Topic: Algebra LO: Being able to do Trial and Improvement. AGREE LEARNING OBJECTIVES PREPARE FOR LEARNING STARTER CAN YOU SOLVE THIS EQUATION…? x 3 + 2x = 110

PRESENT NEW INFO When x=4, x 3 + 2x = 110 TOO HIGH! x 3 + 2x = = = 72 TOO LOW! x 3 + 2x = = = 135 When x=5, So x must be between 4 and 5!

Solve x 2 + x = 53 correct to 1 decimal place This means we need to find a number with one decimal place which gives the closest answer to 53 To get all the marks in the exam we need to: First find the two whole number values of x that will give the closest answers to 53: one will be a bit too small, the other will be a bit too big Then ZOOM in between these two numbers to find the two numbers with one decimal place that give the closest answers to 53: again one will be a bit too small, the other will be a bit too big To work out which one of those to numbers is the BEST answer you need to ZOOM in again to HALFWAY between them, then you will be able to see which one was closest to 53 – and sometimes you may be surprised This last step is the most commonly missed out part because sometimes it seems unnecessary, but missing it out will lose you marks in the exam Let’s do it! CONSTRUCT MEANING

xx 2 +x 642too small 756too big Solve x 2 + x = 53 correct to 1 decimal place First find the two whole number values of x that will give the closest answers to x must be between 6 and 7

Solve x 2 + x = 53 correct to 1 decimal place xx 2 +x 642too small 756too big ZOOM in between these two numbers to find the two numbers with one decimal place that give the closest answers to 53 Let’s zoom in!

Solve x 2 + x = 53 correct to 1 decimal place xx 2 +x 642too small 756too big too small too big too small Now we try sensible values to find the two best values of x with one decimal place. Let’s try halfway for starters Let’s try a bit higher but still just one decimal place The best answer to 1dp will be either 6.7 or 6.8, but which one?

Solve x 2 + x = 53 correct to 1 decimal place xx 2 +x 642too small 756too big too small too big too small ZOOM in between these two numbers to HALFWAY – then we’ll be able to see which side the true answer lies Let’s zoom in! is this side of half way So 6.8 is the best value of x to 1dp 6.8 We write: x = 6.8 to 1dp It may seem like 6.8 was obviously the closest answer, but without this final checking stage you will lose marks!

So In Summary… Find the best two whole number solutions Zoom in to find the best two solutions to 1dp Zoom in halfway to find which one of them was the closest overall xx 2 +x 642too small 756too big too small too big too small Answer: x = 6.8 to 1dp You write this:

DEMONSTRATE UNDERSTANDING Some questions for you to do… WORK IN YOUR BOOKS – COPY DOWN THE QUESTION MORE TRIAL & IMPROVEMENT QUESTIONS: The equation x 3 – 6x = 72 also has a solution between 4 and 5 Use a trial and improvement method to find this solution. Give your answer correct to one decimal place. You must show all your working. x 3 − 3x = 15 (has a solution between 2 and 3) x 3 + 2x = 99 (has a solution between 4 and 5)

CONSTRUCT MEANING Reading x and y values from a graph – An example Extension: What line is this?

DEMONSTRATE UNDERSTANDING A questions for you to do… DRAW THE GRAPH IN YOUR BOOKS – COPY DOWN THE QUESTIONS

DEMONSTRATE UNDERSTANDING – EXTENSION WORK Level ladders… algebra

So what have we learned? REVIEW LO: Being able to do Trial and Improvement. So what are the steps to follow to solve an Equation using Trial and Improvement?