Problem Solving

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This page contains word problems covering a variety of mathematical strategies. The main point of this page is to show that children need to pick out specific information from word problems that will be relevant to the calculation they are required to do. Also to show them that some information in these problems bears no relation to the mathematical procedure. Children are encouraged to do jottings to show how they have worked something out. In some SAT's questions there are extra marks for showing how an answer has been arrived at.

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Click on the words below to go to specific problem type.

ADDITION

SUBTRACTION

MULTIPLICATION

DIVISION

2 STAGE PROBLEMS

Example of a problem needing addition to obtain an answer

I have a box with 6 green pencils and my friend gives me 3 red pencils. How many pencils do I have altogether? Answer 9.

Step 1 The first thing to do is to decide what type of calculation is needed. Children are encouraged to look for clues in the question, in this case the word "altogether" is the clue as it means addition is needed.

Step 2 What is needed to do the addition? Children are encouraged to look for the numbers they will need. In this case 6 and 3. It is important to stress in this instance that the colour of the pencils and the fact that some are in a box bears no relevance to the question which is "how many pencils do I have altogether".

Step 3 Finally the children write down the sum "6 + 3 =" and use whichever addition strategy works best for them to obtain the answer "9".

Step 4 Remember to write the answer next to the original question.

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Example of a problem needing subtraction to obtain an answer

My sister had 12 marbles. She gave me 5 red ones. How many did she have left? Answer 7.

Step 1 Decide which operation (+ - x or ) is needed. In this case marbles were given away therefore my sister would then have less than she started with, so a subtraction sum is needed.

Step 2 Look for the numbers needed to perform the calculation (12 and 5). Once again it is stressed that the fact that we know some of the marbles are red does not make any difference to the calculation.

Step 3 Finally the children write down the sum "12 - 5 =" and use whichever subtraction strategy works best for them to obtain the answer "7".

Step 4 Remember to write the answer next to the original question.

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Example of a problem needing multiplication to obtain an answer

Dad has 4 boxes with 3 golf balls in each box. How many golf balls does he have? Answer 12.

Multiplication is initially taught as repeated addition in order for children to become accustomed to the mechanics of how it works. Times tables are generally not taught parrot fashion at this stage, however if you wish to help your child learn times tables for use later on in their education please click here and you will be taken to a printable times tables page. It is important to be aware that although 6 x 3 and 3 x 6 result in the same answer the sums do not mean the same. 6 x 3 means 6 lots of 3 while 3 x 6 means 3 lots of 6.

Step 1 From the question we know that Dad has 4 lots of 3 and this indicates a multiplication sum.

Step 2 Children are encouraged to draw an array which is a quick sketch pictorial representation of the question. It is stressed that the array can be just circles representing the boxes and carefully drawn dots representing the golf balls. An accurate drawing of boxes and golf balls is not necessary and is very time consuming. Their array might look something like this:-

array

Step 3 Next, the children can count the dots to obtain the answer but are encouraged to write out a repeated addition sum underneath, like this:-

aray with repeated addition

Step 4 Finally the children write the multiplication sum 4 x 3 =. This may seem a long winded way but it has been seen that most children grasp the multiplication concept quicker if they can see a pictorial representation of what they are trying to do. All that remains is to write the answer "12" next to the multiplication sum. To obtain the answer children may count the dots or add up the 3's using whichever way is easiest for them.

Step 5 Remember to write the answer next to the original question.

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First example of a problem needing division to obtain an answer

As well as teaching children to divide things into 2, 3 or 4 sets etc they are also taught the terms halve and quarter. This introduces them to the concept of fractions (taught further on in education as multiplication but this is very difficult to comprehend at 6 years old. It would be extremely hard to teach half of 8 is actually half times 8!). Usually they are only given numbers that divide evenly, however there may be odd occasions when they will have a remainder.

I had 10 cherries. I gave half of them to my Nan. How many have I got left? Answer 5.

Step 1 Decide what kind of operation is needed. In this case the word "half" is the clue that it is a division sum and that half means divide into 2 equal parts.

Step 2 The children will draw 2 circles representing the 2 people in the question.

Step 3 They then begin to count to 10 putting a mark in the first circle at 1, a mark in the 2nd circle at 2, the first circle at 3 and so on until they get to 10.

division array

Step 4 The children count the dots in 1 circle and that's their answer 5.

Step 5 Remember to write the answer next to the original question.

This question could also be phrased as I had some cherries and I gave half of them to my Nan. She had 5. How many did I have to start with? This would be done as above in the multiplication section.

2nd example

Aisha had 12 apples, she decided to share them with her 2 friends Tom and Sarah. How many apples did each child get. Answer 4

In this type of question it is pointed out that the apples are shared between 3 children and not just Aishas 2 friends. This is a common mistake that is made.

Step 1 The children draw 3 circles (could be squares or any simple shape but circles seem to be the easiest and most popular).

Step 2 They then count out the "12" into the 3 circles ( same method as previous question).

division array 2

Step 3 The children count the dots in 1 circle and this is the answer, but just to make sure they are asked to check that the other circles have the same number in them. If this is not the case then they go back and check.

Step 4 Remember to write the answer next to the original question.

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Example of a 2 stage problem 

As with all other word problems children learn to look for the information they will need and disregard the rest.

I have 50p in my purse and in the shop I buy an apple for 15p and a pencil for 12p. How much change will I get? Answer 23p

Step 1 The first thing children need to do is to decide how much they have spent by looking for the prices in the question. In this case 15p and 12p. They then add these together using whichever addition strategy (see addition strategy page) they find the easiest.
15p + 12p = 27p

Step 2 In order to work out how much change will be given they need to subtract 27p from 50p using the subtraction strategy ( see subtraction strategy page) which best suits them. 50p - 27p = 23p.

 

 

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