Problem Solving
Mathematical problem solving can be challenging, but there are a few steps we can follow to help us work out the solutions. Try using our four step ROCS approach:
Read - the question carefully. Underline keywords / information and ignore any irrelevant (unimportant) information.
Operation - what operation do you need to solve the problem? Do you need to add, subtract, multiply or divide? This can be the
hardest part, so see Which Operation below.
Calculate the answer.
Sense - does your answer make sense? If it does, you're probably correct. If not, work through the process again.
For multi-step problems you will need to work through this process more than once.
Which Operation?
Sometimes you work out which operation you need by following a formula such as calculating perimeter, in which case you need to add or calculating area, in which case you need to multiply. With basic word problems though, follow the steps below. You may need to use more than one operation. Work through the word problems one step at a time, asking yourself what you need to work out in order to answer each step of the question. An example is provided below.
Read - the question carefully. Underline keywords / information and ignore any irrelevant (unimportant) information.
Operation - what operation do you need to solve the problem? Do you need to add, subtract, multiply or divide? This can be the
hardest part, so see Which Operation below.
Calculate the answer.
Sense - does your answer make sense? If it does, you're probably correct. If not, work through the process again.
For multi-step problems you will need to work through this process more than once.
Which Operation?
Sometimes you work out which operation you need by following a formula such as calculating perimeter, in which case you need to add or calculating area, in which case you need to multiply. With basic word problems though, follow the steps below. You may need to use more than one operation. Work through the word problems one step at a time, asking yourself what you need to work out in order to answer each step of the question. An example is provided below.
If you are asked to find how many altogether: |
If you already know how many altogether: |
Add or multiply |
Subtract or divide |
With addition and multiplication you have groups of numbers and want to know how many you have altogether. |
Subtraction is the opposite of addition and division is the opposite of multiplication. You know the total number and want to work out the number in smaller groups. |
Add when the numbers are different. |
Subtract when different numbers are being taken away or you want to know the difference between numbers. |
Multiply when the same number is repeated. |
Divide when you want the same number in each group. |
Example - Easier
Max has a packet of textas. If there were 12 textas in the packet but 6 were thrown out because they ran out of ink, how many textas does Max have left?
Read the question carefully and underline the key words.
Operation: We already know the total number. Some have been thrown out so that means we need to subtract because subtract means to take away.
Calculate: 12 - 6 = 6
Sense: It makes sense. Max started with 12 but some were thrown out, so the number left has to be less than 12 and 6 is less than 12, so it makes sense.
Example - Average
The school assembly hall contains 240 chairs. If there is enough space in the hall for 24 rows of chairs, how many chairs would be in
each row?
Read the question carefully and underline the key words.
Operation: We already know the total number. We want to divide the number into 24 groups.
Calculate: 240 ÷ 10 = 24
Sense: It makes sense. There are 240 chairs altogether. If there are 24 rows, there won't be that many chairs in each row. 240 is made up of 24 tens so if 240 is divided by 10, that means there are enough chairs to put 10 in each row, so it makes sense.
Max has a packet of textas. If there were 12 textas in the packet but 6 were thrown out because they ran out of ink, how many textas does Max have left?
Read the question carefully and underline the key words.
Operation: We already know the total number. Some have been thrown out so that means we need to subtract because subtract means to take away.
Calculate: 12 - 6 = 6
Sense: It makes sense. Max started with 12 but some were thrown out, so the number left has to be less than 12 and 6 is less than 12, so it makes sense.
Example - Average
The school assembly hall contains 240 chairs. If there is enough space in the hall for 24 rows of chairs, how many chairs would be in
each row?
Read the question carefully and underline the key words.
Operation: We already know the total number. We want to divide the number into 24 groups.
Calculate: 240 ÷ 10 = 24
Sense: It makes sense. There are 240 chairs altogether. If there are 24 rows, there won't be that many chairs in each row. 240 is made up of 24 tens so if 240 is divided by 10, that means there are enough chairs to put 10 in each row, so it makes sense.