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Algebra

General. Algebra. Tidying up terms. Multiplying terms. Multiplying out Brackets. Solving Simple Equations. www.mathsrevision.com. Solving Harder Equations. Solving Equations with Brackets. Two sided equations. General. Starter Questions. Q1. Calculate.

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Algebra

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  1. General Algebra Tidying up terms Multiplying terms Multiplying out Brackets Solving Simple Equations www.mathsrevision.com Solving Harder Equations Solving Equations with Brackets Two sided equations Created by Mr.Lafferty Maths Dept

  2. General 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. General 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 General + + = First Row : + + 2c c 4c = 7c www.mathsrevision.com + + = 2nd Row : + + 2d 2d 3d = 7d Created by Mr.Lafferty Maths Dept

  5. Tidying Terms General + + = 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 General WE CAN ONLY TIDY UP “LIKE TERMS” Tidy up the following: Q1. 2x + 4x + 5y - 3y Q2. 4a + 3b + 5a - b Q3. 10f + 15g + 5f + g 6x + 2y www.mathsrevision.com 9a + 2b 15f + 16g Created by Mr.Lafferty Maths Dept

  7. Tidying Terms General Chapter 7 Page 85 Ex 1 Q1 and Q2 www.mathsrevision.com Created by Mr.Lafferty Maths Dept

  8. General 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. Write 4 x 4 in terms of powers Created by Mr.Lafferty Maths Dept

  9. Multiplying Terms General Learning Intention Success Criteria • To explain how to multiply terms. • Understand process of multiplying terms. www.mathsrevision.com Created by Mr.Lafferty Maths Dept

  10. Multiplying Terms General Find the area of each square in terms of powers 2 x 8 = 16 3 x 4 = 12 6 x 5 = 30 8 4 5 6 2 3 www.mathsrevision.com 7 x b = 7b 2 x y =2y b y 2 7 Created by Mr.Lafferty Maths Dept

  11. Bracket Equations Solve the following equations: Examples (1) 2 x w = 2w Always put letters in alphabetical order ! (2) 4 x 2y = 8y (3) 3a x 3b = 9ab www.mathsrevision.com (4) 5h x 5g = 25gh (5) 9e x 4m = 36em (6) 8p x a = 8ap Created by Mr.Lafferty Maths Dept

  12. Multiplying Terms General Find the area of each square in terms of powers 32 52 82 3 5 8 3 5 8 www.mathsrevision.com b2 y2 b y y b Created by Mr.Lafferty Maths Dept

  13. Bracket Equations Solve the following equations: (a) 2 x d (d) d x d = 2d = d2 (b) 3 x 2y (e) 6e x 3e = 6y = 18e2 www.mathsrevision.com (c) 5a x 4b (f) 2p x 3p x 4p = 24p3 = 20ab Created by Mr.Lafferty Maths Dept

  14. Multiplying Terms General Your turn ! Chapter 7 Page 86 Exercise 2 www.mathsrevision.com Created by Mr.Lafferty Maths Dept

  15. General Starter Questions www.mathsrevision.com Created by Mr.Lafferty Maths Dept

  16. Removing brackets (1) 3(b + 5) = 3b This means 3 times b Created by Mr.Lafferty Maths Dept

  17. Removing brackets (1) + 3(b + 5) = + 3b 15 This means 3 times 5 Created by Mr.Lafferty Maths Dept

  18. Removing brackets (2) 5(8 - f) = 40 Created by Mr.Lafferty Maths Dept

  19. Removing brackets (2) 5(8 - f) = - 40 5f Tip: Draw lines to keep you right. - 5f 5(8 – f) = 40 Created by Mr.Lafferty Maths Dept

  20. Removing brackets (3) 4(3b + 2) = 12b 4 x 3b = 4 x 3 x b = 12 x b = 12b Created by Mr.Lafferty Maths Dept

  21. Removing brackets (3) + 4(3b + 2) = + 12b 8 Created by Mr.Lafferty Maths Dept

  22. Removing brackets (4) 3(7a – 2b) = 21a Created by Mr.Lafferty Maths Dept

  23. Removing brackets (4) 3(7a – 2b) = - 21a 6b Created by Mr.Lafferty Maths Dept

  24. Removing brackets (5) c(3c + b) = 3c² c x 3c = 3c x c = 3c² Created by Mr.Lafferty Maths Dept

  25. Removing brackets (5) c(3c + b) = + 3c² bc Tip: Remember to draw lines to keep you right. + bc c(3c + b) = 3c² Created by Mr.Lafferty Maths Dept

  26. Removing brackets (6) 6(5e + 3f - 2) = 30e Created by Mr.Lafferty Maths Dept

  27. Removing brackets (6) + 18f 6(5e + 3f - 2) = 30e Created by Mr.Lafferty Maths Dept

  28. Careful! Removing brackets (6) + 18f - 12 6(5e + 3f - 2) = 30e Tip: Remember to draw lines to keep you right. + 18f - 12 6(5e + 3f -2) = 30e Created by Mr.Lafferty Maths Dept

  29. Simplifying (1) 4(3a + 5) - 8 = 12a Created by Mr.Lafferty Maths Dept

  30. \ This is not inside the brackets So don’t multiply! Simplifying (1) +20 -8 4(3a + 5) - 8 = 12a Created by Mr.Lafferty Maths Dept

  31. Simplifying (1) +20 -8 4(3a + 5) - 8 = 12a This can be tidied up = 12a + 12 Created by Mr.Lafferty Maths Dept

  32. This is not inside the brackets So don’t multiply! Simplifying (2) 3b + 2(5b – 6) = 3b + 10b Created by Mr.Lafferty Maths Dept

  33. Careful! Simplifying (2) -12 3b + 2(5b – 6) = 3b + 10b Created by Mr.Lafferty Maths Dept

  34. Simplifying (2) -12 3b + 2(5b – 6) = 3b + 10b This can be tidied up = 13b - 12 Created by Mr.Lafferty Maths Dept

  35. Structured Diagrams Now try Exercise 3 Ch7 (page 86) www.mathsrevision.com Created by Mr.Lafferty Maths Dept

  36. General Starter Questions www.mathsrevision.com Created by Mr.Lafferty Maths Dept

  37. General 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

  38. Equations General 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

  39. Check to see if correct ! Check to see if correct ! Equations General 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

  40. Check to see if correct ! Check to see if correct ! Equations General 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

  41. Equations General Solving Equations Now try Exercise 4 Ch8 (page 87) www.mathsrevision.com Created by Mr.Lafferty Maths Dept

  42. General Starter Questions www.mathsrevision.com Created by Mr.Lafferty Maths Dept

  43. General Solving 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

  44. Equations General 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

  45. Check to see if correct ! Equations General Solving 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

  46. Check to see if correct ! Equations General Solving 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

  47. Equations General Solving Equations Now try Exercise 5 Ch7 (page 88) www.mathsrevision.com Created by Mr.Lafferty Maths Dept

  48. General Starter Questions www.mathsrevision.com Created by Mr.Lafferty Maths Dept

  49. General Equations with Brackets Bracket Equations Learning Intention Success Criteria 1. Multiply out brackets. • 1. To show how to solve equations with brackets . 2. Apply ‘change side change sign’ rule. www.mathsrevision.com Created by Mr.Lafferty Maths Dept

  50. Bracket Equations General Equations with Brackets Multiply out the brackets first and then Apply ‘change side change sign’ rule Example www.mathsrevision.com Created by Mr.Lafferty Maths Dept

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