3Algebra Multiplying Terms Learning Intention Success Criteria 1. To explain how to gather ‘algebraic like terms’.Understand the term ‘like terms’.2. Gather like terms for simpleexpressions.
4+ + = + + + + = + + Tidying Terms 2c c 4c = 7c 2d 2d 3d = 7d First Row :++2cc4c= 7c++=2nd Row :++2d2d3d= 7d
5+ + = + + Tidying Terms 3f f 2f = 6f 7c + 7d + 6f 3rd Row :++3ff2f= 6fCANNOTTIDY UPANYMOREIn Total we have7c + 7d + 6fWE CAN ONLY TIDY UP “LIKE TERMS”
6Tidying Terms Q1. 2x + 4x + 5y -3y + 18 = 6x + 2y + 18 WE CAN ONLY TIDY UP “LIKE TERMS”Tidy up the following:Q1. 2x + 4x + 5y -3y + 18 =Q2. 4a + 3b + 5a + 6 – b =6x + 2y + 189a + 2b + 6
7Algebra Multiplying Terms Learning Intention Success Criteria 1. To explain how to multiply out algebraic terms.Understand the key steps of multiplying terms.2. Apply multiplication rules for simple expressions.
8Algebra Reminder ! Simplifying Algebraic Expressions We can only add and subtract “ like terms “
9Algebra Reminder ! Simplifying Algebraic Expressions Multiplying terms ( NOT 2b )( NOT 8m )
10Algebra Removing brackets Learning Intention Success Criteria 1. To explain how to multiply out simply algebraic brackets.Understand the key steps in removing brackets.2. Apply multiplication rules for integers numbers when removing brackets.
11Removing a Single Bracket Example 13(b + 5) =3b+ 15Example 24(w - 2) =4w- 8
12Removing a Single Bracket Example 32(y - 1) =2y- 2Example 47(w - 6) =7w- 42
13Removing a Single Bracket Example 58(x + 3) =8x+ 24Example 64(3 -2m) =12- 8m
14Removing a Single Bracket Tidy UpExample 77 + 3(4 - y) =7 +12- 3y= yTidy UpExample 89 - 3(8 - y) =9- 24+ 3y= y
16Equations Solving Equations Learning Intention Success Criteria To solve simple equations using the‘Balancing Method’.1. Know the process of the‘Balancing Method’.2. Solving simple algebraic equations.
17Balancing MethodKirsty 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?44What instrument measures balanceHow can we go about solving this using balance ?
18Balancing Method Take a small bag away from each side. 4444Take a big bag awayfrom each side.We can see that a big bagis equal to4 + 4 =8 kg
19Balancing Method Let’s solve it using maths. Let P be the weight What symbol should we use for the scales ?Balancing MethodLet’s solve it using maths.4PPPLet P be the weightof a big bag.444We know that a small bag = 4Subtract 4 from each side2P + 4=P + 12-4-4Subtract P from each side2P=P + 8-P-PP=8
20Balancing Method It would be far too time consuming to draw out the balancing scales each time.We will now learn how to use the rules for solving equations.
21+ + - - x x ÷ ÷ Equations The Balancing Method opposite is opposite is Solving EquationsThe method we use to solve equations isThe Balancing MethodWrite down the opposite of the following :++--opposite isopposite isxx÷÷opposite isopposite is
26Equations Harder Equations Learning Intention Success Criteria To solve harder equations using the rule‘Balancing Method’.repeatedly.1. Know the process of ‘Balancing Method’.2. Solving harder algebraic equations by using rule repeatedly.
27We know that a child price = £2 Balancing MethodGroup 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 £2.2aIf a child’s ticket costs £2. How much for an adult ticket ?a2a2Let a be the priceof an adult ticket.a2We know that a child price = £2
28Balancing Method For balance we have 5a + 6 = 3a + 16 5a = 3a + 10 2a Subtract 3a from each sideSubtract 6 from each sideFor balance we have2a5a + 6=3a + 16a2-6-622215a=3a + 10aa-3a-3aDivide each side by 22a=10a=5Adult ticket price is £5
29Balancing Method It would be far too time consuming to draw out the balancing scales each time.We will now learn how to use the rules for solving equations.
30+ + - - x x ÷ ÷ Equations The Balancing Method opposite is opposite is Level E Harder EquationsThe rule we use to solve equations isThe Balancing MethodWrite down the opposite of the following :++--opposite isopposite isxx÷÷opposite isopposite is