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How many sisters has Louise got?

# Level 5-6 Algebra - Trial and Improvement

In KS3 Maths, tackling algebra means figuring out the value hidden behind a letter. It might seem tricky, but there's a cool method to help: trial and improvement.

Trial and Improvement is like clever guessing. When there's no obvious way to find a letter's value, you use the knowledge you already have to make a smart guess. You'd be surprised at how much the things you've already learned (times tables, factors, multiples etc.) come in useful!

1.
You are given a value for x within an equation and told that you need to work out the answer by trial and improvement. What is the first thing you do?
Try to remember formulas that might help
Multiply x by six different numbers
Make an intelligent guess at the value of x
Move on to the next question
Choose a number which you think is likely to be close to the real value
2.
After you have made an intelligent guess at the value of x what do you do next?
Assume that you guessed correctly
Guess another value for x
Guess another three values for x
Put your guessed value into the equation in place of x
Work the answer out. This will tell you whether your guess was too low, too high or exactly right
3.
After you have put your guessed value into the equation in place of x what do you do next?
Work out the equation using your guessed value
Sing a hymn
Dance a jig
Recite a poem
We expect you got that one right!
4.
When you work out the equation using your guessed value, you find that your value is too high so what do you do next?
Make another guess that is higher than your first
Make another guess that is lower than your first
Make three more guesses that are higher
Make three more guesses that are lower
Make one guess at a time and go through all the processes again. Gradually you will narrow it down to the correct answer
5.
You are told that Louise has some sisters and, within an equation, the number of sisters she has is represented by x. What would be a good first guess for the value of x?
0
2
10
20
We know that Louise has SOME sisters so we know that 0 sisters is impossible. It is not likely that she has 10 sisters and even less likely that she has 20!
6.
Within an equation, the boiling point of a solution is represented by x. What would be a good first guess for the value of x?
50 degrees C
75 degrees C
100 degrees C
200 degrees C
100 degrees C is the boiling point of water and would make a good starting point
7.
You are told that the value of x lies somewhere between 300 and 400, and you are given an equation containing x. What would be a good first guess for x?
301
302
350
399
Going to the midway point is usually a good idea - depending on the answer you will then know in which half the answer is
8.
x2 + x3 = 80, what is the value of x?
2
3
4
5
2 would be too low and 5 too high so 3 and 4 are good numbers to begin with
9.
x3 - 2x = 115, what is the value of x?
3
5
7
9
3 would be too low and 9 too high. I hope you chose 5 or 7 as your original estimate
10.
x2 + 4x + 7 = 14x - 9, which of the following is a possible value of x?
3
4
6
8
Each time that you make a guess, record the guess. Then by a process of trial and error you will find the correct answer
You can find more about this topic by visiting BBC Bitesize - Equations with one unknown

Author:  Frank Evans

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