i'm stuck on my maths homework

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When looking back on their mathematical experiences, we would be pleased if our pupils were able to say that they had an introduction to the subject which prepared them well for the future at whatever level was appropriate to their needs. There is no doubt that this involves more than being able to answer standard test questions. It includes pupils feeling empowered to work independently, try things out, and not think there is something wrong when they get "stuck". When was the last time you felt stuck doing some mathematics and how willing were you to share that feeling, or the few ideas you had about what to do, with others? What does it mean to a problem solver to be stuck? In order to attempt to answer this question, before you read any further, you might like to try the following problem called Nine-pin Triangles which asks how many different triangles you can make on a circular pegboard that has nine pegs.  

As you worked on this problem, were there any times when you felt stuck? What exactly were you stuck on? Were you able to start the problem immediately? Did you want clarification of anything at any stage? Did you feel as if you reached a solution which you're happy with? Why or why not? How did you reconcile any questions you had? Your response to this last question might well depend on whether you were working alone or not. When I first tried this problem (which was inspired by the work of Geoff Faux), one of the barriers I came up against straight away was the notion of difference. What makes one triangle different to another in this context? Linked with this was the horrible feeling that there must be hundreds of triangles! How would I know when I had found them all? I guess being stuck on this problem for me was initially about seeking reassurance to some extent. I wanted to talk to someone else about what "different" meant and then I experienced a feeling that perhaps is quite common for many of our pupils, that the problem was insurmountable because of the huge number of possibilities. In this instance, I was in a room with colleagues so I was able to come to a satisfactory meaning of "different" in discussion with them. Although I was daunted by there being too many triangles to find, my experience of solving problems gave me the confidence to draw on strategies I believed would help - developing a system for finding the triangles one by one, for example. By working systematically I could convince myself that I had found them all. You might have noticed that I used the adjective "horrible" in the previous paragraph to describe how I felt. Is this a common emotion associated with being stuck? How did you feel while tackling the problem? Being stuck is usually thought of as being a negative state of affairs, and so it is, in the sense that progression seems out of reach or pointless. At first glance, it is easy to suggest that we don't want our pupils to get stuck. Surely we shouldn't have a desire for them to be floundering as they work on mathematics? As teachers, our instinct can sometimes be to scaffold to such an extent that the children are not really thinking for themselves. We want them to succeed, to get the "right" answers, not to struggle. Or do we? Going back to my own experience of working on the Nine-pin Triangles problem, the feelings I had as I reached a solution were altogether different to those I've described so far. There was a sense of elation and satisfaction; that somehow I'd triumphed. Would I have had these same emotions if I had known exactly what to do right from the start and there hadn't been any uncertainties? I am sure that it was the fact I'd had to overcome difficulties in order to succeed that was the most significant contributor to my feelings of pride and pleasure. Mason et al. (1982) suggest that it is the sense of slight unease which we experience when up against something challenging which stimulates us to think mathematically and it is this element of challenge that NRICH problems try to offer. However, when we are stuck, how long is it reasonable for us to be stuck for? And what is helpful when we are stuck? James Nottingham (2004) talks about a "pit of uncertainty" in which children should not be frightened of finding themselves on the journey between having been asked a question and reaching an answer. He explains that we shouldn't leave our pupils in the pit unaided, but it is the support we give them to climb out of the other side which is crucial. You might want to share the Nine-pin Triangles problem with your own class and/or colleagues, if appropriate, but in case you are teaching younger or less-experienced learners, you might like to look at Happy Halving instead. In this challenge, you are asked to split each of the shapes in half so that the two parts are exactly the same.  

Before giving this problem to your pupils, think about how they might get stuck as they work on it. What sort of strategies could you use that encourage them to think mathematically and therefore empower them to get themselves "unstuck"? In writing hints on the website, this is exactly the process we go through. Of course there are all manner of difficulties in trying to offer help, both in an online environment and in the classroom. Each child's relationship with a problem is different; each child's experience of solving problems is different. Therefore what is helpful to one may be useless to another. How can we try and offer support without leading our pupils down the route we would take and at the same time leave room for there to be opportunities to find alternatives? There is no doubt that a culture in which being stuck is valued in a meaningful way is difficult to achieve and I don't have definitive answers to my questions. However, we can model what we do when we are stuck and we can be explicit about the ways we try to help learners when they are stuck. In this way, children will begin to develop their ability to think mathematically, as Mason et al. (1982) suggest, and therefore become more independent in their role as problem solvers. They will feel positive that a problem may be difficult but it is worth striving for a solution. The NRICH Team always welcome your comments on the hints and notes they provide with each problem (or on any aspect of the website!). Please get in touch: [email protected]  

Mason, J. with Burton, L. and Stacey, K. (1982) Thinking Mathematically. Wokingham: Addison-Wesley Publishing Company Nottingham, J. Conference keynote, Bristol 2004 This article also appears in Primary Mathematics, a journal published by The Mathematical Association .  

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Homework corner

Aaah - i'm stuck on the maths homework again mners please help (year 6 algebra).

MrsFogi · 02/07/2017 11:47

Isn't it just 64-36=28?

no, divide 28 by 2 for son's age - so son is 14, dad is 50.

Fathers age = f Sons age = s

• F = s + 36 Substitute 2) into 1) (S + 36) + s = 64 Rearrange to give 2s = 64 - 36 Can you solve from here?

X + 36 =64, therefore 64 - 36 = X, as explained above, just in a more homeworkey answer type way. Disclaimer, my own algebraic homework dates from pre-history.

sons age + (sons age + 36) = 64 X + (x+36) = 64 2x + 36 = 64 2x = 28 X = 14

I would expect my Y7 class to do this as sons age = x Dad's age = x + 36 x + x + 36 = 64 2x + 36 = 64 (simplify the algebra) 2x = 28 (subtract the 36 from both sides) x = 14 (divide both sides by 2) So the son is 14, which makes the dad 14 + 36 = 50

Algebra? Ooh ooh I know this. Does it have brackets? If it does, you need to work out that bit first.

You can let your dd practice how to use variables in simple algebra on this site. (free up to 10 question a day.) I think once you get how to use variables, maths seems so much easier and quicker than trial and error!

Sorry, uk.ixl.com/math/algebra

The thing with algebra is to try and get everything into the same terms. You've been told some information in step 1 ' A father's age and a son's age add up to 64 years', but it has two terms: father(f) and son(s). In the second step of the question, you are given the information that allows you to convert it into a single term: 'the father is 36 years older than the son'. Step 1: f + s = 64 Step 2: (s+36) + s = 64 Once you have only one term (s) you can simplify your sum. Depending on how confident your maths is, you can use as many or few steps as you need: Step 3: s + 36 + s = 64 Step 4: 2s + 36 = 64 Step 5: 2s = 64 - 36 = 28 Step 6: s = 14

Thanks for rescuing me mners! I can keep the illusion of maths brilliance for a while longer......

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Why being stuck in maths isn't actually a problem

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Whenever I found myself stuck on a maths question at school, Mr Briggs would smile broadly and say: 'Great! If you're not getting stuck once in a while, you're not trying hard enough.'

As a student, that irritated me no end; as an adult - and as a tutor - I understand where he was coming from. Kids naturally tend to enjoy solving the the simple problems that they get right first time. This is important and shouldn’t be overlooked as it does wonders for confidence levels, but we know that in order to improve at maths (or anything, really) we need to stretch ourselves.  

The further your child gets into learning mathematics, the more time he or she can expect to spend being stuck. This isn't exactly surprising - the problems get harder!

At the very top end of the 'stuckness' scale is a maths puzzle known as Fermat’s Last Theorem which baffled mathematicians for centuries. Fermat, in 1637, wrote down the theorem in the margin of a book basically saying ‘I’ve proven this but don’t have room to write it down here.’ This was the ultimate tease for generations of mathematicians who spent more than 300 years falling over themselves trying to solve it with no success. (So, as you can see, being stuck in maths is fairly common.)

As a parent, it's tough to watch your children struggle with something. Your instinct is usually to help out but that's not always the best thing to do - it can be like telling someone the ending of their favourite TV show, or spoiling a riddle. Being stuck in maths is part of the process, so rather than guide them towards the answer, you can help them develop strategies for getting unstuck themselves. 

Talk about the question... without giving away the answer

One of my favourite ways to get unstuck is to explain the problem to someone who doesn't understand it . It doesn’t even need to be an actual person - I’ve had pretty good results discussing my problems with teddy bears. To explain a problem this way, it helps the child to:

organise their thoughts

get specific about what's holding them up

remember what they've already tried and think about why it didn't work.

This is often enough to crack the problem wide open! 

You can also ask your child questions that force them to look more carefully at the question they’re doing , and to look at it in a different light. Asking:

'What do you know?' helps children to clarify what bits of the answer they do know and find out where the gaps are - better still, ask them to write everything they actually know on a piece of scrap paper and see if they can turn the problem into a picture or diagram.

'Is this like any other question you’ve done?' or asking if they can break the question into parts that they do recognise helps children make links between different parts of their learning.

'How is this different from the last question you did?' encourages a student to try similar methods and see where they fall down.

'Is there anything in the question you haven't used?' reminds them to read carefully.

'What do you understand by this word/symbol?' can start a conversation about the question.

Talking about the question without giving away the answer is a good habit to get into: the odds are, at some point in your child's school career you'll be asked to help with something you don't know the answer to yourself, and this way you’ll still be able to help!

In the 1980s, a professor called Andrew Wiles dedicated himself to proving Fermat’s Theorem after becoming entranced with the problem when he was just a boy. He worked alone and in secret for the best part of a decade, making lots of mistakes and getting stuck many times along the way.

Normally, mathematicians prefer reason and method to experiments, but when someone is properly stuck, anything goes. Some ideas are:

Can you do it with easier numbers? Build up a recipe and then follow it again.

Can you get close with trial and error? Figuring out roughly what the answer should be can be a huge push towards doing it 'properly'.

There's often more than one way to solve a problem. Children who get used to tackling things from different angles generally turn out to be better problem-solvers.

Relax, don’t worry about being stuck

Quite often, the problem isn't that a student can't do a problem, but that a student has become convinced they can't, which is a self-fulfilling prophecy. Coming up with ways out of the spiral of doubt can be the difference between a successful homework session and a big argument.

Being stuck in mathematics isn’t failure, it’s part of the process. Andrew Wiles was unusually persistent in working on one of the greatest unsolved problems in maths, but being stuck is perfectly normal in maths, whether it’s spending eight years on Fermat's Last Theorem or twenty minutes on a tricky percentage problem.

Some things that might help include:

Use positive language. Remind your child that they're smart, and they will crack it eventually. Make sure they're not bullying themselves.

Get moving. Sometimes having a little dance or run-around is enough to get the blood pumping and give a fresh perspective on the problem.

Have a change of scene. Move to a different part of the house, put some music on, work on a fresh bit of paper - just do something differently.

Come back to it later. When Einstein got stuck in his thinking process (yes, even geniuses get stuck) he took breaks to play his violin. Taking a break to do something else gives the subconscious some time to work on things in the background. 

Albert Einstein, who was responsible for some of humanity’s most famous intellectual discoveries, was also known for his daydreaming, violin breaks and unusual approach to thinking. We also know about Archimedes making one of his great discoveries while relaxing in the bath (Eureka!) and Isaac Newton coming up with the theory of gravity while having a cup of tea in an orchard. They weren’t alone - many celebrated musicians, scientists and other people considered to be geniuses depended, and still depend, on the power of taking breaks and ‘doing other things’ to help them connect what they know to what they want to know.

It’s always tricky to find the right balance between helping your child stick at a task and making a strategic retreat - the tactics here will help you to help them build resilience, try harder for longer, and solve problems for themselves. 

A puzzle for you to get stuck on

Since we're talking about unsolved problems, let's look at one that doesn't need much maths to play with - it's known as the Magic Square of Squares.

A *magic square* is a grid of numbers where each row, column and diagonal add up to the same number. For example:

This is a 4-by-4 magic square in which each row and column adds up to 34.

Click here to download a printable worksheet for the following activities

Activity 1: Complete the 3x3 square 

Activity 2 : Can you find other patterns in this magic square that add up to 34?

(We know the rows and columns add to 34)

Activity 3: Can you use the numbers 1 to 9 to make another magic square in a 3 x 3 grid?

A Magic Square of Squares takes things a step further; as well as the rows, columns and diagonals adding to the same total, each number in the grid has to be a square number - a number you can make by multiplying something by itself (for example, 16 is a square number because it's 4 × 4). 

Nobody has so far found a Magic Square of Squares, although a few people have come close. 

Activity 4: Complete the 4x4 square:

Activity 5 : Try to find a Magic Square of Square numbers. (Download your printable worksheet here) Get stuck. Keep trying!

Here’s a list of the smallest square numbers:  1, 4, 9, 16, 25, 36, 49, 64, 81, 100, 121, 144...

Andrew Wiles was just ten days away from giving up on Fermat’s Last Theorem when he finally made the key breakthrough that led to a solution. After more than 350 years of the entire mathematical world being stumped, he finally solved the problem with tenacity, persistence and his ability to accept that maths is all about being stuck and the valuable journey that (eventually) getting unstuck takes you on.

Answer 1 : Complete the 3x3 square

Answer 2: Can you find other patterns in this magic square that add up to 34?

Answer 3: Can you use the numbers 1 to 9 to make another magic square in a 3 x 3 grid?

This is just one example out of hundreds :

Ask yourself:

 - Do the rows and columns add up to the same number?  - Do the diagonals?

If so then it’s a magic square!

Answer 4: Complete the 4x4 square:

Activity 5: Try to find a Magic Square of Square numbers. Get stuck. Keep trying!

Hmmm...I'm stuck!

Hi, I'm Colin Beveridge - a math tutor, former NASA researcher, and writer of maths books including Basic Maths for Dummies .

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Find out more about Komodo and how it helps thousands of children each year do better at maths - you can even try Komodo for free.

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Math home question that im stuck on

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Jim S. answered • 10/06/15

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Related questions, n/6-3n+10 n=-6.

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1/2q^(2)-5/4q-3=0

4t+14=6t/5+7.

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what is 3(10-12/6)^2 i need it worked out to do my home work please

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3(2(x-3)+2)+5(x-3)

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