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This post forms part of our ‘Word Problems Made Easy’ resource. You can find out more here.

Why are word problems such a problem?

In our experience, several issues are true of the teaching of word problems in maths… Firstly, it’s a topic that students tend to find more difficult (and therefore less enjoyable) than many other areas of the subject. This is why much of our focus tends to be about teaching word problems creatively. Secondly, one of the main reasons students find it tricky to answer these sorts of word problems is due to the fact the operation(s) needed (+ — x or ÷) is/are hidden. Deducing the operation needed to solve the problem adds a layer of complexity to what may already be a difficult maths question. This is why several of the tips below relate to pulling out the correct operation. Once students can do this, getting the answer becomes more straightforward — it is simply about whether they know how to do the maths. Finally, it’s important to get away from the idea that all “real life” word problems have to be about DIY or fencing off a farmer’s field. Real life problems are a misnomer. They’re just life. And so, we’d encourage you to find as many everyday examples of maths in action. We’ve tried to collate a few videos and photographs in these Real Life Maths posts.

In order to develop something that is transferable and ultimately of use to your class in the real world, it makes sense initially to look to build a skill rather than simply answering a question. In many ways your pupils’ methods of reaching the solution are much more important than what it actually is. Focus more on the journey than the destination.

Get hold of a buzzer and read them word problems with bleeped out numbers — you’ll be surprised how well it works…

Emma’s teacher has set her {BUZZ!} pages of Maths questions to do for homework. Each worksheet has {BUZZ!} questions on it. How many questions are there in total?

By removing the distraction of the numbers, pupils can now focus on building the skill that leads them to the answer. If you don’t have a buzzer, display the problems with well-placed ink splodges to cover the numbers.

Or tell your class what the solution is straight away…

Look, I know what the answer is – you’re forgetting I’m the one who wrote the questions! It’s 120 chickens. I don’t care who got it first! What I’m really interested in is how you got there!

Again, by removing the need to hunt for an answer, your class can now think about the skills they might use to get there. Use a ‘think, pair, share’ activity to give them opportunities to share their ways of working. Look for a variety of ways of working.

How often do you serve up a worksheet of word problems on division, for example, directly after studying division? This could be one of the biggest barriers to your pupils actually reading the word problems and thinking carefully about what is needed. Most will have cottoned on to the fact that the questions are all going to be division, will not pay a lot of attention to the words, divide the numbers and move onto the next one. Why bother visualising the scenario and thinking about the words if your teacher has already told you in big letters at the top of the worksheet that they are all ‘DIVISION WORD PROBLEMS’?!

So, mix them up! Get your class playing detective to try and work out which operation is needed for each question…

If you want your class to be able to spot the necessary operation, set up activities where that is all you ask them to do. Give them a collection of word problems and don’t ask for the answers. Just ask for a +, -, x or ÷ to show that they have identified the correct method(s) to work out the answer. When you’re teaching the skill of spotting key information, again teach that step separately.

Provide another load of word problems and a coloured pencil/highlighter. Again, don’t answer the questions, simply get your class to pull out the important facts from the irrelevant information.

The skills that you are looking to develop primarily are not to complete tricky calculations. Don’t be afraid to keep things really simple to start. Teach students the skill of plugging in one-digit numbers to a word problem in order to ascertain what it is really asking.

By using simple numbers, your students can focus on choosing the correct operations to use and breaking the question down to see what it is asking. Once these skills are in place, then the numbers can get as messy as you like!

Who says that word problems can’t be looked at in a comprehension lesson? Or that you can’t ask “What operation would we use to find out that?” in a Science lesson? Look for cross-curricular opportunities to bombard your class with problem-solving. If these skills really are transferable, you need to practise transferring them in as many curricular areas as possible. Yes, your pupils may get fed up, but they’ll also get better.

When deciding whether a word problem is going to be solved by addition, subtraction, multiplication or division, we often encourage our students to look for those all-important key words that we have hanging up on the wall… SHARE, TOTAL, PRODUCT OF, LESS THAN, LOTS OF and so on.

Be aware, though, that an over-reliance on the posters you’re displaying can be confusing. The ambiguity of key words forms a key part of Word Problems Made Easy. We need to teach this to our students. For example, although “MORE THAN” is usually linked to addition…

What is 34 more than 45?

…it can just as easily crop up in a calculation that can be solved by subtraction…

How many more than 25 is £59?

Key word lists have their place, but they can be a double-edged sword. Be careful that they don’t take precedence over reading questions carefully and thinking! In fact, we’d argue that the ambiguity of key words isn’t taught enough. If you can teach students to be critical in their thinking and aware of the ambiguities of vocabulary, you’ll be halfway there.

Is the following and addition or subtraction problem?

In a game of football between East Fife and Forfar, there were 9 goals altogether. East Fife scored four. How many goals did Forfar score?

Nine times out of ten, pupils will think of it as a subtraction…

9 – 4= ??

…which of course is how the question can be solved. But is this true? Is anything being taken away or lost? Is it not more accurate, mathematically speaking, to view it as an addition…

4 + ?? = 9

…which can then, of course, be solved by subtracting the numbers.

Not every calculation involves a number missing from the end. By making sure you know exactly what is being asked, you can teach the skills of solving equations where the middle or start is needed.

If you can make your word problems vaguely appealing, you’ll motivate your class. Don’t just rely on sharing out sweets and cutting up pizzas… Use humour. Tell a story through the word problems. Use your pupils’ names – they especially enjoy this and can’t wait for the next instalment to come around (and, let’s face it, have your class ever been energized by a sheet of word problems before?)

Get in there and personalise your questions. It won’t take a couple of minutes and your class will be enthused.

There are only so many types of word problems. Take away the scenario, the strange names and the numbers and you are left with what we’re calling a skeleton question.

At the end of the day, word problems are just a handful of basic questions dressed up in different ways. If your class can recognise that word problems are just these skeleton questions with a bit of padding, they will be better placed to identify what operation they should be doing.

For example…

There are several people all with different amounts.What is the total? (ADDITION)
There are several people all with the same amount. What is the total? (MULTIPLICATION)
Same question, but this time you know the total and how many people there are. How much does each person have? (DIVISION)
Two people have unequal amounts. What is the difference between them? (SUBTRACTION)

Collect together others that crop up and have a go at making them slightly more interesting! How about using them as rapid-fire lesson starters? Skeleton question bingo?

This is a useful way of looking at the patterns behind word problems, but be aware that your lower-ability students may well struggle with the theory. Keeping the names, numbers and the “story” intact will help them visualise the question.

Remind your class that the people who write word problems up are merciless, inhumane creatures who are always looking to catch pupils out by adding pointless information or trying to trick them with a change of measurement units. If you’re inspired by this idea, The ‘M’ Files will be right up your street!

Provide a collection of word problems where there is irrelevant information to ignore…

I have 23 new messages in my e-mail inbox. While unsuccessfully attempting to balance a cup of coffee in one hand, a chocolate-chip cookie in the other and trying to see whether my best mate has replied, I accidentally click delete and get rid of 8 messages. How many do I have left?

…or a conversion to make.

Zac is 140 cm tall and so he is too small to be able to ride on the ‘Belly Flop’ rollercoaster. The height limit is 190cm. How high does he need to grow? (Give your answer in metres)

Model your thought process for inventing word problems to your class as if you really do try to catch them out…

The whole question is in millilitres and then, right at the end, I’m going to ask for the answer in litres. That’ll fool you.

Make mistakes on purpose while modelling how to answer a question and reward the first person to spot any errors you make. All of these strategies should get your class poring over their word problems with renewed energy.

So there we have it. Ten of our favourite ways to teach word problems effectively and with half an eye on the future — when these transferable skills really will come into good use. Now check out the rest of our Word Problems Made Easy resource.

MORE SPARKY RESOURCES FOR CREATIVE MATHS TEACHERS:
MATHEMATIPS: where good design meets maths revision.
THEFILES: maths questions from the point of view of the dastardly people who write them.
GAME SHOW MATHS: investigational maths based on game shows.
REAL LIFE MATHS: a collection of scenarios you can use to stimulate real life maths investigations.

## So, what do you think?

1. As a newly-qualified Year 5 teacher, I found this useful, thanks. My class find word problems tough and I’m finding it tough to teach them. Thank you for the ideas which were a godsend.

12:36 am on April 27th, 2014
1. Thank you for posting this. My favorite tip is creating word problems in front of my class, which I will implement next week! –Fourth grade teacher from across the pond

9:51 pm on May 8th, 2014
1. Great ideas thanku hope I can make my kids solve their problem in maths

1:19 pm on September 5th, 2014
1. I had a remedy to my pupils problem.
Thank You.

10:00 pm on December 23rd, 2015
1. this has really been an interesting insight. i plan to implement this strategies immediately.

10:09 am on June 24th, 2016
1. Fab! Really struggling with teaching year 1 mulitplication word problems in a way that they can clearly see which operation to choose! This has been really helpful!

8:57 pm on July 5th, 2016
1. I am an artist who goes into schools to teach skills that typically challenge both students and teachers. Next month, I work with 5th graders using art to teach word problems and symbols. Your Sparky Teaching website is right up my alley! You have inspired me with ideas to make my time with students entertaining and relevant. Thank You!

6:11 pm on October 10th, 2016
1. An excellent summary with some useful practical ideas. Thanks!

11:55 pm on November 24th, 2016

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