Link to Online Lesson
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Starter / Introduction
We start the lesson using multilink cubes to show the mean as the sum of the data divided by the sample size. Next, we use written and calculator methods to find the average of larger sample sizes.
Questions / Prompts
Click here to watch the video.
To introduce finding the mean from a frequency table, we discuss what the total shoe size would be if all the students placed their feet in a line. Working through the problem this way makes it intuitive to find the product of the shoe size and frequency.
I demonstrated how to calculate the boy’s shoe size and asked the class to find the girl’s. I find this example works well as most students would expect boys to have a larger shoe size, so this backs that up.
If the class is large enough, I put a student in charge of collecting shoe sizes for boys and girls and repeat the question using primary data. It’s always funny when boys are proud to have the largest feet in the class.
I ask the class to work through the question on the third slide using mini-whiteboards. I use mini-whiteboards for this as there is quite a bit of working out, and it helps the students keep track of their methods. It also helps me to assess the progress so I can give feedback.
The plenary takes between 10 to 15 minutes. It is essential to leave plenty of time for this, as some students can be a little overwhelmed working with a bar chart as they have to read off the frequencies. I print a copy of the bar chart as a handout to save time. Likewise, students sitting at the back of the classroom need help reading the bar chat’s correct frequencies.
Students need at least a few hours to interpret data from the frequency table, so the following lesson is usually about finding a combination of the median, mode, mean and range from frequency tables.
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My name is Jonathan Robinson and I am passionate about teaching mathematics. I currently teach mathematics in the South East of England. I am proud to have helped teachers all over the world to continue to engage and inspire their students with my lessons.
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Gwen Tresidder says:
I like the way you start, with the multilink towers. My bugbear is with the data you use later. I think students should be using real and meaningful data, not just any numbers that can be dreamed up so they divide conveniently with a spurious context that is uninteresting to students. You are right that they always find this procedure, mean from frequency table, difficult. But I would suggest that if the data were such that the mean meant something that they cared about, then they would be more likely to notice when they get a ridiculous answer (which is almost always the effect of carrying out the procedure incorrectly). Furthermore, they are more likely to really understand what the mean is, why we use it, and its power. It’s not easy finding good raw data, but I’d argue it is essential. At least if you collect shoe sizes from the class you are using real data, and students will have to deal with all the grey areas of numbers that don’t necessarily divide nicely, but who is really interested in who has bigger feet? I’ve done a stats project a couple of times with Y8s where they collect data on amount of housework each child does at home – interesting comparisons between girls and boys, eldest siblings and others etc. etc. And believe me, they really do care!! And they have to deal with all the questions of respondent honesty, varied interpretation etc. etc. I think if we are to develop a genuine understanding in what statistics is, we have to make it meaningful, not a set of procedures to be memorised.
mrmath_admin says:
Hi Gwen
Many thanks for the comment. I agree the data has to be meaningful and of interest to the students. Too often students have to answer questions on things they have little or no interest in which makes the mathematics seem boring.
I used shoe size as the first example on this new topic because in my experience boys and girls can relate to it and like you mentioned it does lead on to collecting a set of primary data once the students have worked through their first question.
I like to scaffold the learning in lessons so students can focus on the intended learning objective at the start. When they become more confident with applying this skill we, as you suggest, introduce other aspects that are relevant to the subject matter.
Many thanks for taking the time to respond to my blog.