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Algebra

Algebra. Collecting Like Terms. Removing Brackets. Removing Brackets & Simplifying. Solving Simple Equations. www.mathsrevision.com. Solving Equations with Brackets. Evaluating Expressions & Formulae. Constructing Formulae. Starter Questions. www.mathsrevision.com. 2cm. 3cm. 6cm.

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Algebra

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  1. Algebra Collecting Like Terms Removing Brackets Removing Brackets & Simplifying Solving Simple Equations www.mathsrevision.com Solving Equations with Brackets Evaluating Expressions & Formulae Constructing Formulae Created by Mr. Lafferty Maths Dept.

  2. Starter Questions www.mathsrevision.com 2cm 3cm 6cm 2cm Created by Mr. Lafferty Maths Dept.

  3. Algebra Simplifying Algebraic Expressions Learning Intention Success Criteria • Understand the techniques for simplifying terms. • We are learning to simplify terms. • 2. Be able too simplify algebraic expressions. www.mathsrevision.com Created by Mr. Lafferty Maths Dept.

  4. Algebra Simplifying Algebraic Expressions Collecting LIKE terms - m + a 1 + 4g (NOT 5g ) www.mathsrevision.com 7 k2 (NOT 7k6) Created by Mr. Lafferty Maths Dept.

  5. Algebra Simplifying Algebraic Expressions Multiplying Terms 6 d 4 h www.mathsrevision.com e2 (NOT 2e ) a2 8 (NOT 8a) Created by Mr. Lafferty Maths Dept.

  6. Algebra Simplifying Algebraic Expressions Dividing Terms 4 www.mathsrevision.com e 3 Created by Mr. Lafferty Maths Dept.

  7. What is the total area of the downstairs house? Algebra Simplifying Algebraic Expressions Below is a floor plan of the down stairs of a house. y 5 Living Room y y2 5y Tidy up ! Bedroom www.mathsrevision.com 3y 15 3 Kitchen Bathroom y2 + 8y + 15 Created by Mr. Lafferty@mathsrevision.com

  8. Algebra Removing Brackets Now try TJ3a Ex 1 Ch7 (page 54) www.mathsrevision.com Created by Mr. Lafferty Maths Dept.

  9. Starter Questions 100o 60o 2a 6h www.mathsrevision.com Created by Mr. Lafferty Maths Dept.

  10. Algebra Removing brackets Learning Intention Success Criteria • Understand the key steps in removing brackets. • 1. We are learning how to multiply out simply algebraic brackets. • 2. Apply multiplication rules for positive and negative numbers when removing brackets. www.mathsrevision.com Created by Mr. Lafferty Maths Dept.

  11. Removing a Single Bracket Example + 15 3(b + 5) = 3b Example www.mathsrevision.com - 8 4(w - 2) = 4w Created by Mr. Lafferty@mathsrevision.com

  12. Removing a Single Bracket Example + 24 8(x + 3) = 8x Example www.mathsrevision.com - 8m 4(3 -2m) = 12 Created by Mr. Lafferty@mathsrevision.com

  13. Removing a Single Bracket Example : Write down an expression for the amount indicate below in two difference ways. y-2 y-2 y-2 www.mathsrevision.com - 10 5(y - 2) = 5y y-2 y-2 5-Nov-19 Created by Mr. Lafferty@mathsrevision.com

  14. Removing a Single Bracket Example + 5a a(b + 5) = ab Example www.mathsrevision.com - 2p p(w - 2) = pw Created by Mr. Lafferty@mathsrevision.com

  15. Removing a Single Bracket Example - y y(y - 1) = y2 Example www.mathsrevision.com - 21w 7w(w - 3) = 7w2 Created by Mr. Lafferty@mathsrevision.com

  16. Removing a Single Bracket Example + 3ab a(a2 + 3b) = a3 Example www.mathsrevision.com - 2cy2 y2(3y -2c) = 3y3 Created by Mr. Lafferty@mathsrevision.com

  17. Removing a Single Bracket Example - y -(x + y) = -x Example www.mathsrevision.com + 35 -5(a - 7) = -5a Created by Mr. Lafferty@mathsrevision.com

  18. Algebra Removing brackets Question : Find the area of the rectangle (i) With brackets (ii) Without brackets. y + 5 (i) A = L x B www.mathsrevision.com 4 = 4(y + 5) (ii) = 4(y + 5) = 4y + 20 Created by Mr. Lafferty Maths Dept.

  19. Algebra Removing Brackets Now try TJ3a Ex 2 Ch7 (page 56) www.mathsrevision.com Created by Mr. Lafferty Maths Dept.

  20. Starter Questions www.mathsrevision.com (x-6)cm 3cm Created by Mr. Lafferty Maths Dept.

  21. Algebra Removing brackets Learning Intention Success Criteria • Understand the key steps in removing brackets and simplifying. • 1. We are learning how to multiply out simply algebraic brackets and collecting like terms. • 2. Apply multiplication rules for positive and negative numbers when removing brackets. www.mathsrevision.com Created by Mr. Lafferty Maths Dept.

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

  23. Removing a Single Bracket Example 12 10 Find my Area Find my Area x (x - 2) www.mathsrevision.com A = L x B A = L x B A = 10(x – 2) A = 12x Created by Mr. Lafferty@mathsrevision.com

  24. Removing Two Single Brackets Tidy Up Example - m - 2 4(m - 3) - (m + 2) = 4m - 12 = 3m - 14 Tidy Up Example www.mathsrevision.com - 2y - 8 7(y - 1) - 2(y + 4) = 7y - 7 = 5y - 15 Created by Mr. Lafferty@mathsrevision.com

  25. Removing a Single Bracket Example : Find area of the orange border 12 Area =Big Rec – Small Rec 10 x (x - 2) = 12x – 10(x - 2) www.mathsrevision.com = 12x -10x + 20 = 2x + 20 Created by Mr. Lafferty@mathsrevision.com

  26. Removing Two Single Brackets Example : Find an expression for the difference in the areas. (y - 5) A = 4(y – 5) 7 4 A = 7(y - 4) www.mathsrevision.com (y - 4) Calculate difference if y = 14 Diff = 3 x 14 – 8 = 34 Difference = 7(y - 4) - 4(y – 5) = 7y - 28 - 4y + 20 = 3y - 8 Created by Mr. Lafferty@mathsrevision.com

  27. Removing Two Single Brackets Example : Find an expression for the difference in the areas. (x + 1) A = 7(x + 1) 9 7 A = 9(x + 3) www.mathsrevision.com x + 3 Calculate difference if x = 4 Diff = 2 x 4 + 20 =28 Difference = 9(x + 3) - 7(x + 1) = 9x + 27 – 7x - 7 = 2x + 20 Created by Mr. Lafferty@mathsrevision.com

  28. Algebra Removing Brackets & Simplifying Question : Find the area of the large rectangle, then the small rectangle and hence find the area of the red section. x x-3 4 Ab= 6x 6 www.mathsrevision.com As= 4(x - 3) = 4x - 12 As= 6x - 4(x - 3) = 6x - 4x + 12 = 2x + 12 Created by Mr. Lafferty Maths Dept.

  29. Algebra Removing Brackets Now try TJ3a Ex 3 Ch7 (page 57) www.mathsrevision.com Created by Mr. Lafferty Maths Dept.

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

  31. Equations Revision of Level 2 Learning Intention Success Criteria • To revise Level 2 • using the rule • ‘Balancing Method’ • 1. Understand the process of the • ‘Balancing Method’ • 2. Solving simple algebraic equations. www.mathsrevision.com Created by Mr. Lafferty Maths Dept.

  32. Balancing Method 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? 4 www.mathsrevision.com 4 4 4 What instrument measures balance How can we go about solving this using balance ? Created by Mr Lafferty Maths Dept

  33. Balancing Method Take a small bag away from each side. 4 4 4 4 Take a big bag away from each side. www.mathsrevision.com We can see that a big bag is equal to 4 + 4 = 8 kg Created by Mr Lafferty Maths Dept

  34. Balancing Method What symbol should we use for the scales ? Lets solve it using maths. 4 P P P Let P be the weigh of a big bag. 4 4 4 We know that a small bag = 4 www.mathsrevision.com Subtract 4 from each side 2P + 4 P + 12 = -4 -4 Subtract P from each side 2P = P + 8 -P -P P = 8 Created by Mr Lafferty Maths Dept

  35. Balancing Method 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 ? www.mathsrevision.com 2 2 2 2 a 2 a 2 2 a 2 Let a be the price of an adult ticket. 2 a a 2 a a 2 a We know that a child price = £2 Created by Mr Lafferty Maths Dept

  36. Balancing Method Subtract 3a from each side Subtract 6 from each side For balance we have 2 a 2 a a 5a + 6 3a + 16 2 = a 2 2 2 -6 -6 a a 2 2 2 2 1 a 2 5a = 3a + 10 a -3a -3a Divide each side by 2 www.mathsrevision.com 2a = 10 a = 5 Adult ticket price is £5 Created by Mr Lafferty Maths Dept

  37. Balancing Method It would be far too time consuming to draw out the balancing scales each time. We will now review how to use the rules for solving equations. www.mathsrevision.com Created by Mr Lafferty Maths Dept

  38. Equations Revision of Level 2 Examples x – 5 = 11 x + 8 = 37 + 5 + 5 - 8 - 8 x = 16 x = 29 www.mathsrevision.com Created by Mr. Lafferty Maths Dept.

  39. Equations Revision of Level 2 Examples 6x = 72 2x = 11 6 6 2 2 x = 5.5 x = 12 www.mathsrevision.com Created by Mr. Lafferty Maths Dept.

  40. Equations Revision of Level 2 Examples ¾x = 9 ½x = 5 (x 2) (x 4) 3 3 x = 10 3x = 36 www.mathsrevision.com x = 12 Created by Mr. Lafferty Maths Dept.

  41. Equations Revision of Level 2 Examples 4x – 2 = 34 2x + 9 = 31 + 2 + 2 - 9 - 9 2 4 2 4 4x = 36 2x = 22 www.mathsrevision.com x = 11 x = 9 Created by Mr. Lafferty Maths Dept.

  42. Algebra Removing Brackets Now try TJ3a Ex 4 Ch7 (page 58) www.mathsrevision.com Created by Mr. Lafferty Maths Dept.

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

  44. Equations Equations with Brackets Learning Intention Success Criteria 1. Remember rule for Multiply out brackets. • 1. We are learning how to solve equations with brackets and fractions . 2. Apply ‘Balancing Method’ to solve fractional equations. www.mathsrevision.com Created by Mr. Lafferty Maths Dept.

  45. Each group has 2 minutes come up with a method for solving this type of equation Equations Equations with Brackets Multiply out the brackets first and then Balancing Method Example 3(x – 2) = 33 3x - 6 = 33 3 3 + 6 + 6 www.mathsrevision.com 3x = 39 x = 13 Created by Mr. Lafferty Maths Dept.

  46. Equations Equations with Brackets Example 5(3x + 2) – 2(4x - 3) = 2x + 36 15x + 10 – 8x + 6 = 2x + 36 Tidy up terms ! 5 5 7x + 16 = 2x + 36 - 16 - 16 www.mathsrevision.com 7x = 2x + 20 - 2x - 2x 5x = 20 Created by Mr. Lafferty Maths Dept. x = 4

  47. Each group has 2 minutes come up with a method for solving this type of equation Equations Equations with Fractions Example x + 3 = 7 Multiply EVERY term to get rid of fractional term. and then apply ‘Balancing Method’ 1 2 (x 2) x + 6 = 14 - 6 - 6 www.mathsrevision.com x = 8 Created by Mr. Lafferty Maths Dept.

  48. Equations Equations with Fractions 1 Example x - = 4 Multiply EVERY term to get rid of fractional term. and then apply ‘Balancing Method’ 2 3 (x 4) 4 3x - 2 = 16 3 3 + 2 + 2 www.mathsrevision.com 3x = 18 x = 6 Created by Mr. Lafferty Maths Dept.

  49. Algebra Removing Brackets Now try TJ3a Ex 5 Ch7 (page 59) www.mathsrevision.com Created by Mr. Lafferty Maths Dept.

  50. Starter Questions www.mathsrevision.com (x+2)cm 7cm Created by Mr. Lafferty Maths Dept.

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