MTH 3-14a MTH 4-14a MTH 4-14b 9-Jun-15Created by Mr. Lafferty Maths Dept. Simplifying Algebraic Expressions Removing Brackets Algebra Removing Brackets & Simplifying Evaluating Expressions Factorising – The common factor

MTH 3-14a MTH 4-14a MTH 4-14b 9-Jun-15Created by Mr. Lafferty Maths Dept. Starter Questions Starter Questions 6cm 2cm 3cm

MTH 3-14a MTH 4-14a MTH 4-14b 9-Jun-15Created by Mr. Lafferty Maths Dept. Learning Intention Success Criteria 1.To remember the phrase ‘ like terms.’ ‘ like terms.’ 1.To review tidying up expressions. Algebra Simplifying Algebraic Expressions 2. Understand and be able too simplify simple algebraic expressions by collecting ‘ like terms.’

9-Jun-15Created by Mr. Lafferty Maths Dept. Algebra Simplifying Algebraic Expressions Reminder ! We can only add and subtract “ like terms “ MTH 3-14a MTH 4-14a MTH 4-14b

9-Jun-15Created by Mr. Lafferty Maths Dept. Algebra Simplifying Algebraic Expressions Reminder ! Multiplying terms ( NOT 2b ) ( NOT 8m ) MTH 3-14a MTH 4-14a MTH 4-14b Rule Multiply the numbers together multiply the letters together.

9-Jun-15Created by Mr. Lafferty Maths Dept. Algebra Simplifying Algebraic Expressions y2 y 2 Question : Find the area of each of the 3 sections of this shape. What is the total area. 123 MTH 3-14a MTH 4-14a MTH 4-14b

9-Jun-15Created by Mr. Lafferty Maths Dept. Now try Exercise 1 Ch11 (page 46) Algebra Simplifying Algebraic Expressions MTH 3-14a MTH 4-14a MTH 4-14b

MTH 3-14a MTH 4-14a MTH 4-14b 9-Jun-15Created by Mr. Lafferty Maths Dept. Starter Questions Starter Questions 6h 2a 100 o 60 o

MTH 3-14a MTH 4-14a MTH 4-14b 9-Jun-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

3(b + 5) =3b + 15 Example 1 4(w - 2) =4w - 8 Example 2 9-Jun-15Created by Mr. Removing a Single Bracket MTH 3-14a MTH 4-14a MTH 4-14b

2(y - 1) =2y - 2 Example 3 7(w - 6) =7w - 42 Example 4 9-Jun-15Created by Mr. Removing a Single Bracket MTH 3-14a MTH 4-14a MTH 4-14b

8(x + 3) =8x + 24 Example 5 4(3 -2m) =12 - 8m Example 6 9-Jun-15Created by Mr. Removing a Single Bracket MTH 3-14a MTH 4-14a MTH 4-14b

Example 7 : Write down an expression for the amount indicate below in two difference ways. 3(x + 3)=3x Jun-15Created by Mr. Removing a Single Bracket x+3 MTH 3-14a MTH 4-14a MTH 4-14b

Example 8 : Write down an expression for the amount indicate below in two difference ways. 5(y - 2)= 5y Jun-15 Created by Mr. Removing a Single Bracket y-2 MTH 3-14a MTH 4-14a MTH 4-14b

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

9-Jun-15Created by Mr. Lafferty Maths Dept. Now try Exercise 2 Ch11 (page 48) Algebra Removing brackets MTH 3-14a MTH 4-14a MTH 4-14b

MTH 3-14a MTH 4-14a MTH 4-14b 9-Jun-15Created by Mr. Lafferty Maths Dept. Starter Questions Starter Questions 7cm (x+2)cm

MTH 3-14a MTH 4-14a MTH 4-14b 9-Jun-15Created by Mr. Lafferty Maths Dept. Learning Intention Success Criteria 1. We are learning how to remove brackets and simplify. 1. Understand how to remove brackets Algebra Removing Brackets & Simplifying 2. Understand the need to show clear working. 3. Apply to context questions.

a(b + 5) =ab + 5a Example 1 p(w - 2) =pw - 2p Example 2 9-Jun-15Created by Mr. Removing a Single Bracket MTH 3-14a MTH 4-14a MTH 4-14b

y(y - 1) =y2y2 - y Example 3 7w(w - 3) =7w w Example 4 9-Jun-15Created by Mr. Removing a Single Bracket MTH 3-14a MTH 4-14a MTH 4-14b

a(a 2 + 3b) =a3a3 + 3ab Example 5 y 2 (3y -2c) =3y 3 - 2cy 2 Example 6 9-Jun-15Created by Mr. Removing a Single Bracket MTH 3-14a MTH 4-14a MTH 4-14b

-(x + y) =-x - y Example 7 -5(a - 7) =-5a + 35 Example 8 9-Jun-15Created by Mr. Removing a Single Bracket MTH 3-14a MTH 4-14a MTH 4-14b

7 + 3(4 - y) = Example (8 - y) = Example 10 9-Jun-15Created by Mr. Removing a Single Bracket - 3y = y + 3y Tidy Up = y MTH 3-14a MTH 4-14a MTH 4-14b Tidy Up

A = 10(x – 2) Example 11 9-Jun-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 4-14a MTH 4-14b

Example 12 : Find area of the orange border 9-Jun-15Created by Mr. Removing a Single Bracket (x - 2) 10 x 12 Area =Big Rec – Small Rec = 12x – 10(x - 2) = 12x = 2x + 20 MTH 3-14a MTH 4-14a MTH 4-14b -10x+ 20

4(m - 3) - (m + 2) =4m m - 2 Example 13 Example 14 9-Jun-15Created by Mr. = 3m (y - 1) - 2(y + 4) =7y y - 8 = 5y - 15 Tidy Up Removing Two Single Brackets MTH 3-14a MTH 4-14a MTH 4-14b Tidy Up

Calculate difference if y = 14 Diff = 3 x 14 – 8 = 34 A = 4(y – 5) Example 15 : Find an expression for the difference in the areas. 9-Jun-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 MTH 3-14a MTH 4-14a MTH 4-14b - 4y + 20

Calculate difference if x = 4 Diff = 2 x =28 A = 7(x + 1) Example 16 : Find an expression for the difference in the areas. 9-Jun-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 MTH 3-14a MTH 4-14a MTH 4-14b – 7x - 7

A s = 4(x - 3) 9-Jun-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 MTH 3-14a MTH 4-14a MTH 4-14b A b = 6x = 4x A s = 6x - 4(x - 3) = 6x= 2x x+ 12

9-Jun-15Created by Mr. Lafferty Maths Dept. Now try Exercise 3 Ch11 (page 50) Algebra Removing Brackets & Simplifying MTH 3-14a MTH 4-14a MTH 4-14b

MTH 3-14a MTH 4-14a MTH 4-14b 9-Jun-15Created by Mr. Lafferty Maths Dept. Starter Questions Starter Questions 7cm (x+2)cm

MTH 3-14a MTH 4-14a MTH 4-14b 9-Jun-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

9-Jun-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 MTH 3-14a MTH 4-14a MTH 4-14b 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

9-Jun-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 MTH 3-14a MTH 4-14a MTH 4-14b 2a 2 + 3b + 30c = 2 x (3) x x (-1) = = 0

9-Jun-15Created by Mr. Lafferty Maths Dept. Now try Exercise 4 Ch2 (page 51) Algebra Evaluating Expressions – number for letter MTH 3-14a MTH 4-14a MTH 4-14b

MTH 3-14a MTH 4-14a MTH 4-14b 9-Jun-15Created by Mr. Lafferty Maths Dept. Starter Questions Starter Questions

MTH 3-14a MTH 4-14a MTH 4-14b 9-Jun-15Created by Mr. Lafferty Maths Dept. Learning Intention Success Criteria 1. We are learning the process of factorising’. 1. Understand the term factorising. Algebra 2. Apply previous knowledge to recognise the HCF for a set of values. Factorising – The Common Factor 3. Analysis answer to validate it is correct.

9-Jun-15Created by Mr. Factorising Example Factorise 3x Find the HCF for 3x and HCF goes outside the bracket3( ) 3.To see what goes inside the bracket divide each term by HCF = 5 3( x + 5 ) Check by multiplying out the bracket to get back to where you started MTH 3-14a MTH 4-14a MTH 4-14b = x 3x

9-Jun-15Created by Mr. Factorising Example 1.Find the HCF for 4x 2 and 6xy2x 2.HCF goes outside the bracket2x( ) 3.To see what goes inside the bracket divide each term by HCF 2x( 2x - 3y ) Factorise 4x 2 – 6xy Check by multiplying out the bracket to get back to where you started MTH 3-14a MTH 4-14a MTH 4-14b = 2x 4x 2 2x = 3y 6xy 2x

9-Jun-15Created by Mr. Lafferty Maths Dept. Algebra Simply find the HCF for a given set of data and write the data using brackets :- Factorising – The Common Factor MTH 3-14a MTH 4-14a MTH 4-14b 6x – 12 = ( ) 6x- 2 8a – 12b = ( ) 42a- 3b

9-Jun-15Created by Mr. Lafferty Maths Dept. Algebra Simply find the HCF for a given set of data and write the data using brackets :- Factorising – The Common Factor MTH 3-14a MTH 4-14a MTH 4-14b am + an = ( ) am+ n 9f – 6f 2 = ( ) 3f3- 2f

9-Jun-15Created by Mr. Factorising Factorise the following : (a)3x + 6 (b) 4xy – 2x (c) 6a + 7a 2 (d)y 2 - y MTH 3-14a MTH 4-14a MTH 4-14b = ( ) 3x+ 2 = ( ) 2x2y- 1 = ( ) a6+ 7a = ( ) yy- 1

9-Jun-15Created by Mr. Lafferty Maths Dept. Now try Exercise 5 Ch11 (page 54) Algebra Factorising – The Common Factor MTH 3-14a MTH 4-14a MTH 4-14b