Solving Equations Foundation Tier GCSE

Starter Activity – Evaluate when…... Put the cards in order of smallest on the left to largest on the right….when…. Put the cards in order of smallest on the left to largest on the right….when…. x = 10 x = 10 x = 1 x = 1 x = 3 x = 3 x = -5 ( hard!!) x = -5 ( hard!!)

Aims for today’s lesson To understand what an equation is…. To understand what an equation is…. To be able to make an equation….. To be able to make an equation….. To know what solving an equation means, and be able to solve simple equations To know what solving an equation means, and be able to solve simple equations

What is an Equation? An equation looks a bit like the algebra we were doing in earlier lessons…… An equation looks a bit like the algebra we were doing in earlier lessons…… The key difference is suggested by the word itself…… The key difference is suggested by the word itself……EQUALS An equation always has an equals sign somewhere (usually in the middle of the problem). An equation always has an equals sign somewhere (usually in the middle of the problem). TIONS

How to make an Equation… OK – think of a number……. OK – think of a number……. Double your number….. Double your number….. Subtract (take off) 3…. Subtract (take off) 3…. You get the answer 9. What was the original number you thought of? You get the answer 9. What was the original number you thought of?

How to make an Equation… OK – think of a number……. Call it x OK – think of a number……. Call it x Double your number………..that’s 2x Double your number………..that’s 2x Subtract (take off) 3……….so 2x - 3 Subtract (take off) 3……….so 2x - 3 You get the answer 9…..so 2x – 3 = 9 You get the answer 9…..so 2x – 3 = 9 What was the original number you thought of? What was the original number you thought of? Reverse the steps….start with the 9 …. Now add 3….that’s 12…..divide by 2….so my original number, x = 6. I now know what x is – which means I’ve solved my equation!! Reverse the steps….start with the 9 …. Now add 3….that’s 12…..divide by 2….so my original number, x = 6. I now know what x is – which means I’ve solved my equation!!

How to make an Equation… OK – think of a number…………x OK – think of a number…………x multiply your number by 5…….that’s 5x multiply your number by 5…….that’s 5x add 2……………now that gives 5x + 2 add 2……………now that gives 5x + 2 You get the answer 22…..so that’s 5x+2=22 You get the answer 22…..so that’s 5x+2=22 Now to solve it…..start with the 22 …..subtract the 2….that’s 20….divide by 5 …..so x=4 Now to solve it…..start with the 22 …..subtract the 2….that’s 20….divide by 5 …..so x=4

Solving Equations…. Example: Solve3x + 4 = 25 Method: write the equation down: 3x + 4 = 25 Subtract 4 from the equation….. 3x + 4 – 4 = 25 – 4 3x = 21 3x = 21 Divide the equation by 3……. x = 7(Check!!) x = 7(Check!!) Notice how an equation is like a balance – what you do to one side of the equals, you must also do on the other side…..

Now for the HUMAN EQUATION!! Solve 4x + 6 = 20

Solving Equations….2 Example: Solve7x - 5 = 30 Method: write the equation down: 7x - 5 = 30 Add 5 to both parts of the equation…. 7x = x = 35 7x = 35 Divide the equation by 7……. x = 5(Check!!) x = 5(Check!!) Again – the equation is a balancing act….

Solving Equations….3 Example: Solve8x + 1 = 13 Method: write the equation down: 8x + 1 = 13 Subtract 1 from both parts of the equation…. 8x = x = 12 8x = 12 Divide the equation by 8……. x = 1.5(Check!!) x = 1.5(Check!!) Here we do the same thing to both sides – but try to isolate the x term…

Equations on the web….. Use 11-14, Equations, level 2

Review today’s lesson To understand what an equation is…. To understand what an equation is…. To be able to make an equation….. To be able to make an equation….. To know what solving an equation means, and be able to solve simple equations To know what solving an equation means, and be able to solve simple equations Try this algebra pyramid Try this algebra pyramid

Aims for today’s lesson 1. To know what solving an equation means, and be able to solve simple equations with only one x term 2. To understand how to solve equations with an x term on each side (grade C +)

Solving Equations…. Example: Solve2x + 14 = 25 Method: write the equation down: 2x + 14 = 25 Subtract 14 from the equation….. 2x + 14 – 14 = 25 – 14 2x = 11 2x = 11 Divide the equation by 2……. x = 5.5(Check!!) x = 5.5(Check!!) Notice how an equation is like a balance – what you do to one side of the equals, you must also do on the other side…..

Try these quickly….. Solve: 1. 3x + 6 = x – 3 = x + 2 = x = = x

Solving Equations with TWO x terms Example: Solve3x + 4 = 2x + 9 Method: write the equation: 3x + 4 = 2x + 9 Subtract 4 from the equation….. 3x + 4 – 4 = 2x + 9 – 4 3x = 2x + 5 3x = 2x + 5 Now subtract 2x from the equation ……. 3x – 2x = 2x – 2x + 5 x = 5(Check!!) x = 5(Check!!)

Solving Equations with TWO x terms Example: Solve5x - 6 = 3x + 8 Method: write the equation: 5x - 6 = 3x + 8 Add 6 to both sides of the equation….. 5x = 3x x = 3x x = 3x + 14 Now subtract 3x from both sides ……. 5x – 3x = 3x – 3x + 14 Now 2x = 14 so x = 7

Solving Equations with TWO x terms Example: Solvex - 6 = 5x + 10 Method: Swap the equation: 5x + 10 = x – 6 Subtract 10 from both sides of the equation….. 5x + 10 – 10 = x – 6 – 10 5x = x – 16 5x = x – 16 Now subtract x from both sides ……. 5x – x = x – x – 16 Now 4x = - 16 so x = - 4

Equations on the web….. Use 11-14, Equations, level 4

These were the aims for today’s lesson: 1. To know what solving an equation means, and be able to solve simple equations with only one x term 2. To understand how to solve equations with an x term on each side (grade C +) Now check your learning by having a go at this question from a GCSE paper:

Aims for today’s lesson 1. To understand how to solve equations involving a divide and an x term (grade C ) 2. To know how to deal with brackets in the equation (grade C)

Dealing with fractions….. Solve: x = 10 3 Now begin by looking carefully at what the equation is actually saying: “ x divided by 3 equals 10” or…. “ what number, divided by 3, is 10?” The answer is obviously x = 30 – so it seems all you need to do is let the 10 be multiplied by the 3…..In fact, this must be right, because the opposite of divide by 3 is multiply by 3….. x = 30

Dealing with fractions 2 Solve: x = 4 5 Again, what the equation is actually saying is: “ x divided by 5 equals 4” or…. “ what number, divided by 5, is 4?” The answer is obviously x = 20 – so again all you need to do is let the 4 be multiplied by the 5…..this must be right, because the opposite of divide by 5 is multiply by 5….. x = 20

Dealing with fractions 3 Solve: x + 6 = 10 2 First, take 6 from both sides…..gives you…. x = 4 2 Now multiply both sides by 2…..giving: x = 8

Dealing with fractions 4 Solve: 2x - 4 = 6 7 First, add 4 to both sides…..gives you…. 2x = 10 7 Now multiply both sides by 7…..giving: 2x = 70 Finally divide both sides by 2, giving…. x = 35

These were the aims for today’s lesson: 1. To understand how to solve equations involving a divide and an x term (grade C +) 2. To know how to deal with brackets in the equation (grade C+) Now check your learning by having a go at this question from a GCSE paper: