Averages is a completely new topic for fifth class, so most of the kids have no idea what you’re talking about!
The very first thing I did was to ask the kids to explain what the word ‘average’ meant, then give them sentences with the word ‘average’ in it, because they’ve probably heard it in context before and might be able to work out what it means.
e.g. The average temperature this month was 25 degrees // The average test score in the class was 8/10 // Would you want to be told you were ‘average’ at your favourite sport? etc.
- Line up the kids stand in a line from shortest to tallest, and explain that the middle child is around the ‘average’ height for the class.
- Repeat with number of sports they play, number of countries they have visited, etc.
- Call up five children and give them ten cubes. Ask them to stack any number between 1-10, then line them up lowest to highest, and ask the children what the average looks like.
Show the kids one stack of 9 cubes, one of 5 cubes, and one of 7 cubes. Ask them what the average is. Explain that we can find the average by adding all the numbers (stack the cubes) and making equal piles (one for Pile 1, one for Pile 2, etc). Is there a quicker way? We could have divided by the number of piles, i.e. 21 divided by 3 = 7.
Maths Fact: The average of x amount of numbers can be found by adding up all of the numbers, and divided the total by x.
We did a number of examples of these on mini-whiteboards, then from the book as homework.
e.g. The average of three numbers is 6. Two of the numbers are 9 and 4. What is the missing number?
This one caused quite a bit of hassle! The kids were all able to find the average of x amount of numbers, but when you introduce a ‘missing number’, it really tests whether they understand the concept or have just memorized what to do! They’ll write things like 9 + 3 = 12, 12 – 6 = 6, or even 9 + 3 = 12, 12 divided by 3 = 4.
I put the kids in groups of two or three, and gave each group a bag of matchsticks. I asked them to take 28 sticks, and make four groups, putting however many they wanted into each group. Then I wrote up on the whiteboard all of the different combinations – 10, 3, 7, 8 // 12, 10, 4, 2 etc. Each group then told me their average – 7 sticks. I drew four boxes with 7 sticks on the board, and drew out one of the previous examples above it, this time with a number missing (see the picture below). This helped the kids to visualise the total number of sticks, and therefore the missing number.
The rule we came up with was ‘if there’s a missing number, you have been told the total. Use it!’
Dividing with Decimals.
One further complication with averages is division with a decimal, e.g. what is the average of 3, 4 and 5? This requires quite a bit of practice – I like to get the stronger kids up to the board to do the sums so the kids aren’t listening to me the whole time!
To make this a bit more interesting, I brought the kids outside and measured how many centimetres each person could jump from a standing position. The kids kept track of the scores and calculated the average for the class!