A short YouTube teacher-training video teaching Year 6 pupils about the mean (average). Presenter Ellie demonstrates how to work backwards from a given mean of 12 for four pupils (12×4 = 48), shows simple score combinations (all 12s; adjust one pupil to 11 and another to 13 while keeping total 48), and recommends extending the task to ask pupils to find all possible combinations to build logical problem-solving skills.
Chapters
Hi, I'm Ellie, and in this video, we're going to look at how we can get our pupils working at greater depth in statistics, specifically looking at averages. Now, with the new curriculum, we don't need to look at mode and median anymore. We're just focusing on mean in year six. This question here gets your pupils really understanding the concept of mean and applying it to solve this problem. So let's look at what it's asking us. Four children took part in a spelling test. The mean average was 12 marks. What could the marks of the pupils be? And can you find two possibilities? Now, with this question, I would always start by getting my pupils to work backwards. So what we do know is that the mean average was 12 marks. So ask your pupils, how do we find out the mean? They should be able to tell you that you total all your values together and then you divide by the number of values that you have. So if we've got four pupils, we've divided something by four, and what is the number that we've divided by four? Well, we can put this as a missing value here. So we've got four numbers which have been added together to give us this value divided by 4 is 12. Now, using inverse, pupil should be able to tell you that has to be 48. 12 times by four is 48. So then what they're doing is finding four values. Something, add something, add something, add a fourth value gives us 48, and then that divided by four gives us 12. So what could the marks of the pupils be? The first thing that they can tell you is that they could all be the same and they could all be 12. That's the most simple answer they can give. If all four pupils had 12, it would add up to 48, and that divided by four would give you 12. But the question doesn't just ask us that. It says to find two possibilities. And this is where you want to get your pupils thinking logically. Where could they go to find the next potential answer? So some pupils might decide to take off one from the first number and see what happens there. Or maybe they're going to adjust the the third and the fourth numbers. Let's start by taking one off pupil one score. But because we still need to get a total of 48, we need to put that one somewhere else. So we're going to give pupil 2 13, and then we can keep pupil 3 and pupil 4 on the same score. So already here we've got two possibilities. Now, the way that you could really extend this question is rather than by saying, can you find two possibilities? You, you could say, how many different possibilities can you find? That's a really nice open ended task and it really gets pupils thinking about finding all the possibilities and working in logical order to think what those different combinations could be. That's a really key skill when it comes to answering all different types of problem questions, regardless of whether it's just to do with averages. So I would take this question to begin with, ask and define two, and I'd extend it and say, how many different possibilities can you find? And that's how we can work on developing an understanding of averages.
