All pupils can solve inequalities algebraically and graphically Further Algebra Recap L.O. All pupils can rearrange a variety of algebraic expressions and equations All pupils can solve inequalities algebraically and graphically All pupils can rearrange to solve simultaneous equations (by substitution)

Pre Starter: Key Words Equation Solve Variable Simultaneous Substitute Linear

Revision Tarsia Activity Starter: rearrange a variety of algebraic expressions and equations Revision Tarsia Activity

All pupils can solve inequalities algebraically and graphically Further Algebra Recap L.O. All pupils can rearrange a variety of algebraic expressions and equations All pupils can solve inequalities algebraically and graphically All pupils can rearrange to solve simultaneous equations (by substitution)

Main 1: What is an inequality? 2 mins: spider diagram inequalities algebraically and graphically What is an inequality? 2 mins: spider diagram

Main 1: inequalities algebraically and graphically What are the possible values of x if x>14 and x is an integer? What are the possible values of x if x>14? How does the solution change if x≥14?

Main 1: What are the possible values of x if x>14? inequalities algebraically and graphically What are the possible values of x if x>14? How could we show this on a number line?

Main 1: How does the solution change if x≥14? inequalities algebraically and graphically How does the solution change if x≥14? How could we show this on a number line?

Main 1: inequalities algebraically and graphically Ext.

How does the fact x>1 relate to the fact –x<-1? Mini Discussion: show inequalities on a number line How does the fact x>1 relate to the fact –x<-1?

Main 1: 2 mins: How could you show 3x + 7 ≤ 28 on a number line? inequalities algebraically and graphically 2 mins: How could you show 3x + 7 ≤ 28 on a number line?

Main 1: 3x + 7 ≤ 28 3x ≤ 21 x ≤ 7 Minus 7 from each side inequalities algebraically and graphically 3x + 7 ≤ 28 Minus 7 from each side 3x ≤ 21 Divide by 3 on each side x ≤ 7

Main 1: inequalities algebraically and graphically x ≤ 7

Main 1: inequalities algebraically and graphically So they are solved just like equations and then drawn on a number line. Answer each of the questions below, your working must be shown and your solutions should be shown on a number line.

Main 1: Write some questions fitting the description: inequalities algebraically and graphically Write some questions fitting the description: Find the set of solutions by showing graphically on a Cartesian plane these linear inequalities with one variable.

Main 1: What are these graphs displaying? inequalities algebraically and graphically What are these graphs displaying? Ext. Write a question with the graph as the solution for each of the graphs

Main 1: inequalities algebraically and graphically What are the two variables usually associated with the Cartesian plane? What is the usual general form of an equation of a line with two variables?

Main 1: inequalities algebraically and graphically Write this inequality so it looks like the general form of a linear equation. 3x – y > 12

Main 1: How could you plot it? 3x – 12 > y OR y < 3x - 12 inequalities algebraically and graphically How could you plot it? 3x – 12 > y OR y < 3x - 12

Main 1: y < 3x - 12 inequalities algebraically and graphically x -2 2 4 y -18 -12 -6

Main 1: y < 3x - 12 inequalities algebraically and graphically x -2 2 4 y -18 -12 -6

Main 1: y < 3x - 12 inequalities algebraically and graphically x -2 2 4 y -18 -12 -6

Shade each of the described regions on the board Main 1: inequalities algebraically and graphically Shade each of the described regions on the board

All pupils can solve inequalities algebraically and graphically Further Algebra Recap L.O. All pupils can rearrange a variety of algebraic expressions and equations All pupils can solve inequalities algebraically and graphically All pupils can rearrange to solve simultaneous equations (by substitution)

Main 2: simultaneous equations

Main 2: simultaneous equations

Clue: Plot x=3y+1 and y= 𝒙 𝟐 -2 Clue: When does (x-1)/3= 𝒙 𝟐 -2? Main 2: simultaneous equations By drawing the graphs, find the point where x=3y+1 and y= 𝒙 𝟐 -2 intersect. Clue: Plot x=3y+1 and y= 𝒙 𝟐 -2 Clue: When does (x-1)/3= 𝒙 𝟐 -2?

Main 2: Steps to find solutions to simultaneous equations graphically: 1. Draw/complete the table of values 2. Plot the graphs 3. Find the point of intersection 4. At the point of intersection, y=… and x=…

Main 2: simultaneous equations

Main 2: Find the point where x=3y+1 and y= 𝒙 𝟐 -2 intersect. simultaneous equations Find the point where x=3y+1 and y= 𝒙 𝟐 -2 intersect. Number the equations 1 and 2 Choose an equation to make y the subject of the formula Substitute into the other equation Rearrange to find x Substitute x into an original equation Rearrange to find y

Solve graphically and then check algebraically: Main 2: simultaneous equations Solve graphically and then check algebraically:

Main 2: simultaneous equations

All pupils can solve inequalities algebraically and graphically Further Algebra Recap L.O. All pupils can rearrange a variety of algebraic expressions and equations All pupils can solve inequalities algebraically and graphically All pupils can rearrange to solve simultaneous equations (by substitution)

Plenary:

All pupils can solve inequalities algebraically and graphically Further Algebra Recap L.O. All pupils can rearrange a variety of algebraic expressions and equations All pupils can solve inequalities algebraically and graphically All pupils can rearrange to solve simultaneous equations (by substitution) WWW? EBI?