Word problems can trip the brightest of maths minds. There are often two or three different bits of maths involved and all those facts at the beginning of a question can be confusing because really, when you think about it, the facts don’t matter – not yet. Ask your child to explore this simple, explosive path to solving multi-step problems. You could help model a few together first. (I’ve modelled one for you below.)
- Go straight to the end of the problem. Skip out all the opening bits of information. (You’ll come back to it soon, promise.) It might be the last sentence, or else may be part of a longer sentence. Find the part of the question where it actually tells you what it wants you to do. What will finished look like? When will your child know he or she has finished, i.e. answered the question?
- Look for key maths words in this last part of the question – these will be your instructions. What is the total…? How much left…? After how many days will the bottle be full? What percentage is not sold? These all tell you quite clearly what you have to do to reach the final answer.
- Now, go back a sentence at a time and find the information you need to answer the question. Is there anything helpful in the sentence before? Okay, go to the sentence before that and see if there’s anything there that can help you. Continue until you have the info needed.
Why? For a start, all the information loaded into the start of the question is just that – information – and it’s not going anywhere. It stays there on the page. What this means is your child doesn’t need to waste their time and mental processing power in an exam reading everything and trying to remember and retain all this information until they can get to the part where they know what they are supposed to do with it. Go to the end and find out what you are supposed to do with the information first. The question is about this doing.
Secondly, the information at the beginning is not interesting – honestly. Your brain will be fairly indifferent to finding out that Janet has two jugs of water for a party. BUT, the brain is massively interested and curious in questions and solving problems. So, go to the end and find the problem immediately and BAM, the mind switches on. Now, all that information at the start becomes fascinating! How so? Because as you read it, you are asking automatically: Does this help answer my problem? Your child will evaluate and pay more attention to the information.
Don’t believe? Try it for a few weeks and see if you notice the difference. Here’s a problem to model the process.
Q. Gusts orders 220 red biscuits for his 10th birthday party and stores them in a cupboard for a week before his party. Each biscuit weighs 12 grams. However, on the day of his party, he notices only 55 biscuits are still red. The rest have strangely turned yellow in the cupboard. a) What percentage of biscuits had turned yellow before the party? b) What is the weight of yellow biscuits in kg?
- Go to the end and find out what finished looks like:
a) What percentage of biscuits had turned yellow before the party? b) What is the mass of yellow biscuits in kg?
2. What key maths words are in this last section? There are two – percentage and mass. We also know we are looking for the yellow biscuits. This is a trick if you remember the numbers at the start (220 and 55) are about red biscuits. You can bet that in a multiple choice paper, the answers would include these red biscuit numbers, trying to make your child rush. Your child is especially likely to rush if they start at the beginning of this question because they see red biscuits and numbers and may think they’ve found the answer, rather than worked through the steps.
So, reading this last part, we know we will have finished this question when we have calculated both the percentage of biscuits that have turned yellow and found the mass of all the yellow biscuits. (We will also now look for units of mass – g or kg – in the information and care about these units when we find them.)
3. Fantastic. We now have a goal to excite our brain. Next, read the sentences from bottom up to top and search out any information you need to solve this.
The rest have strangely turned yellow in the cupboard. Nothing helps here except the word ‘rest’. It suggests a leftover amount, so we’re probably going to have to take something away. We will have to work out what this ‘rest’ is by taking it away from another quantity of biscuits.
However, on the day of his party, he notices only 55 biscuits are still red. ‘Only 55‘ and ‘still‘ tells us that he started with more, so we need more information to find out how many biscuits Gusts started with. (But we are getting close to cracking the code.)
Each biscuit weighs 12 grams. Aha. We have found information that will help us answer part b) of the question. Don’t worry, it’s not going anywhere, it will still be written here when you come back to it. (Just note that here the unit is grams, so we will have to convert it to kilograms to answer the question.)
Gusts orders 220 red biscuits for his 10th birthday party and stores them in a cupboard for a week before his party. 220 biscuits is all we’re after. Other info like his age and how long he stores them in a cupboard is blah blah irrelevant. Thankfully, you didn’t read this bit first, or you would be trying to remember it and make sense of it before you knew what the question actually wanted you to do. It would have wasted brain power and been a trick, because age and time (days) are maths words and ideas, so you might have expected them to be relevant to the question.
Now, let’s use the info. It doesn’t tell us the percentage that stayed red or turned yellow, but it gives us two numbers and we can work out the percentage using these.
Total = 220 biscuits.
We could take away 55 from 220 to get 165 and work a percentage from there, but if you are encouraging your child to look for patterns in numbers, you might recognise quickly that: 10% of 220 is 22 biscuits (divide by 10 to find 10%) , so 5% is half of this, giving you 11 biscuits.
If you double 22 and add 11, you get 55, so you have 10% + 10% +5% = 55, so 25% of 220 = 55. This means 25% of the biscuits stayed red.
(You might also recognise 11 x 5 = 55, so you may have worked out 11 x 5% = 25%.)
This also means 75% of the biscuits must have turned yellow, as the red and yellow biscuits must add up to 100%. (None of the biscuits have disappeared, so we still have 100% (all) of the biscuits we started with.
Did you spot another pattern? Perhaps you saw that if you half 220 and half it again, you get 55, so a quarter of the biscuits stayed red. (Sing out, “A quarter is a half and half again!”) Convert a quarter into a percentage and you get 25%. (Of course, you have to have learned to convert between fractions and percentages to know this. Get your child learning this topic now if they are unsure.)
Okay, we’ve answered a). Now onto part b). Take away 55 from 220 and you get 165 yellow biscuits, as we did above. What do we do now?
Multiply 165 x 12g (each biscuit has a mass of 12g, remember?) and convert your answer to kg. (Remember, it asked for kg. A common trick in maths questions is to give amounts in one unit, then ask for answers in a different unit.)
A possible mental method to solve this would be to split the 12 into 10 and 2, then join the answers back together: (10 x 165) plus (2 x 165) = 1650 + 330 = 1980g.
To get this into kg, divide by 1000 (there are 1000g in 1kg) 1980 becomes 1.980kg or 1.98kg.
We have now answered part b).
Okay, that was a thorough example that took longer to read than it actually would to solve. Well done for seeing it through. Now, with your child, go and find what finished looks like with your next 20 multi-step word problems and see if it becomes a helpful, efficient, logical, time-saving, accurate method. Reading maths words problems is very much about interpreting them to get to each question’s core problem. They are not stories, so you don’t need to think beginning, middle and end.
Let me know how you get on. Please keep visiting 11plushappy.com for more helpful ideas and 11 plus books to support you on your way to success. You can also sign up for a free course on how time can help your child pass the 11 plus.
Stay 11plushappy! The best of success to your child.