Solving Equations x + 3 = x Great Marlow School Mathematics Department Lesson Objective : To be able to solve linear equations.

21 6x The length of this line is 21 units. It is made up of two parts. x units; and 6 units. The equation for this line is x + 6 = 21 Great Marlow School Mathematics Department

6x 21 6? x + 6 = x = Great Marlow School Mathematics Department What is the equation for this line?We should think of the “21” like this. Now we can take 6 from both parts of the line, i.e. both sides of the equation.

z + 8 = 23 Draw the number line for this equation. 23 8z Now solve the equation. Remember to show the working out. z + 8 = z = 15 ? 8 15 Slide 7 Great Marlow School Mathematics Department

x + 4 = 25 Draw the number line for this equation. 25 4x Now solve the equation. Remember to show the working out. x + 4 = x = 21 Slide 7 ? 4 21 Great Marlow School Mathematics Department

y + 5 = 17 Draw the number line for this equation. 17 5y Now solve the equation. Remember to show the working out. y + 5 = y = 12 Slide 7 ? 5 12 Great Marlow School Mathematics Department

Try this exercise. First, draw the number line, then solve the equation. 1.x + 5 = 92. y + 6 = 143. a + 3 = b + 8 = 135. z + 9 = 236. c + 7 = x x + 5 = x = 4 y 14 6 y + 6 = y = 8 6 Great Marlow School Mathematics Department

Try this exercise. First, draw the number line, then solve the equation. 1.x + 5 = 92. y + 6 = 143. a + 3 = b + 8 = 135. z + 9 = 236. c + 7 = 38 a + 3 = a = 23 b + 8 = b = b38 26 a Great Marlow School Mathematics Department

Try this exercise. First, draw the number line, then solve the equation. 1.x + 5 = 92. y + 6 = 143. a + 3 = b + 8 = 135. z + 9 = 236. c + 7 = 38 z + 9 = z = 14 c + 7 = c = c97 23 z Great Marlow School Mathematics Department

15 3x What if the number line is made up of more than two parts? What if it looks like this???? What would the equation of this line be? x 2x + 3 = x = 12 x = 6 (because 12 ÷ 2 = 6) ?12 Great Marlow School Mathematics Department

How would this equation be represented on a number line? Now solve the equation. 3x + 5 = x = 18 x = 6 (because 18 ÷ 3 = 6) 23 5 xxx ? Great Marlow School Mathematics Department

Now try this exercise. Remember to draw the number line to represent the equation before you solve the equation. 1.2x + 7 = y + 4 = z + 6 = x = 4 3y = 15 4z = 20 x = 2 y = 5 z = 5 4.2a + 9 = b + 8 = c + 6 = a = 12 4b = 12 5c = 15 a = 6 b = 3 c = 3 Great Marlow School Mathematics Department

15 5 2x x x 3x The equation for this line is 3x + 5 =x x -x 5 ? 2x + 5 = x = 10 x = 5 Great Marlow School Mathematics Department Let’s think of the 3x as x + 2x. We can take x from both parts of the line, i.e. both sides of the equation. Now we can proceed just as we did in the last exercise.

Draw number lines for the following equations and them solve them. 1.2x + 4 = x y + 6 = y z + 3 = z x -x -y -y -z -z x + 4 = 10 2y + 6 = 15 3z + 3 = x = 6 2y = 9 3z = 21 y = 4.5 z = 7 4.3a + 7 = a x + 8 = 2x b + 5 = 3b a -a -2x -2x -3b -3b 2a +7 = 35 3x + 8 = 23 3b + 5 = a = 28 3x = 15 3b = 15 a = 14 x = 5 b = 5 Great Marlow School Mathematics Department

Plenary: Three children all solved the same equation. Only one has the correct answer. Who is it? What did the other 2 do wrong? Ann 4x + 6 = 2x x -2x 2x +6 = x = 20 X = 10 Bilal 4x + 6 = 2x x 2x + 6 = x = 14 x = 7 Charlie 4x + 6 = 2x x + 4 = x = 16 x = 4 The question is worth 3 marks. How many points would you give to each student and why? Great Marlow School Mathematics Department

Teacher’s Notes I put this together for my 8 set 4 pupils who struggle with abstract topics. They need lots of practice and things need to be gone over several times. Some of the animations move on mouse click where I knew that I wanted to talk about what and why, others are on after previous where I wanted it to flow. The hyperlink on slides 4, 5 and 6 will take you to the exercise on slide 7 if your group doesn’t need the reinforcement of the procedure. There are speed up sheets on slides 16, 17 and 18 for drawing the number lines. I didn’t try to put anything like 3x – 4 = 11 into the presentation as I couldn’t think of a way to represent it without confusing the pupils. However when we did equations with the negative they transferred the skills easily enough and could see the link to using the opposite operation. This took me 2 full lessons to get through with my set 8 – 4. The plenary was added later using answers I got from a homework set after the lesson. If you spot any mistakes please me at Debbie Beach