The following article features as part of our ‘We have a problem!’ thinking skills resources.
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.
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…
…which leads us on to…
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.
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. 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!
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?)
It is for this reason that our new word problems resource pack contains cards provided in an editable .PPT format. Get in there and personalise them. 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? Our new word-problem resources include a presentation containing a selection of skeleton questions for use with an interactive whiteboard.
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.
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.
Click here to get your free sample…
