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!
A Parent's Secret Weapon for Smart Kids
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Here's an example: if x2 = 64, then 5 is too low while 10 is too high, let's guess x = 7. Test it out: 72 = 49, a bit low. How about 8? Success! 82 = 64.
Not all variables are as easy, but that's the idea. Try this quiz to get the hang of it. Take your time, read each question carefully, and give it your best shot. Good luck with your KS3 Maths journey!
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1.
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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? |
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[ ] |
Try to remember formulas that might help |
[ ] |
Multiply x by six different numbers |
[ ] |
Make an intelligent guess at the value of x |
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Move on to the next question |
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2.
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After you have made an intelligent guess at the value of x what do you do next? |
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Assume that you guessed correctly |
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Guess another value for x |
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Guess another three values for x |
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Put your guessed value into the equation in place of x |
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3.
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After you have put your guessed value into the equation in place of x what do you do next? |
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Work out the equation using your guessed value |
[ ] |
Sing a hymn |
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Dance a jig |
[ ] |
Recite a poem |
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4.
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When you work out the equation using your guessed value, you find that your value is too high so what do you do next? |
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Make another guess that is higher than your first |
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Make another guess that is lower than your first |
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Make three more guesses that are higher |
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Make three more guesses that are lower |
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5.
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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? |
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0 |
[ ] |
2 |
[ ] |
10 |
[ ] |
20 |
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6.
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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? |
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50 degrees C |
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75 degrees C |
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100 degrees C |
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200 degrees C |
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7.
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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? |
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301 |
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302 |
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350 |
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399 |
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8.
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x2 + x3 = 80, what is the value of x? |
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9.
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x3 - 2x = 115, what is the value of x? |
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10.
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x2 + 4x + 7 = 14x - 9, which of the following is a possible value of x? |
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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 |
[x] |
Make an intelligent guess at the value of x |
[ ] |
Move on to the next question |
|
|
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 |
[x] |
Put your guessed value into the equation in place of x |
|
|
3.
|
After you have put your guessed value into the equation in place of x what do you do next? |
|
[x] |
Work out the equation using your guessed value |
[ ] |
Sing a hymn |
[ ] |
Dance a jig |
[ ] |
Recite a poem |
|
|
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 |
[x] |
Make another guess that is lower than your first |
[ ] |
Make three more guesses that are higher |
[ ] |
Make three more guesses that are lower |
|
|
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 |
[x] |
2 |
[ ] |
10 |
[ ] |
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 |
[x] |
100 degrees C |
[ ] |
200 degrees C |
|
|
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 |
[x] |
350 |
[ ] |
399 |
|
|
8.
|
x2 + x3 = 80, what is the value of x? |
|
|
|
9.
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x3 - 2x = 115, what is the value of x? |
|
|
|
10.
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x2 + 4x + 7 = 14x - 9, which of the following is a possible value of x? |
|
|
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