Hey diddle diddle
The medians the middle
You add then divide for the mean
The mode is the one that you see the most
And the range is the difference between.
If you do nothing else with this hub I suggest you take this rhyme and make a display from it in your class. Ideas I did when I taught averages:
- Use it as a starter to the lesson. Then practice using the averages before testing the children's recall of the rhyme as the plenary.
- Homework was to remember it off by heart. Then I got every student the next week to stand up and say it in front of the class. I did this at random times during the day and not only within the maths lesson. Anyone who stuttered or who got it wrong had to do it again after they had gone away and actually done their homework!
- After the topic was done and we had moved onto other things I still got children to stand up and say the rhyme in front of the class. Maybe as a starter when we had some data to look at.
So how do we use these averages?
Time for some examples to help you explain it to your children:
Range of data = 2,3,4,6,6,10,4
- Add up all the values and divide them by how many values you have
- 2+3+4+6+6+10+4 = 35
- You have 7 values in total
- 35 ÷ 7 = 5
- This is the middle value so I need to re-order the values into numerical order
- There are 7 values so the middle value will be the fourth value. It doesn't matter which way we count from when working out the middle but I suppose working from the start value is the easiest to understand for students.
- So the fourth value, starting at 2, is 4.
- This is the most common value that occurs
- We have, two 6's, two, 4's, one 2, one 3 and one 10.
- So the most common values here are 6 and 4.
- And yes we can have more than one answer for the mode.
- This is the highest value take away the lowest
- So that would be 10 - 2 = 8
- The range is 8.
Straight away we should be asking about the tally chart and what the frequency means. Make sure the children know that when the tally is added up they can ignore this column from then on. Also point out the colour of the car column -
- do we need this in our maths?
- When would we need it?
These are the sort of questions you should be asking to get an indepth knowledge behind date handling of this kind. We do not want our children concentrating on data that has nothing to do with the question so the more times you can ask questions like this and give them examples the better. I have actually used things like this for mental maths starters plenty of times. Using tally charts, or bar charts, or just data like that of example 1.
So what do we do with this chart?
We need to tackle each average in differenet ways:
- Add up all the values and divide by how many you have:
- 11+5+8+4+1+7 = 36
- We have six different types of colours for the cars so this is the number we need to divide by to work out the average number of cars per colour.
- 36 ÷ 6 = 6.
- (Make sure that the children understand we have just worked out the average number of cars per colour and explain and talk through it so they do.)
- This is the most popular value
- Straight away we can see the most popular would be the biggest number here because that colour occurred most times. This is how it would differ from example 1 as we are not looking for the value which occurs the most number of times but the colour which occurs the most number of times. In this case 11.
- This refers to the colour red.
- Make sure the children understand that the answer is red and not 11.
- Asking to find the median of this table wouldn't actually show anything in particular so I would avoid it.
- This is the highest value take away the smallest.
- 11-1 = 10
There are plenty of resources you can download from the internet:
I picked these resources up from sparklebox but you can find loads of great resources from plenty of websites.
A great little guide to help you with all your maths work:
I bought the punctuation version of this book and was impressed so I invested in this too. These set of books are great to help you with your knowledge of maths.
I love this book and in fact I bought aload of them for my year 6's and sold them for revision guides. So much better than anything we had in school.
Everything your children need in maths are in this book. Take a look and you will find explanations and examples to help everyone with maths, including yourself!