DS(11) struggling with maths problem solving questions

[CharbaLabaDingDong]

My DS(11) has always struggled with maths problem solving questions.

We worked really hard on this when he was in Year 6 and he did improve, to a point.

We raised it with his maths teacher during parents' evening in January and felt reassured that it was something they were on top of.

During Easter break his tutor (who is also a maths teacher) has been setting them a daily maths question, some of which are problem solving questions, and he literally doesn't know where to start. Not a clue. Even when I give him a hint he struggles.

We will be raising this at the parents' evening in May, but I was just wondering if anyone else's DC has a similar issue and if the can recommend anything to help.

Thank you

Some advice we were given is to always pull the numerical information out from the words because some people have brains that just process the information better once it’s presented that way.
Really simplistic version, but along the lines of:
3 apples cost £75p and a bag of oranges costs £2.10, would become:
3A = £0.75
O = £2.10
Get rid of all the extra information!

Thank you Whyisitallsostressful

We do try and get him to pull out the relevant information, which he can do if it's a one step question (I.e. 3 apples cost 75p and 3 oranges cost £1. What is the total cost).

2 step questions pose more of a problem (I.e. 3 apples cost 75p and 3 oranges cost £1. You have £5. How much change would you get if you bought the apples and oranges?). Again, this is much simpler than the questions he's actually doing but he would be able to pull out the relevant information but then wouldn't know whether to add, subtract, multiply or divide.

I'm just at a loss as to how to help him without actually doing it for him!

A few things that might help:

start at the end. If the question says 'how much change', what do you wish you knew that would make it an easy problem? If he can then say 'how much I spent', you can then go one step back. What do you wish you knew that would help find out how much you spent? 'how much I spent on apples and on oranges'. Does the problem tell you that? Does it give you information to work it out? What would you need to know? How many you bought, what price? Do you have all that? Yes. Then you have a plan. Work out how much you spent on apples, and how much on oranges, and put them together, and then work out the change.

If he finds it hard to work out which operation to do, try simplifying the question to really easy numbers, and see if he can work it out. So if he can't work out 3 apples at 75p, try 3 apples at 10p. If he can do that in his head, then get him to think about what he did. What operation linkes the 3 and 10 and 30? If he can say 'added it up three times' or 'multiplied', then get him to do the same with the more complicated numbers. Sometimes this can be a useful step to work out unconnected to a particular problem - ask children to work out what they did with the numbers 15 and 7 to get the answer 8, or with 16 and 2 to get the answer 8. They can often see the relationship (e.g., that you add 7 and 8 to get 15, or that double 8 is 16, but don't know how to put that in a mathematical 'sentence') to get the answer part coming out as the answer.

It can also help a lot to use drawings, diagrams, practical objects, concrete visual aids, etc., and to imagine actually going through the motions. Money can sometimes be quite a good sort of problem for this, and it can help to convert other problems to money at times. So if you're trying to work out 8 tickets at £2.50, actually having them picture/draw 8 two-pound coins, and 8 50p coins, and add them up. Because money is so familiar to children, especially older children, they can often do problems that they can't do when they're just ordinary numbers (especially decimals). I know children who insist they can't find half of 1.5, but have no problem splitting £1.50 between two, etc.

I used to really struggle with maths problems (went on to pass maths A-Level when I was older so it is possible to learn to do it!).

I used to start at the end as has been suggested and follow it through like that.

It really is just practice, practice, practice.

Thank you. I will definitely try starting at the end and working back. And I agree, practicing lots is very important.

Units of the different quantities (starting from the end of the question) is helpful (eg is it a cost -£; or length - m; or area m^2; or weight - kg; or speed - m/s).

If you are supposed to calculate a speed (m/s) then the values you will need are a distance (m) divided by a time (s) - as is shown in the units.

I came on to say tell him to start at the end but picklefish has a great reply there.

He needs to figure out what they are looking for first and work backwards from there. In two part questions the piece of info found in the first bit is usually what is needed to solve the end question.

I’m sitting functional skills maths this coming week, which is an scam based entirely on word problems. I’ve had to learn how to decode these and it can be very confusing! I now look at the end first to check exactly what kind of answer they are looking for. Then I go back and read the whole question carefully and work through it step by step.
Honestly it’s a case of practice practice and practice for these sort of problems. And like anything eventually it starts to get easier.

exam not scam!

If he is getting completely stuck on the two step problems. My advice would be to do lots with him. (Literally sitting beside him). Start off by telling him the intermediate step. E.g. Three Oranges cost £1.50. If I buy 5 oranges how much change do I get from £5. You could initially tell him what is the price of one orange? What is the price of 5 Oranges? What is your change?. Do lots of very similar questions until he can work out the intermediate questions himself. Still sit by him but ask him - what do we need to work out next? A good intermediate step is to pick out a single piece of information from the text. e.g. Three oranges cost £1.50 and ask him what we could use this information to work out. Once he's got that example start by giving him an almost identical example. E.g. five chocolate bars cost £2 how many could I buy for £2.50? Do the intermediate steps with him if necessary. Then move to slightly different questions.

Another technique I've found is to try and have him rewrite the information more simply. For example instead of three oranges cost £1.50 have him write 3 x oranges = £1.50.

Thank you all. I think I'll find some problems from the KS2 SATS papers to have a go at and get him to pull out the relevant information to simplify it and then work backwards.

Remember RUCSAC.
R - Read the question - what does it really say, if you can't read a word or it doesn’t make sense ask an adult to read it to you.

U - Understand the question - what is it asking for, visualise what is happening, underline the key information, draw a diagram if necessary. Consider/ estimate what a sensible answer might be.

C - Choose the calculation - the clue will be in the language - you can find lists online of which operations key words would indicate, but context is key. Write the calculation in a mixture of words and symbols.

In a two-step operation, one piece of information in the calculation is missing and has to be derived as the first step. Put the calculation to obtain the missing information in a box beside the main calculation. Dividing the page in half and putting the second-step calculation on the right hand side, and then the first step calculation in a box on the left hand side can make things more organised.

S - Solve the calculation(s). Write it down, even if solved mentally. Always show the working out as often there are method marks. Start each part of the calculation on a new line so each line makes mathematical sense (what is each side of the = should be equal).

A - Answer the question. Sometimes this involves rounding up or down, depending on the context e.g. if the solution to the calculation is a fraction but the question is “How many children...” the answer needs adjusting to the next whole number above or below. Similarly, a money or measurement question may need converting into the requested units.

C - Check the answer. Is it reasonable? e.g. if your answer suggests a cat weighs 500kg or 500g, it's likely to be wrong. If you multiplied by 5 then the answer should end in 0 or 5. Have you put the right units in?

Sometimes, having a similar question with different numbers, and the answer, and working out how to reach the answer is a useful strategy.

One thing I have seen recommended, but not tried myself, is give the information, but not the final question, and instead say 'What can you work out from this?'

So 3 Apples cost 75p and an orange is 50p and I have £10.

I can work out

• price of a single apple
• how much more an orange costs than an apple
• how much 3 apples and 1 orange costs (and any other combination)
• the change from £10 depending on what I buy

It turns it from having to do 1 hard looking thing, to spotting what you can do, apparently.