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” Created by Mr.Lafferty Maths Dept

  6. 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 Created by Mr.Lafferty Maths Dept

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

  8. MTH 3-14a MTH 3-15a MTH 3-15b Starter Questions 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 Created by Mr.Lafferty Maths Dept

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

  10. 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: www.mathsrevision.com Created by Mr.Lafferty Maths Dept

  11. 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 www.mathsrevision.com 3b 3b+9 Created by Mr.Lafferty Maths Dept

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

  13. 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 www.mathsrevision.com Created by Mr.Lafferty Maths Dept

  14. 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 www.mathsrevision.com Created by Mr.Lafferty Maths Dept

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

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

  17. 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

  18. 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 Created by Mr.Lafferty Maths Dept

  19. 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 www.mathsrevision.com Sub in a=3 = 3 x 9 Sub in b=9 = 27 Created by Mr.Lafferty Maths Dept

  20. 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 Created by Mr.Lafferty Maths Dept

  21. 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 Created by Mr.Lafferty Maths Dept

  22. 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 + www.mathsrevision.com Sub in b=3 = 10 12 + = 22 Created by Mr.Lafferty Maths Dept

  23. 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 Created by Mr.Lafferty Maths Dept

  24. 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 www.mathsrevision.com Sub in a=15 = 5 Sub in b = 3 Created by Mr.Lafferty Maths Dept

  25. 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 www.mathsrevision.com 3) b2 =36 =3 Created by Mr.Lafferty Maths Dept

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

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

  28. 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

  29. 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 Created by Mr.Lafferty Maths Dept

  30. 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 www.mathsrevision.com Created by Mr.Lafferty Maths Dept

  31. 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 www.mathsrevision.com Created by Mr.Lafferty Maths Dept

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

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

  34. 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

  35. 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

  36. 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 www.mathsrevision.com Created by Mr.Lafferty Maths Dept

  37. 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 www.mathsrevision.com Created by Mr.Lafferty Maths Dept

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

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

  40. 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

  41. 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 or equal to greater than less than or equal to less than Created by Mr.Lafferty Maths Dept

  42. 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 www.mathsrevision.com y ≤ -5 means y can take the value -5 or less Created by Mr.Lafferty Maths Dept

  43. 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 Created by Mr.Lafferty Maths Dept

  44. 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 Created by Mr.Lafferty Maths Dept

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

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

  47. 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

  48. 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” Created by Mr.Lafferty Maths Dept

  49. 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

  50. 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 www.mathsrevision.com Created by Mr.Lafferty Maths Dept

More Related