planetqhe and the IB

Random Behaviour

Experimental vs Theoretical

Compound Events I

Compound Events II

Expectations and Distributions

Distributions and Hypotheses

Probability in the real world



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This resource is primarily focused on the Group 5 subjects of the International Baccalaureate diploma. It is intended to help meet the IB Group 5 Aims and Objectives, not least the Aim to "Develop logical, critical and creative thinking in mathematics".

The prerequisites expected for students to use this site effectively really depends on your own modes of teaching, the kind of classroom you run and the motivation of your students. Knowledge of how to calculate simple probabilities, the use of tree diagrams and tables to find compound probabilities would be most useful. Also, for the Chevalier de Mere and Birthday Problems, knowledge of complementary events is useful. The multiplication rule for independent events is also of great utility.

The activities in this website are of two types. The QHE Questions follow the framework offered by Hatano and Inagaki (1987), who advocate a "Hypothesis-Experiment-Instruction" model for learning mathematics; See about this site for more details.

The other type are the Essential Questions. They are more general questions aimed at unifying probabilistic themes across a range of activities and curriculum areas.

Essential questions are a crucial driver for teaching and learning. They engage the students in the study and create a bridge between performance-based activities and deeper, conceptual understandings (Erickson, 1998)
Essential questions serve to unify and revitalize our curriculum work no matter whether the option in discipline-based, interdisciplinary, student-centred or setting-centred. (Jacobs, 1999)
Jacobs gives the following example of three essential questions adopted by English, science and humanities teachers for an interdisciplinary unit on The Origins of the Species:

  • What are the different views of the origins of human beings?

  • How have these views reflected contemporary values and events over time?

  • What are the current views on the origin of the species?

Update on advice for implementing this site in your classroom- February 2003. The following is an extract from my entry proposal for the European Teachmath Excellence award; Read the entire proposal here

Description of the used materials, availability, and classification according to the process followed;

Each lesson consists of a question and a simulation. Put the question to the class and ask the students to individually make their initial hypotheses. Then ask each student for their response and collate their answers on the board.

This gives the impetus for an initial discussion in which opposing views can be explored and compared. Then ask students to run the simulation and collect data, perhaps finding the mean, median and standard deviation or an experimental probability so that their results can be compared with their colleagues.

A further discussion can take place and the students can be encouraged to try to find the theoretical probability that answers the question. It is often appropriate to ask students to complete this part for homework and/or prepare a presentation for to give in the next lesson.

Advice for implementation of

As with any new teaching initiative, thorough preparation is essential - especially if you have planned in advance enough to book a computer lab.

Make sure you have checked the lab's machines for compatibility with Java and Microsoft Excel. Further, ensure that the random number generating add-in is installed, as described in the tech help section. You should also make sure that you have tried out the simulations for yourself.

Ensure that the students know how to calculate mean, median, mode, standard deviation, box and whisker etc. I have also found it best to teach the basics of probability theory before and during using planetqhe; complementary events, Venn diagrams, compound events - the intersection and union of events - tree diagrams and tables. All these skills can be useful in the write-up of each question. Your students could use a template to present their work, perhaps under the headings Question, Hypothesis, Experimental Data, then Theoretical Result, in which they write a 'proof' of the theoretical result.

I have found that a concrete experience is the best way to start the discourse. For example use dice to run the Chevalier de Mere experiment a few times at the start of that lesson. Or ask the class their birthdays at the start of either of the birthday problem lessons. I created a cardboard set of three doors to introduce the Monty Hall problem.

You may want to prepare students for these sessions by telling them that it is ok to discuss and share methods across groups; in fact they are encouraged and expected to do so. These are not problems where they can seek the answer in the back of their textbook - in fact planetqhe deliberately avoids giving answers.

Make sure that you are clear on how each student will record and share their data collection - by floppy disc? Email? Network?