Algebra Collecting Like Terms Removing Brackets Removing Brackets & Simplifying Solving Simple Equations Solving Equations with Brackets Evaluating Expressions & Formulae Constructing Formulae 17-Sep-18

Algebra Simplifying Algebraic Expressions Learning Intention Success Criteria We are learning to simplify terms. Understand the techniques for simplifying terms. 2. Be able too simplify algebraic expressions. 17-Sep-18

Algebra - m + a 1 + 4g (NOT 5g ) 7 k2 (NOT 7k6) Simplifying Algebraic Expressions Collecting LIKE terms - m + a 1 + 4g (NOT 5g ) 7 k2 (NOT 7k6) 17-Sep-18

Algebra 6 d 4 h e2 (NOT 2e ) 8 a2 (NOT 8a) Simplifying Algebraic Expressions Multiplying Terms 6 d 4 h e2 (NOT 2e ) 8 a2 (NOT 8a) 17-Sep-18

Algebra e 4 3 Simplifying Algebraic Expressions Dividing Terms 17-Sep-18

Algebra y2 5y 3y 15 y2 + 8y + 15 y 5 y 3 www.mathsrevision.com 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 y Living Room y2 5y Tidy up ! Bedroom www.mathsrevision.com 3y 15 3 Bathroom Kitchen y2 + 8y + 15 17-Sep-18

Algebra Now try TJ3a Ex 1 Ch7 (page 54) www.mathsrevision.com Removing Brackets Now try TJ3a Ex 1 Ch7 (page 54) www.mathsrevision.com 17-Sep-18

Starter Questions 2a 6h www.mathsrevision.com 100o 60o 17-Sep-18

Algebra www.mathsrevision.com Removing brackets Learning Intention Success Criteria 1. We are learning how to multiply out simply algebraic brackets. Understand the key steps in removing brackets. 2. Apply multiplication rules for positive and negative numbers when removing brackets. www.mathsrevision.com 17-Sep-18

Removing a Single Bracket Example 3(b + 5) = 3b + 15 www.mathsrevision.com Example 4(w - 2) = 4w - 8 17-Sep-18

Removing a Single Bracket Example 8(x + 3) = 8x + 24 www.mathsrevision.com Example 4(3 -2m) = 12 - 8m 17-Sep-18

Created by Mr. Lafferty@mathsrevision.com 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 5(y - 2) = 5y - 10 y-2 y-2 17-Sep-18 17-Sep-18 Created by Mr. Lafferty@mathsrevision.com

Removing a Single Bracket Example a(b + 5) = ab + 5a www.mathsrevision.com Example p(w - 2) = pw - 2p 17-Sep-18

Removing a Single Bracket Example y(y - 1) = y2 - y www.mathsrevision.com Example 7w(w - 3) = 7w2 - 21w 17-Sep-18

Removing a Single Bracket Example a(a2 + 3b) = a3 + 3ab www.mathsrevision.com Example y2(3y -2c) = 3y3 - 2cy2 17-Sep-18

Removing a Single Bracket Example -(x + y) = -x - y www.mathsrevision.com Example -5(a - 7) = -5a + 35 17-Sep-18

Algebra (i) A = L x B www.mathsrevision.com = 4(y + 5) (ii) = 4(y + 5) 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(y + 5) 4 (ii) = 4(y + 5) = 4y + 20 17-Sep-18

Algebra Now try TJ3a Ex 2 Ch7 (page 56) www.mathsrevision.com Removing Brackets Now try TJ3a Ex 2 Ch7 (page 56) www.mathsrevision.com 17-Sep-18

Starter Questions www.mathsrevision.com (x-6)cm 3cm 17-Sep-18

Algebra www.mathsrevision.com Removing brackets Learning Intention Success Criteria 1. We are learning how to multiply out simply algebraic brackets and collecting like terms. Understand the key steps in removing brackets and simplifying. 2. Apply multiplication rules for positive and negative numbers when removing brackets. www.mathsrevision.com 17-Sep-18

Removing a Single Bracket Tidy Up Example 7 + 3(4 - y) = 7 + 12 - 3y = 19 - 3y Tidy Up www.mathsrevision.com Example 9 - 3(8 - y) = 9 - 24 + 3y = -15 + 3y 17-Sep-18

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 17-Sep-18

Removing Two Single Brackets Tidy Up Example 4(m - 3) - (m + 2) = 4m - 12 - m - 2 = 3m - 14 Tidy Up Example www.mathsrevision.com 7(y - 1) - 2(y + 4) = 7y - 7 - 2y - 8 = 5y - 15 17-Sep-18

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 17-Sep-18

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) Diff = 3 x 14 – 8 = 34 Calculate difference if y = 14 Difference = 7(y - 4) - 4(y – 5) = 7y - 28 - 4y + 20 = 3y - 8 17-Sep-18

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 Diff = 2 x 4 + 20 =28 Calculate difference if x = 4 Difference = 9(x + 3) - 7(x + 1) = 9x + 27 – 7x - 7 = 2x + 20 17-Sep-18

Algebra Ab= 6x As= 4(x - 3) As= 6x - 4(x - 3) www.mathsrevision.com 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 Ab= 6x 6 4 www.mathsrevision.com As= 4(x - 3) = 4x - 12 As= 6x - 4(x - 3) = 6x - 4x + 12 = 2x + 12 17-Sep-18

Algebra Now try TJ3a Ex 3 Ch7 (page 57) www.mathsrevision.com Removing Brackets Now try TJ3a Ex 3 Ch7 (page 57) www.mathsrevision.com 17-Sep-18

Starter Questions www.mathsrevision.com 17-Sep-18

Equations www.mathsrevision.com 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 17-Sep-18

Balancing Method www.mathsrevision.com 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 What instrument measures balance How can we go about solving this using balance ? 17-Sep-18

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 17-Sep-18

Balancing Method Lets solve it using maths. Let P be the weigh What symbol should we use for the scales ? Balancing Method 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 17-Sep-18

We know that a child price = £2 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. 2 a If a child’s ticket costs £2. How much for an adult ticket ? a 2 www.mathsrevision.com a 2 Let a be the price of an adult ticket. a 2 We know that a child price = £2 17-Sep-18

Balancing Method For balance we have 5a + 6 = 3a + 16 5a = 3a + 10 Subtract 3a from each side Subtract 6 from each side For balance we have 2 a 5a + 6 = 3a + 16 a 2 -6 -6 2 2 2 1 5a = 3a + 10 a a -3a -3a Divide each side by 2 www.mathsrevision.com 2a = 10 a = 5 Adult ticket price is £5 17-Sep-18

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 17-Sep-18

Equations x – 5 = 11 x + 8 = 37 x = 16 x = 29 www.mathsrevision.com Revision of Level 2 Examples x – 5 = 11 x + 8 = 37 + 5 + 5 - 8 - 8 x = 16 x = 29 www.mathsrevision.com 17-Sep-18

Equations 6x = 72 2x = 11 6 6 2 2 x = 12 x = 5.5 www.mathsrevision.com Revision of Level 2 Examples 6x = 72 2x = 11 6 6 2 2 x = 12 x = 5.5 www.mathsrevision.com 17-Sep-18

½x = 5 ¾x = 9 Equations x = 10 3x = 36 3 3 x = 12 Revision of Level 2 Examples ½x = 5 ¾x = 9 (x 2) (x 4) x = 10 3x = 36 www.mathsrevision.com 3 3 x = 12 17-Sep-18

Equations 4x – 2 = 34 2x + 9 = 31 4x = 36 2x = 22 4 4 2 2 x = 9 x = 11 Revision of Level 2 Examples 4x – 2 = 34 2x + 9 = 31 + 2 + 2 - 9 - 9 4x = 36 2x = 22 www.mathsrevision.com 4 4 2 2 x = 9 x = 11 17-Sep-18

Algebra Now try TJ3a Ex 4 Ch7 (page 58) www.mathsrevision.com Removing Brackets Now try TJ3a Ex 4 Ch7 (page 58) www.mathsrevision.com 17-Sep-18

Starter Questions www.mathsrevision.com 17-Sep-18

Equations www.mathsrevision.com 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 17-Sep-18

Equations 3(x – 2) = 33 3x - 6 = 33 3x = 39 3 3 x = 13 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 + 6 + 6 www.mathsrevision.com 3x = 39 3 3 x = 13 17-Sep-18

Equations 5(3x + 2) – 2(4x - 3) = 2x + 36 15x + 10 – 8x + 6 = 2x + 36 Equations with Brackets Example 5(3x + 2) – 2(4x - 3) = 2x + 36 15x + 10 – 8x + 6 = 2x + 36 Tidy up terms ! 7x + 16 = 2x + 36 - 16 - 16 www.mathsrevision.com 7x = 2x + 20 - 2x - 2x 5x = 20 5 5 17-Sep-18 x = 4

Equations x + 3 = 7 x + 6 = 14 x = 8 www.mathsrevision.com Each group has 2 minutes come up with a method for solving this type of equation Equations Equations with Fractions Multiply EVERY term to get rid of fractional term. and then apply ‘Balancing Method’ Example x + 3 = 7 1 2 (x 2) x + 6 = 14 - 6 - 6 www.mathsrevision.com x = 8 17-Sep-18

Multiply EVERY term to get rid of fractional term. Equations Equations with Fractions Multiply EVERY term to get rid of fractional term. and then apply ‘Balancing Method’ Example x - = 4 3 4 1 2 (x 4) 3x - 2 = 16 + 2 + 2 www.mathsrevision.com 3x = 18 3 3 x = 6 17-Sep-18

Algebra Now try TJ3a Ex 5 Ch7 (page 59) www.mathsrevision.com Removing Brackets Now try TJ3a Ex 5 Ch7 (page 59) www.mathsrevision.com 17-Sep-18

Starter Questions www.mathsrevision.com (x+2)cm 17-Sep-18 7cm

Algebra www.mathsrevision.com Evaluating Expressions – number for letter Learning Intention Success Criteria 1. Be able to substitute numbers for letters in an expression. 1. We are learning how to evaluate an expression. www.mathsrevision.com 2. Use previous knowledge of Number to evaluate a expression. 17-Sep-18

Algebra a = 3 ; b = 4 and c = -1 2a + c b2 – a2 2b2 = 2x3 + (-1) Evaluating Expressions – number for letter BODMAS Given the following information find the values of :- a = 3 ; b = 4 and c = -1 2a + c b2 – a2 2b2 = 2x3 + (-1) = 42 – 32 = 2x(4)2 www.mathsrevision.com = 2x3 - 1 = 16 – 9 = 2x16 = 6 - 1 = 7 = 32 = 5 17-Sep-18

Algebra 2a2 + 3b + 30c = 2x(3)2 + 3x4 + 30x(-1) = 18 + 12 - 30 = 0 Evaluating Expressions – number for letter Given the following information find the values of :- a = 3 ; b = 4 and c = -1 2a2 + 3b + 30c = 2x(3)2 + 3x4 + 30x(-1) www.mathsrevision.com = 18 + 12 - 30 = 0 17-Sep-18

Algebra ¾(d + f2) d = 3 ; e = 4 and f = -1 2(d - f) √(16e) Evaluating Expressions – number for letter BODMAS Given the following information find the values of :- d = 3 ; e = 4 and f = -1 2(d - f) ¾(d + f2) √(16e) = 2(3 -(-1)) = ¾(3 + (-12)) = √(16x4) www.mathsrevision.com = 2 x 4 = ¾(4) = √64 = 8 = 3 = 8 17-Sep-18

Algebra Now try TJ3a Ex 6 Ch7 (page 60) www.mathsrevision.com Removing Brackets Now try TJ3a Ex 6 Ch7 (page 60) www.mathsrevision.com 17-Sep-18

Starter Questions www.mathsrevision.com 17-Sep-18

Formulae www.mathsrevision.com Learning Intention Success Criteria To explain how to work with formulae expressed in words. Understand formulae expressed in words. 2. Solve problems given formulae in words. www.mathsrevision.com 17-Sep-18

Sometimes formulae are expressed in words. A tile fitter charges £20 per hour. How much will he charge for 8 hours of work. www.mathsrevision.com C = 20xh For h = 8 C = 20 x 8 = £160 17-Sep-18

Formulae C = 30 + 3d For d = 7 C = 30 + 3 x 7 = £51 The cost for hiring a carpet cleaner is £30 plus £3 a day How much will it cost to hire for a week. www.mathsrevision.com C = 30 + 3d For d = 7 C = 30 + 3 x 7 = £51 17-Sep-18

Formulae p = s - b £2.01 Profit = 12 – 9.99 = Profit : Subtract how much you paid for goods in the first place from the amount you actually sold them for. How much profit did Daniel make if he bought a CD for £9.99 and sold it for £12 www.mathsrevision.com p = s - b Profit = 12 – 9.99 = £2.01 17-Sep-18

Have you updated your Learning Log ? Algebra Removing Brackets Now try TJ3a Ex 7 Ch7 (page 62) www.mathsrevision.com Are you on Target ? I can ? 17-Sep-18