Unit 4 - 1 Variable data
In unit 4 we get stuck in to the world of statistics and probability. This feels quite different mathematically than the previous units and there is an obviously strong focus on applications. As ever, the GDC does a lot of the heavy lifting for us but the subtleties of the concepts here are quiet sophisticated and a good deal of time and care is required to help students understand what they are asking their calculators to do for them. It is a rich unit with lots of good thinking!
What is this unit about?
The syllabus items in this unit are addressed as follows. Nothing is really in perfect one week units and so the following weeks will likely blur at the edges a bit!
Week 20 - Thinking about statistics - Start this unit with this Box plots - why? activity that gets students up out of their seats and thinking about the the ways in which statistical diagrams help to tell important stories. Follow this up with some good discussion about the typical statistical quantities they know about already with this Meaning activity. This makes for a week of good thinking and discussion to set the tone nicely for what follows
Week 21 - Measures of central tendency and dispersion - Look at this page of resources for learning and practising SL Central tendency & spread and learning how to use the GDC to help. Many of these skills are worth a single mark in an exam and so students need to know how to do this efficiently so the focus can be on what it all means! There is a good chance to see this in an exploration context with Carbon emissions - central tendency
Somewhere in these two weeks it could be good to explore Comparing Data Distributions and some of the ideas on SL Presenting Data page like the Gender gap index or Graduate Outcomes & Wages or UK Number ones. Perhaps here is some toolkit time available for this.
Week 22 - Probability 1 - Students wil have seen probability before in most cases so much of this feels like review. This Nerf gun roulette activity is provocative for getting started! Then there are lots of resources and practise exercises on this SL Probability of events
Week 23 - Probability 2 - Using resources from the SL Probability of events page the focus this week might shift to conditional probability and the laws of probability. These are productive if time allows. False Positives and Monty Hall
Week 24 - Distributions - This is a sophisticated idea and it is worth giving this a careful introduction with this Frequency Distribution Match. Once we now what a distribution is we can consider the ideas about discrete random variables, probability distributions and expected outcomes.
Week 25 - Binomial Distribution - I had some real fun with this The glass bridge game last year. It is based on one of the games from the sinister Netflix series 'Squid Game' and our less sinister version is an excellent introduction to thinking about Binomial distributions and how we build to really efficient ways of calculating probabilities with large numbers of events. The activity takes you all the way through. Then there are practice resources on the SL Binomial Distribution page.
Week 26 - Normal Distribution - Another week and another sophisticated concept. Lots of resources available here on the SL Normal Distribution page to help get our heads around this. Try the Making Normal spreadsheet activity.
Week 27 - More on Distributions - A week each for the two big distribution topics is probably not enough so this week is spill over to make sure I have given enough time to these two sophisticated topics.
Week 28 - Practice and test - Then a week of practice ending with a test.
Phew!
Why does it matter?
This is a tough question to answer in a short paragraph. The links above do include some important related detail. I am currently thinking of how I can get students reading this wonderful book from Tim Harford called 'How to make the world add up' which really feels like it should be compulsory reading for the general understanding of statistical ideas as the general public mostly see them. This is a great summary of why it matters!
I think this unit offers a golden opportunity to help students understand why it is so important to understand and think critically about even the simple statistics we see in the news. What is the key difference between a mean and a median? Why do we use both? What don't they tell us? Same question for standard deviation and interquartile range. This really matters. As the unit crosses in to one variable dat in the context of probability I have often described how the topics cross a kind of 'intuition line'. One side of this line is intuitive, but very quickly we cross in to very complex stuff that has lots of layers that our intuition does not deal with very well. Are we good ant knowing where this line is? What are the consequence sof people not recognising it? Tis paragraph merely hints at the significance this stuff has! It matters.
Opportunities for broader goals of education
The IB philosophy as detailed under 'Approaches to teaching and learning' (ATTL and planning) , invites is to always be thinking about the broader goals of teaching these units. It can be really hard to detail all the things that we do, big and small, planned and spontaneous, to do this, but it is important to try and reference some of them so that we get a strong sense of how we are doing against these objectives. Each of the pages and activities referenced above will also include references specific to those activities.
Each of the links above have extensive details about the nature of the tasks and the opportunities within them to address the broader goals of teaching and learning. For example..
- Box plots - why? is a very thought provoking enquiry that helps students understand the significance of statistical diagrams in telling stories as well as showing how it is quite an intuitive process.
- With Comparing Data Distributions which was inspired by 'Anscombes quartet' we have a golden opportunity for practise and ToK. The idea that data sets can have a number of things in common but still have significant differences is pretty important!
- We have lots of opportunities for applications in context here with things like Carbon emissions - central tendency, Gender gap index, Graduate Outcomes & Wages and UK Number ones.
- Probability concepts are explored collaboratively and critically through activities like The glass bridge game, Nerf gun roulette and Frequency Distribution Match
- The key topic pages provide all the practise resources needed and more.
There is more written about all of this on the individual pages, but the unit is richly charged with opportunity to be broad in our attention to ATTL.
Assessments
Coming soon - This is a test written for the fourth unit in this SL Scheme 2 that I
Help and support
Many of the tasks in the unit have different access points that should help students to engage at all levels. In addition, students have access to their text book and studyIB.net/mathapplications, where they can watch video lessons and get help and support. This is of course in addition to help from the teacher during lessons.