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 Post subject: AdvicePosted: Thu Oct 25, 2007 10:31 am
I have been told not to teach my son algebra that i should let him do trial and testing?

Question like there are 324 pupil in a class and the girl are 36 more than the boys, how many girls are in the class?

Can the Maths teachers here please advice. What is trial and testing?

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 Post subject: Posted: Thu Oct 25, 2007 11:10 am

Joined: Thu Jan 12, 2006 3:29 pm
Posts: 625
Hi Guest23

To work this sum out

Divide 324 by 2 = 162

Divide 36 by 2 = 18

Add 18 to 162 = 180

There are 180 girls

Subtract 18 from 162 = 144

There are 144 boys

The difference between 180 and 144 is 36

Algebra is not necessary to answer this type of question.

Trial and testing related to algebra questions tend to be based around working out equations, for example

2x + 4 = 4x - 10

Test with a random number i.e. 2, substitute to give

4 + 4 = 8 - 10
8 = -6
Does not work

Try 5

10 + 4 = 20 - 10
14 = 10
Does not work, but the values are getting closer

Try 7

14 + 4 = 28 - 10
18 = 18
The correct answer is x = 7

In a multiple-choice format test five answer options are provided. Trial and testing would involve the student substituting the given answer options into the equation until the correct answer is found.

Regards

Mike

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 Post subject: Posted: Thu Oct 25, 2007 11:20 am

Joined: Tue Dec 13, 2005 12:49 pm
Posts: 1647
Location: berkshire
I dont think you need 'trial &testing' for this type of question.

324 less 36 = 288

288 divide by 2 = 144

144 + 36 = 180

Girls 180, boys 144

trial and testing tends to be used when you are given an equation.

4x + 1= 33

start with say 5.....4x5 =20 + 1 + 21 therefore x must be larger than 5

hope this makes sense.

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 Post subject: Re: AdvicePosted: Thu Oct 25, 2007 11:22 am
Trial and testing or "Trial and Improvement" in essence means to try values out and then refine the value initially tried.
In this case the girls outnumber the boys by 36, so choose a value for the boys eg 100, so there would be 136 girls. I teach my students to set up a table to record their results, see below.
boys girls total
100 136 236 [total too small] so try a number larger than 100
150 186 336 [total too big] so try a value between these
148 184 332 [too big]
146 182 328 [too big]
143 179 322 [too small]
144 180 324

therefore there are 180 girls altogether.
This method is tested at KS3 & KS4 although the questions are of the type: solve x-squared + 3x = 56 giving your answer to 1 decimal place using trial and improvement.

You don't mention the year group your son is in. Is he in KS2?
I hope this is of help to you.
C.

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 Post subject: Posted: Thu Oct 25, 2007 3:47 pm

Joined: Mon Feb 12, 2007 1:21 pm
Posts: 13994
Trial amd improvement is only recommended for questions that CAN'T be tackled any other way - or where the question specifically tells you to use that method.
It is not used for linear equations as Mike suggests - in fact pupils will be penalised at KS3 and GCSE for doing this.

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 Post subject: Posted: Thu Oct 25, 2007 3:53 pm
Thank you all, my son is doing 11plus soon.

I am always comfortable with algebra as i know that most maths problem can be solved with algebra.

The trial and improvement is a very long method of solving problem but i have been told that it is the best way for this age group.

Once again, thank you all

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 Post subject: Posted: Fri Oct 26, 2007 2:59 pm

Joined: Thu Jan 12, 2006 3:29 pm
Posts: 625
Hi Guest55

Guest23's son is sitting 11+ tests not KS3 or GCSE tests. This, although not known at the time, was assumed when I gave my explanation as this is an 11+ forum. I did not make any reference to KS3 or GCSE in my posting.

There are two clear methods to working out 11+ Mathematics questions that are of a multiple-choice format, firstly to work the question out directly from the information provided and check that the answer arrived at is one of the answer options, secondly to use the answer options provided and use a trial and improvement technique to work the question out. No child will be penalised in the 11+ test for using trial and improvement to work out a linear equation.

Given the following question:

4x -10 = 2x + 4
Choose the value of x from the options provided

A 8
B 5
C 7
D 6
E 4

Option 1 work out the answer (using any conventional method)
4x - 10 = 2x + 4
Subtract 2x from both sides
2x -10 = 4
2x = 14
Divide both sides by 2
x = 7

The correct answer is C x=7

We cannot assume that a child sitting the 11+ test has been taught a conventional method of working the question out, so therefore they need to apply an alternative technique such as substituting each value from the answer options until they find a correct answer. When tutoring children for 11+ tests the following technique is "most adviseable".

4x - 10 = 2x + 4

A 8
B 5
C 7
D 6
E 4

Substitute 8 gives
32 - 10 = 16 + 4
22 = 20
Incorrect

Substitute 5 gives
20 - 10 = 10 + 4
10 = 14
Incorrect

Substitute 7 gives
28 - 10 = 14 + 4
18 = 18
Correct

There is only one correct answer so we do not have to test for answer options D or E.

The correct answer is C, x=7

Regards

Mike

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 Post subject: Posted: Fri Oct 26, 2007 4:59 pm

Joined: Mon Feb 12, 2007 1:21 pm
Posts: 13994
Sorry Mike - I do not agree - you should never teach a method that has to be unlearnt -

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 Post subject: Posted: Fri Oct 26, 2007 5:31 pm
Dear Guest 23,
I would not overly concern yourself with which method is 'best' - It is the method that works for your son (at this stage) that is important. I work with primary children (as a parent helper I hasten to add) and I am amazed at the number of 'different' methods children are taught to answer 234 x 432! Grid method etc etc. The methods that have been explained here are merely that - different methods to get the same result. Be guided by your child and follow his/her lead.
Belinda

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 Post subject: Posted: Fri Oct 26, 2007 8:20 pm
To teach algebra properly you need quite a few lessons. I used to try and teach the children the proper way of solving equations but many found it difficult and it was time consuming. Being pragmatic, I know suggest they substitute answers until they get the right one. I also don't really worry if they don't get it, as we're probably only talking about 1 mark's worth.

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