Mathematics

Introduction to word problems

Many problems in mathematics are written in words. These are designed to give you information about the problem that you have to solve.

For example.
If I walk 2 miles per day how many miles will I walk in total in seven days?

How do we start to tackle this type of problem? This one is easy; we can see that we have 7 lots of 2 so we multiply 7 by 2 and get 14.

Or 7 X 2 = 14 miles, ( notice how I put the units in). This is important because the answer 14 has got no units.

There is always a way to approach word problems. Here are some simple steps to follow:

This sounds obvious but the number of answers that show the pupil has not read the question would surprise you.
(a) Look at any information given to you in pictures.
(b) Look at the marks for the question. This will show you the detail required in your answer.
If a question is showing 2 marks then a one-word answer will not be enough!

STEP 2. Try and find out what operation(s) you need to use + - x or ÷.

STEP 3. Make an estimate of your answer. This way you can tell that something has gone badly wrong if your estimate is way out.

STEP 4. Work out the solution

STEP 6. Re-read the question and make sure you have answered it.

This 6 step process seems complicated but you get used to it very quickly and it stops you making silly mistakes that cost valuable marks.

Here is an example of the 6 step process in action:

Peter buys 4 chocolate bars at 24p each and 2 cans of drink at 19p each.
What is the total cost?

2 marks

This sounds obvious but the number of answers that show the pupil has not read the question would surprise you.
(a) Look at any information given to you in pictures.
(c) Look at the marks for the question. This will show you the detail required in your answer.
If a question is showing 3 marks then a one-word answer will not be enough.

STEP 2. Try and find out what operation(s) you need to use + - x or ÷.

STEP 3. Make an estimate at your answer. This way you can tell that something has gone badly wrong if your estimate is way out.

STEP 4. Work out the solution

STEP 6. Re-read the question and make sure you have answered it.

Step 1. Read the question carefully and pull out the maths from the words.

Step 2. Here we must multiply and then add two sets of figures. So 4 X 24p + 19p X 2

Step 3. 24p is nearly 25p so 4 x 25 is £1.00. 19p is almost 20p,so 2 x 20p is forty.
So we estimate our answer should be nearly £1.40.

Step 4. We now work out the solution

24p x 4 = 96p

19p x 2 = 38p

So 96p + 38p = £1.34

Step 5 Does this make sense? It agrees well with our estimate (£1.40).

On reading the question again you can see the answer should be in money our answer is in £ so it is right.
That wasn't too bad, was it?

Here are a few problems to get you started.

I will put the 6 step process above each problem to help you get used to using it.
The answers for the first few will be in detail.
If you get an answer wrong go back over it and see where you went wrong.
You will get quicker and better with practice.

(a) Look at any information given to you in pictures.
(b) Look at the marks for the question. This will show you the detail required in your answer.
If a question is showing 3 marks then a one-word answer will not be enough.
STEP 2. Try and find out what operation(s) you need to use + - x or ÷.
STEP 4. Work out the solution
STEP 6. Re-read the question and make sure you have answered it.

Question 1.

A school needs to order 70 maths books. The book come in packs of 20. How many packs must the school order? Show your working. 2 marks

Question 1. A school needs to order 70 maths books. The books come in packs of 20. How many packs must the school order?

Step 1. Having read the question carefully you will see some words in bold. They are a clue to your answer.
Step 2. We need to ÷ here 70 ÷ 20
Step 3. Estimate how many 20's in 70 = 3 and a half.
Step 4. The school should order 3 and half packs.
Step 5 The question does not say that you can order 1/2 a pack so you must order full packs. If the school orders 3 packs it will only have 60 books but it needs 70 so it must order 4
Step 6. The question asks for HOW many packs so the answer is 4 Packs. There are two marks for this question 1 for getting 3.5 and one for seeing that you needed 4 packs

70 ÷ 20 = 3.5

 4 packs

(a) Look at any information given to you in pictures.
(b) Look at the marks for the question. This will show you the detail required in your answer.
If a question is showing 3 marks then a one-word answer will not be enough.
STEP 2. Try and find out what operation(s) you need to use + - x or ÷.
STEP 4. Work out the solution
STEP 6. Re-read the question and make sure you have answered it.

Question 2.

In a sale a shop sells music CDs for £3.99 each. If I wanted to buy 6, how much would it cost me? 1 mark

Would I get any change from £25 and if so how much? 1 mark

Step 1. This question is in two parts (you need the answer from the first part to answer the second.
Step 2. I need to X £3.99 by 6
Step 3. 6 X £4 = £24
Step 4. 6 X £3.99 is 6 X £4 - 6p = £23.94.
Step 5 this is very close to the estimate and it gives me some change from the second part of the question.

Would I get any change from £25 and if so how much? 1 mark

Step one The information is needed from part one.
Step 2. I need to subtract my first answer from £25
Step 3. I estimate £25-£24 = £1
Step 4 25- 23.94 = 1.06
Step 5 this is close to the estimate. ( I could check by adding 1.06 to 23.94 and get back to 25)
Step 6 the question is about money and my answer is not in money form

Here is the last one for today with just the answer.

Question 3

A shopkeeper buys crisps from the warehouse at £6.99 per box. How much change will he get from £80 if he buys 11 boxes?

The answer is £3.11 because 11X 6.99 = £76.89 then £80 - 76.89 = £3.11.

Did you follow the six step process? How did you do?

The six step process is listed below for you to print and put in your maths book.
We will tackle many more of these before the SATS

Good luck!