MTH 3-14a MTH 3-15a MTH 3-15b MTH 4-14a MTH 4-15a 16-Nov-15Created by Mr. Lafferty Maths Dept. Algebra Collecting Like Terms Removing Brackets Removing Brackets & Simplifying Evaluating Expressions & Formulae Solving Simple Equations Solving Equations with Brackets Constructing Formulae

MTH 3-14a MTH 3-15a MTH 3-15b MTH 4-14a MTH 4-15a 16-Nov-15Created by Mr. Lafferty Maths Dept. Starter Questions Starter Questions 6cm 2cm 3cm

MTH 3-14a MTH 3-15a MTH 3-15b MTH 4-14a MTH 4-15a 16-Nov-15Created by Mr. Lafferty Maths Dept. Learning Intention Success Criteria 1.Understand the techniques for simplifying terms. 1.We are learning to simplify terms. Algebra Simplifying Algebraic Expressions 2. Be able too simplify algebraic expressions.

MTH 3-14a MTH 3-15a MTH 3-15b MTH 4-14a MTH 4-15a 16-Nov-15Created by Mr. Lafferty Maths Dept. Algebra Simplifying Algebraic Expressions Collecting LIKE terms - m + a 1 + 4g(NOT 5g ) 7 k 2 (NOT 7k 6 )

MTH 3-14a MTH 3-15a MTH 3-15b MTH 4-14a MTH 4-15a 16-Nov-15Created by Mr. Lafferty Maths Dept. Algebra Simplifying Algebraic Expressions Multiplying Terms 6 d 4 h (NOT 2e ) 8(NOT 8a) e 2 a 2

MTH 3-14a MTH 3-15a MTH 3-15b MTH 4-14a MTH 4-15a 16-Nov-15Created by Mr. Lafferty Maths Dept. Algebra Simplifying Algebraic Expressions Dividing Terms 4 3 e

MTH 3-14a MTH 3-15a MTH 3-15b MTH 4-14a MTH 4-15a Below is a floor plan of the down stairs of a house. 16-Nov-15Created by Mr. y 5 y 3 y 2 + 8y + 15 Living Room Kitchen Bathroom Bedroom y 2 5y 3y15 Tidy up ! Algebra Simplifying Algebraic Expressions What is the total area of the downstairs house?

MTH 3-14a MTH 3-15a MTH 3-15b MTH 4-14a MTH 4-15a 16-Nov-15Created by Mr. Lafferty Maths Dept. Now try TJ3a Ex 1 Ch7 (page 54) Algebra Removing Brackets

MTH 3-14a MTH 3-15a MTH 3-15b MTH 4-14a MTH 4-15a 16-Nov-15Created by Mr. Lafferty Maths Dept. Starter Questions Starter Questions 6h 2a 100 o 60 o

MTH 3-14a MTH 3-15a MTH 3-15b MTH 4-14a MTH 4-15a 16-Nov-15Created by Mr. Lafferty Maths Dept. Learning Intention Success Criteria 1.Understand the key steps in removing brackets. 1. We are learning how to multiply out simply algebraic brackets. Algebra 2. Apply multiplication rules for positive and negative numbers when removing brackets. Removing brackets

MTH 3-14a MTH 3-15a MTH 3-15b MTH 4-14a MTH 4-15a 3(b + 5) =3b + 15 Example 4(w - 2) =4w - 8 Example 16-Nov-15Created by Mr. Removing a Single Bracket

MTH 3-14a MTH 3-15a MTH 3-15b MTH 4-14a MTH 4-15a 8(x + 3) =8x + 24 Example 4(3 -2m) =12 - 8m Example 16-Nov-15Created by Mr. Removing a Single Bracket

MTH 3-14a MTH 3-15a MTH 3-15b MTH 4-14a MTH 4-15a Example : Write down an expression for the amount indicate below in two difference ways. 5(y - 2)= 5y Nov-15 Created by Mr. Removing a Single Bracket y-2

MTH 3-14a MTH 3-15a MTH 3-15b MTH 4-14a MTH 4-15a a(b + 5) =ab + 5a Example p(w - 2) =pw - 2p Example 16-Nov-15Created by Mr. Removing a Single Bracket

MTH 3-14a MTH 3-15a MTH 3-15b MTH 4-14a MTH 4-15a y(y - 1) =y2y2 - y Example 7w(w - 3) =7w w Example 16-Nov-15Created by Mr. Removing a Single Bracket

MTH 3-14a MTH 3-15a MTH 3-15b MTH 4-14a MTH 4-15a a(a 2 + 3b) =a3a3 + 3ab Example y 2 (3y -2c) =3y 3 - 2cy 2 Example 16-Nov-15Created by Mr. Removing a Single Bracket

MTH 3-14a MTH 3-15a MTH 3-15b MTH 4-14a MTH 4-15a -(x + y) =-x - y Example -5(a - 7) =-5a + 35 Example 16-Nov-15Created by Mr. Removing a Single Bracket

MTH 3-14a MTH 3-15a MTH 3-15b MTH 4-14a MTH 4-15a 16-Nov-15Created by Mr. Lafferty Maths Dept. Algebra y Question : Find the area of the rectangle (i) With brackets (ii) Without brackets. Removing brackets = 4(y + 5) (i)A = L x B (ii)= 4(y + 5)= 4y+ 20

MTH 3-14a MTH 3-15a MTH 3-15b MTH 4-14a MTH 4-15a 16-Nov-15Created by Mr. Lafferty Maths Dept. Starter Questions Starter Questions 3cm (x-6)cm

MTH 3-14a MTH 3-15a MTH 3-15b MTH 4-14a MTH 4-15a 16-Nov-15Created by Mr. Lafferty Maths Dept. Now try TJ3a Ex 2 Ch7 (page 56) Algebra Removing Brackets

MTH 3-14a MTH 3-15a MTH 3-15b MTH 4-14a MTH 4-15a 16-Nov-15Created by Mr. Lafferty Maths Dept. Learning Intention Success Criteria 1.Understand the key steps in removing brackets and simplifying. 1. We are learning how to multiply out simply algebraic brackets and collecting like terms. Algebra 2. Apply multiplication rules for positive and negative numbers when removing brackets. Removing brackets

MTH 3-14a MTH 3-15a MTH 3-15b MTH 4-14a MTH 4-15a 7 + 3(4 - y) = Example 9 - 3(8 - y) = Example 16-Nov-15Created by Mr. Removing a Single Bracket - 3y = y + 3y Tidy Up = y Tidy Up

MTH 3-14a MTH 3-15a MTH 3-15b MTH 4-14a MTH 4-15a A = 10(x – 2) Example 16-Nov-15Created by Mr. Removing a Single Bracket Find my Area (x - 2) 10 Find my Area x 12 A = 12x A = L x BA = L x B

MTH 3-14a MTH 3-15a MTH 3-15b MTH 4-14a MTH 4-15a 4(m - 3) - (m + 2) =4m m - 2 Example 16-Nov-15Created by Mr. = 3m (y - 1) - 2(y + 4) =7y y - 8 = 5y - 15 Tidy Up Removing Two Single Brackets Tidy Up

MTH 3-14a MTH 3-15a MTH 3-15b MTH 4-14a MTH 4-15a Example : Find area of the orange border 16-Nov-15Created by Mr. Removing a Single Bracket (x - 2) 10 x 12 Area =Big Rec – Small Rec = 12x – 10(x - 2) = 12x = 2x x+ 20

MTH 3-14a MTH 3-15a MTH 3-15b MTH 4-14a MTH 4-15a Calculate difference if y = 14 Diff = 3 x 14 – 8 = 34 A = 4(y – 5) Example : Find an expression for the difference in the areas. 16-Nov-15Created by Mr. (y - 5) 47 A = 7(y - 4) (y - 4) Difference = 7(y - 4) - 4(y – 5) = 7y - 28 = 3y - 8 Removing Two Single Brackets - 4y + 20

MTH 3-14a MTH 3-15a MTH 3-15b MTH 4-14a MTH 4-15a Calculate difference if x = 4 Diff = 2 x =28 A = 7(x + 1) Example : Find an expression for the difference in the areas. 16-Nov-15Created by Mr. (x + 1) 79 A = 9(x + 3) x + 3 Difference = 9(x + 3) - 7(x + 1) = 9x + 27 = 2x + 20 Removing Two Single Brackets – 7x - 7

MTH 3-14a MTH 3-15a MTH 3-15b MTH 4-14a MTH 4-15a A s = 4(x - 3) 16-Nov-15Created by Mr. Lafferty Maths Dept. Algebra x 6 Question : Find the area of the large rectangle, then the small rectangle and hence find the area of the red section. 4 x-3 Removing Brackets & Simplifying A b = 6x = 4x A s = 6x - 4(x - 3) = 6x= 2x x+ 12

MTH 3-14a MTH 3-15a MTH 3-15b MTH 4-14a MTH 4-15a 16-Nov-15Created by Mr. Lafferty Maths Dept. Now try TJ3a Ex 3 Ch7 (page 57) Algebra Removing Brackets

MTH 3-14a MTH 3-15a MTH 3-15b MTH 4-14a MTH 4-15a 16-Nov-15Created by Mr. Lafferty Maths Dept. Starter Questions Starter Questions

MTH 3-14a MTH 3-15a MTH 3-15b MTH 4-14a MTH 4-15a 16-Nov-15Created by Mr. Lafferty Maths Dept. Equations Learning Intention Success Criteria 2.Solving simple algebraic equations. 1.To revise Level 2 using the rule ‘Balancing Method’ Revision of Level 2 1.Understand the process of the ‘Balancing Method’

MTH 3-14a MTH 3-15a MTH 3-15b MTH 4-14a MTH 4-15a 16-Nov-15Created by Mr Lafferty Maths Dept 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? What instrument measures balance How can we go about solving this using balance ?

MTH 3-14a MTH 3-15a MTH 3-15b MTH 4-14a MTH 4-15a 16-Nov-15Created by Mr Lafferty Maths Dept Balancing Method 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 =8 kg

MTH 3-14a MTH 3-15a MTH 3-15b MTH 4-14a MTH 4-15a 16-Nov-15Created by Mr Lafferty Maths Dept Balancing Method PP 4 P 44 4 Lets solve it using maths. Let P be the weigh 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

MTH 3-14a MTH 3-15a MTH 3-15b MTH 4-14a MTH 4-15a 16-Nov-15Created by Mr Lafferty Maths Dept 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 ? 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

MTH 3-14a MTH 3-15a MTH 3-15b MTH 4-14a MTH 4-15a 16-Nov-15Created by Mr Lafferty Maths Dept Balancing Method 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 aa a Divide each side by 2 a=5 Adult ticket price is £5 1

MTH 3-14a MTH 3-15a MTH 3-15b MTH 4-14a MTH 4-15a 16-Nov-15Created by Mr Lafferty Maths Dept 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.

MTH 3-14a MTH 3-15a MTH 3-15b MTH 4-14a MTH 4-15a 16-Nov-15Created by Mr. Lafferty Maths Dept. Revision of Level 2 Examples Equations x – 5 = x = 16 x + 8 = x = 29

MTH 3-14a MTH 3-15a MTH 3-15b MTH 4-14a MTH 4-15a 16-Nov-15Created by Mr. Lafferty Maths Dept. Revision of Level 2 Examples Equations 6x = 72 x = 12 (÷ 6) 2x = 11 x = 5.5 (÷ 2)

MTH 3-14a MTH 3-15a MTH 3-15b MTH 4-14a MTH 4-15a 16-Nov-15Created by Mr. Lafferty Maths Dept. Revision of Level 2 Examples Equations ½ x = 5 x = 10 (x 2) ¾ x = 9 3x = 36 (x 4) x = 12 (÷ 3)

MTH 3-14a MTH 3-15a MTH 3-15b MTH 4-14a MTH 4-15a 16-Nov-15Created by Mr. Lafferty Maths Dept. Revision of Level 2 Examples Equations 4x – 2 = x = 36 x = 9 (÷ 4) 2x + 9 = x = 22 x = 11 (÷ 2)

MTH 3-14a MTH 3-15a MTH 3-15b MTH 4-14a MTH 4-15a 16-Nov-15Created by Mr. Lafferty Maths Dept. Now try TJ3a Ex 4 Ch7 (page 58) Algebra Removing Brackets

MTH 3-14a MTH 3-15a MTH 3-15b MTH 4-14a MTH 4-15a 16-Nov-15Created by Mr. Lafferty Maths Dept. Starter Questions Starter Questions

MTH 3-14a MTH 3-15a MTH 3-15b MTH 4-14a MTH 4-15a 16-Nov-15Created by Mr. Lafferty Maths Dept. Equations Learning Intention Success Criteria 1. We are learning how to solve equations with brackets and fractions. 1. Remember rule for Multiply out brackets. 2. Apply ‘Balancing Method’ to solve fractional equations. Equations with Brackets

MTH 3-14a MTH 3-15a MTH 3-15b MTH 4-14a MTH 4-15a 16-Nov-15Created by Mr. Lafferty Maths Dept. Multiply out the brackets first and then Balancing Method Equations with Brackets Equations 3(x – 2) = 33 3x - 6 = 33 3x = x = 13 (÷ 3) Example Each group has 2 minutes come up with a method for solving this type of equation

MTH 3-14a MTH 3-15a MTH 3-15b MTH 4-14a MTH 4-15a 16-Nov-15Created by Mr. Lafferty Maths Dept. Example Equations with Brackets Equations 5(3x + 2) – 2(4x - 3) = 2x x + 16 = 2x x = 2x x 5x = 20 (÷ 5) x = 4 15x + 10 – 8x + 6 = 2x + 36 Tidy up terms !

MTH 3-14a MTH 3-15a MTH 3-15b MTH 4-14a MTH 4-15a 16-Nov-15Created by Mr. Lafferty Maths Dept. Multiply EVERY term to get rid of fractional term. and then apply ‘Balancing Method’ Equations with Fractions Equations x + 3 = (x 2) x + 6 = 14 x = Each group has 2 minutes come up with a method for solving this type of equation Example

MTH 3-14a MTH 3-15a MTH 3-15b MTH 4-14a MTH 4-15a 16-Nov-15Created by Mr. Lafferty Maths Dept. Equations with Fractions Equations x - = (x 4) 3x - 2 = 16 3x = (÷ 3) x = 6 Multiply EVERY term to get rid of fractional term. and then apply ‘Balancing Method’ Example

MTH 3-14a MTH 3-15a MTH 3-15b MTH 4-14a MTH 4-15a 16-Nov-15Created by Mr. Lafferty Maths Dept. Now try TJ3a Ex 5 Ch7 (page 59) Algebra Removing Brackets

MTH 3-14a MTH 3-15a MTH 3-15b MTH 4-14a MTH 4-15a 16-Nov-15Created by Mr. Lafferty Maths Dept. Starter Questions Starter Questions 7cm (x+2)cm

MTH 3-14a MTH 3-15a MTH 3-15b MTH 4-14a MTH 4-15a 16-Nov-15Created by Mr. Lafferty Maths Dept. Learning Intention Success Criteria 1. We are learning how to evaluate an expression. 1. Be able to substitute numbers for letters in an expression. Algebra 2. Use previous knowledge of Number to evaluate a expression. Evaluating Expressions – number for letter

MTH 3-14a MTH 3-15a MTH 3-15b MTH 4-14a MTH 4-15a 16-Nov-15Created by Mr. Lafferty Maths Dept. Algebra Evaluating Expressions – number for letter Given the following information find the values of :- a = 3 ; b = 4 and c = -1 BODMAS 2a + c = 2 x 3 + (-1) = 2 x = = 5 b 2 – a 2 = 4 2 – 3 2 = 16 – 9 = 7 2b 2 = 2 x (4) 2 = 2 x 16 = 32

MTH 3-14a MTH 3-15a MTH 3-15b MTH 4-14a MTH 4-15a 16-Nov-15Created by Mr. Lafferty Maths Dept. Algebra Evaluating Expressions – number for letter Given the following information find the values of :- a = 3 ; b = 4 and c = -1 2a 2 + 3b + 30c = 2 x (3) x x (-1) = = 0

MTH 3-14a MTH 3-15a MTH 3-15b MTH 4-14a MTH 4-15a 16-Nov-15Created by Mr. Lafferty Maths Dept. Algebra Evaluating Expressions – number for letter Given the following information find the values of :- d = 3 ; e = 4 and f = -1 BODMAS 2(d - f) = 2(3 -(-1)) = 2 x 4 = 8 ¾ (d + f 2 ) = ¾(3 + (-1 2 )) = ¾(4) = 3 √(16e) = √(16 x 4) = √64 = 8

MTH 3-14a MTH 3-15a MTH 3-15b MTH 4-14a MTH 4-15a 16-Nov-15Created by Mr. Lafferty Maths Dept. Now try TJ3a Ex 6 Ch7 (page 60) Algebra Removing Brackets

MTH 3-14a MTH 3-15a MTH 3-15b MTH 4-14a MTH 4-15a 16-Nov-15Created by Mr. Lafferty Maths Dept. Starter Questions Starter Questions

MTH 3-14a MTH 3-15a MTH 3-15b MTH 4-14a MTH 4-15a Learning Intention Success Criteria 1.To explain how to work with formulae expressed in words. 1.Understand formulae expressed in words. Formulae 2.Solve problems given formulae in words.

MTH 3-14a MTH 3-15a MTH 3-15b MTH 4-14a MTH 4-15a Sometimes formulae are expressed in words. Formulae A tile fitter charges £20 per hour. How much will he charge for 8 hours of work. C =20 x h For h = 8 C = 20 x 8 =£160

MTH 3-14a MTH 3-15a MTH 3-15b MTH 4-14a MTH 4-15a Formulae The cost for hiring a carpet cleaner is £30 plus £3 a day How much will it cost to hire for a week. C =30+3d For d = 7 C = x 7 = £51

MTH 3-14a MTH 3-15a MTH 3-15b MTH 4-14a MTH 4-15a Formulae 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 Profit = 12 – 9.99 = £ p = s - b

MTH 3-14a MTH 3-15a MTH 3-15b MTH 4-14a MTH 4-15a 16-Nov-15Created by Mr. Lafferty Maths Dept. Now try TJ3a Ex 7 Ch7 (page 62) Algebra Removing Brackets