How to help DD solve percentage word problems??

[eliphant]

DD is doing KS3 Maths... Percentages. She can do simple sums like finding what is 30% of 150. No problem.

But questions like the following really stump her :

"Sue used to earn £70 per week. Now her salary has increased by 30%, so how much does she earn now?"

Or

"Tom earns £60 a week now but he used to earn 20% less than that per week. How much did he used to earn?"

She's tried Conquermaths videos, Mathshub videos, she's seen loads of example questions worked out in front of her, and even I tried to explain it to her too, but once she's on her own, she just cannot do those word questions by herself. She doesn't even know how to start. Or she would attempt to do some random calculations in an attempt to try and do "something" about solving the question, but they don't make logical sense and don't solve any part of the problem.. She can't really make sense of them either

I don't know if it's just the complexity of word problems that floor her.. Wonder if anyone has any advice?

[TeaBelle]

Could she underline the numbers in coloured pen. In the examples there are only 2 numbers so getting the sentences into a sum shouldn't be a huge step from there.

[Pregasaurusrex]

As a teacher, the best way to get children to solve word problems is for them to visualise what the question is asking. If that makes sense. I've always got children to draw the problem. Might help!

[winchester1]

It is just practicing making a sum.from.the sentence. Also practicing working percentages backwards would be good so I now earn 120,after a 20% pay rise,what did I earn yesterday. For me at least it made the words less scary as I could work it out either way.

[dementedpixie]

Make it clear that there is more than one step in the process: first step is doing the percentage bit and the next is to add or subtract to get the correct answer. Maybe she is rushing to try and work it all out at once rather than breaking it down into stages

[Smartiepants79]

I would ask her to look first at what we already know
-what she used to earn
-the percentage the salary has gone up by

Then look at what she needs to find out
-how much is the salary now


Does she understand the language - that increased means it will be larger.
Also look at bar modelling, we use it and it's meant my yr 6 kids can answer this type of question fairl easily.

Does she find all 2 step word problems difficult or is it just percentages?

[eliphant]

Yes she knows she has to make a sum from the sentence first before solving it. She struggles to do that. She gets confused about the old amount and the new amount.

In the second question example I gave above for instance, she'd go and try to find out what 20% of £60 is, then try to minus the answer from £60 to find what Tom used to earn. When she should be working out what 1% is by doing 60/120 then multiply that answer by 100 to find the answer.

In the first question example I gave, she would for instance, try to find out what 1% of £70 is, then multiply that answer by 30 to find out what 30% is. When she could just find it by finding out what 30% of £70 is first, straight away. Then add that to £70 to find the new wage.

She seems confused by the methods to work out the old or new amounts. You've got working out percentage increases and decreases - different steps involved. When she sees a percentage word problem like that, she can't seem to understand what method she must do.

How to help her figure out which method for each percentage word problem she sees? Seems like there are ever only these 2 types of percentage word problems they ask her at this level (the examples I gave above). And two distinct ways of working out the answers - trick is to figure out whether it is a reverse percentage word problem or not.

I'll give her more practice at it...not sure how else to go about it.

[thecatfromjapan]

I agree with all the above but I would listen to how she is trying to work these sort of questions out at the moment. What bit of the problem is she finding most difficult? Is it the word problem aspect? Is it working out what is going on in the situation the question poses? Is it the method of finding the percentage?

My guess is that she has been shown lots of methods to attack word problems, so it is going to be the last two areas that are throwing her.

As a Pegasaurus said, visualising what is going on is fantastic. Get her to actually draw or write what is going on, in whatever way she feels most comfortable with. I, personally, actually like to draw things out, but she could also visualise these things in a more formal way, eg.

70 -> ???
70 --> 70 + (30%


It might then be a question of how comfortable she is working with percentages. It's worth remembering that there are SO many different ways of working out percentages, and she needs to experiment to find out the method that she likes best.

She should try lots of different ways, and find out (for herself) which way makes most sense to her and is therefore mnemonic and obvious to her.

For instance, my favourite way is to would also try to think of the "now" figure/amount as 100% and to look at the question that way:

eg. 100% --->130%
70 ---> ?

Now, when I look at that, I know that if I want to find 100% of a number, I multiply it by 1 (100% of 70 is 70 x 1), so a quick way of working out 130% is to multiply 70 by 1.3 (70 x 1.3).

However, there are lots of different ways of finding out the percentage, she has to find her favourite.

Does that make sense, or is it more confusing?

[thecatfromjapan]

Tom earns £60 a week now but he used to earn 20% less than that per week. How much did he used to earn?

Step 1. Rephrase the question, until it makes more sense:

Tom earns £60. He used to earn 20% less.

• OK. So, right now, what Tom earns is 100%. It is also £60. £60 = 100%.
  

(Perhaps draw it/visualise it in some way at this point. :-) )

• Right, so Tom was earning 20% less than that.
  

• So if this figure - the now figure; the £60 - is 100%, what is 20% less than 100%?
  

(Answer: 80%)



Step 2. Draw it out, in whatever way makes sense to you:

???

[eliphant]

I don't think she is comfortable working with percentages. She has been taught 100% of something is 1 x that thing. However even in simple sums like the first one, she would never do 1.3 x 70 to find the answer. She just tries to find what 30% of 70 is, then add that to it.

She struggled a lot with compound interest calculations. If the question says "If Jim has £60 in the bank, and the bank pays 5% interest yearly, how much would Jim have in the bank after 5 years if he doesn't add to it or take any money from it?" What's instinctive to her is to first find out what 5% of 60 is, then add that to 60 to find out what Jim has in the bank after 1 year (£63). Then she'd find out what 5% of £63 is, then add that to £63 to find out what Jim has in the bank after 2 years. Then repeat the process another 3 times laboriously to find out what Jim has in the bank after 5 years.

She really struggled with understanding that doing 1.03^5 x 60 would get her the final answer straight away. Formulating this was hard for her to understand. Now she can write out this formula for compound interest by practicing it many times, but I suspect she still never really understood the concept behind it. Which is why I have never seen her use 1.(something) x the old amount to find the new, increased amount of something. She will always want to solve questions like the first one I gave by first finding out the percentage of the old amount in absolute figures, then adding that to the old amount to find the new amount.

Problem is with percentage word problems, she can no longer just memorise a certain way of solving the problem in order to solve it, as these percentage word problems can come in many ways and phrased in many ways... I think she needs to understand the underlying concept somehow in order to work out how to solve each individual question she comes across. Concept is the same no matter what question is asked, but she can't seem to apply what she's learnt about percentages to solve the word problems.

I don't know how to help her with that... I really do appreciate all the responses so far though. It does give me some alternative ways of thinking to work with... I suspect she needs help with understanding how to apply what she's learnt so far about percentages to solving word problems. Because she has no problems at all doing simple straightforward percentage problems like "What is 30% of 360?" Or "write 30% as a fraction/decimal."

[eliphant]

Sorry should have said above 1.055 x 60, not 1.035 x 60

[thecatfromjapan]

I don't think there's anything wrong with working out what 80% of 60 is by doing something like working out 10% (£6) and then multiplying that by 8. I think that would be grand, actually, and possibly quicker than multiplying by 0.8 for some children.

I think you're right that it comes down to lack of comfort with percentages.

What about going backwards to go forwards? Have some stratightforward percentage questions (eg., find 130% of blah; find 70% of blah) and the two of you have a mini-competition to see how many ways you can think of to find the answer?

That might help her feel comfortable with percentages, and help her find the method she likes best?

Then, when she's comfortable, move forward to word problems again?

Lots of people hate these!!! But she has loads of time to practice!

I'm really rubbish at making mayonnaise but I intend to practice quite a lot over the next few months, and see if I can (finally) crack it.

Bits and bobs of maths (and everything else in life) are daunting when you meet them for the first time, but practice makes most things less tricky.

[eliphant]

On a separate note, she does understand that 100% of something is 1 of something though...😕

So she seems to understand the percentage concepts if taken separately, but not have any idea how to use those concepts to solve percentage word problems.

I will try working with her on visualising more.

Hopefully that will be it.

We have always gone through visualising with her but she never seemed to take to it. Visualising seems difficult for ger.

[Tillyscoutsmum]

Check out bar modelling (lots of online videos) to help with visualising word problems.

[thecatfromjapan]

Translator's note:

By the way, I don't quite understand what you mean by 1.03^5. I take that to mean 1.03 multiplied by itself 5 times. I'm not so good with mathematical notation on keyboards. Sorry.

If you mean 130% as a decimal, I'd write that as 1.3

[eliphant]

I notice that unless prompted, she never visualises stuff or writes down things like that. In fact she used to really resent doing working so when she got an answer wrong in Maths, she could not explain how she got the answer... It took a long time. She seems to find it hard to explain her process of thought and doesn't attempt to visualise things in word problems (though she's been shown lots of times to do this).

[eliphant]

Catinjapan : 1.035 means 1.03 to the power of 5. But anyway that was a typo on my part sorry. I should have typed 1.055 instead!

[thecatfromjapan]

Oh!

D'oh!!!! That was compound interest!!!!

That'll teach me to speed read!

[thecatfromjapan]

[eliphant]

:)

[eliphant]

By the way I don't think her method of working out compound interest is bad. I agree with you. It is just laborious. And the problem is, every time she tries to do it like that, her final answer is inevitably wrong! She would get muddled up in the process by the numbers. Plus the final answer would be a couple of pence more or less than the answer scheme because of all the rounding off she has to do for each laborious step..

[eliphant]

And that is if she didn't get muddled up by the numbers along the way... Most times though she'd get a totally wrong answer because she would muddle up some numbers along the way - forgetting to add the interest to the amount of money in the bank in the 3rd year, but rather adding the interest to the amount of money in the bank in the first year... Etc.

[thecatfromjapan]

Perhaps she doesn't need to visualise most things and thinks it's a bit "young" for her? Children are funny animals, and their self-esteem can be quite fragile. You could try suggesting she just try to draw out percentage things until the penny drops for her.

Or it might just be that she needs to do a number of them until she has that penny drop moment.

Children are very strange. Lovely, but strange. I think dealing with their self-esteem and confidence is the toughest thing.

[thecatfromjapan]

I feel for her - and you.

Do you think there are many people in the world who get wildly excited about those compound interest questions?

I suspect it will all come in time.

I think it's great that she will let you work with her. I'm jealous. Neither of my two will. Though my dd will show me how to do stuff. which is something, I guess.

[eliphant]

She has never liked showing working or visualising, even when she was younger. She used to just write her answers down with no working. Only in the past year or so she has been taught to set out her working to answers systematically and she really hated it and resisted doing it.

She's always struggled with Maths. I guess it's going to get harder but I was just wondering how to help her with this one. It might just be that she just needs more time to mature and grow. I don't think there's much more I can do about it, it seems.

[PreAdvent13610]

"Tom earns £60 a week now but he used to earn 20% less than that per week. How much did he used to earn?" your daughter's method is right.

"Tom earns £60 after a 60% pay rise. How much did he used to earn?" your method is right.