Solving Equations Foundation Tier GCSE Starter Activity Evaluate

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…. n x = 10 n x = 1 n x = 3 n x = -5 ( hard!!) n

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

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

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

How to make an Equation… n n n OK – think of a number……. Call it x Double your number………. . that’s 2 x Subtract (take off) 3………. so 2 x - 3 You get the answer 9…. . so 2 x – 3 = 9 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!!

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

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

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

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

Solving Equations…. 3 Example: Solve 8 x + 1 = 13 Method: write the equation down: Here we do the 8 x + 1 = 13 same thing to Subtract 1 from both parts of the equation…. both sides – 8 x + 1 - 1 = 13 - 1 but try to isolate the x 8 x = 12 term… Divide the equation by 8……. x = 1. 5 (Check!!)

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

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

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

Solving Equations…. Example: Solve 2 x + 14 = 25 Method: write the equation down: Notice how an 2 x + 14 = 25 equation is like a Subtract 14 from the equation…. . balance – what you do to one side of the equals, you must also do on the other side…. . 2 x + 14 – 14 = 25 – 14 2 x = 11 Divide the equation by 2……. x = 5. 5 (Check!!)

Try these quickly…. . Solve: 1. 2. 3. 4. 5. 3 x + 6 = 15 4 x – 3 = 13 5 x + 2 = 27 23 + 3 x = 44 50 = 26 + 8 x

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

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

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

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

These were the aims for today’s lesson: 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: 1.

Aims for today’s lesson 1. 2. To understand how to solve equations involving a divide and an x term (grade C ) 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: 2 x - 4 = 6 7 First, add 4 to both sides…. . gives you…. 2 x = 10 7 Now multiply both sides by 7…. . giving: 2 x = 70 Finally divide both sides by 2, giving…. x = 35

These were the aims for today’s lesson: 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: 1.