Probability

The new GCSE specification has some changes in the content for Probability. Time for a look at that content and some resources we can use to teach it.

To start at the very beginning we can look at the Mathematics GCSE subject content and assessment objectives for Probability; we should also check the Key Stage 3 content to see what we should have done already! It is worth noting that Probability has been removed from the Primary curriculum so this will be new at Key Stage 3.

KS3 Probability Content

KS3 Probability Content

GCSE Probability Content

GCSE Probability Content

Note that at GCSE, all students will be assessed on the content identified by the standard and the underlined type; more highly attaining students will develop confidence and competence with all of this content. Only the more highly attaining students will be assessed on the content identified by bold type.

Each examination board has clear GCSE specifications, all included in the Further resources section of the GCSE New Content – Resources page. Specimen and Practice Papers provide us with important clues as to how content will be assessed and thanks to the wonderful Mel Muldowney of Just Maths we can see examination questions by topic, which of course includes Probability. These questions have been collated by Mel as the basis for a GCSE working party set up by the GLOW maths hub. (You can see more on the work of the Maths Hubs here). Whatever we are teaching, referencing the specification, any exemplification documents and also examination questions is essential in understanding how students will be assessed.

AQA Teaching Guidance

AQA Teaching Guidance

Looking at AQA’s excellent Teaching Guidance document for example and searching for Probability, as well as exemplification questions we can see suggested links to other areas of the syllabus. Probability could be assessed with N5, Apply systematic listing strategies for example, or perhaps with Ratio or Algebra problems. This is a document I personally reference constantly in my teaching for the new GCSE specification, the questions are excellent and show clearly the changes in emphasis on the new specification. Note that there is a sample available and the full document is available to registered members of All About Maths.

Probability - New Content

Probability – New Content

Formulae

GCSE: Formulae

If you have been teaching GCSE for a number of years then perhaps the biggest changes will be the inclusion of Venn Diagrams and Frequency Trees and of course the emphasis on Problem Solving including the kind of question like the now well known Hannah’s Sweets question from Edexcel combining Algebra and Probability. Also note that although the formulae shown here are not specified in the content they should be derived or informally understood by candidates. These formulae will not be given in the examination.

As well as the resources already mentioned, Venn Diagrams and from TES, Frequency Trees we have Prize Giving from Nrich, note the Frequency Tree representation.

Further resources follow:

AQA Venn Diagrams

AQA – Bridging the Gap

From AQA’s excellent Bridging the Gap resources: Set notation, number lines and Venn Diagrams

From OCR’s Check In tests, we have for the basics, Basic probability and experiments and then to follow, Combined events and probability diagrams.

 

Nrich Short Problems

Nrich Short Problems

From Nrich see the resources below; the short problems are based on the UKMT Junior and Intermediate Maths Challenges:

 

Standards Unit

Standards Unit

The outstanding set of Standards Units resources includes, S1, S2, S3 and S7 on Probability.

From Kangaroo Maths, for younger students (KS2, KS3) see the ‘Build-a-Mathematician’ tasks; the stage 8 and stage 9 resources include Probability and Tree Diagrams respectively.

6 comments on “Probability

  1. Hi Colleen, Do you by any chance have any resources for N5 Listing strategies, in particular the product rule? I found a quiz on Mr Barton’s sight but can’t find much else, so I thought of you 🙂
    Thanks for any help you may be able to give.
    Thalia

    Liked by 1 person

  2. So translation: Unbiased = random, and the word “empirical” seems redundant. I am pretty sure that at age 15 I didn’t even know that this word existed! I have a thing about “language in maths”.

    Like

  3. This looks quite good to me, but after many years teaching probability and statistics at all levels I don’t understand this:
    “5. understand that empirical unbiased samples tend towards theoretical probability
    distributions, with increasing sample size”
    I am guessing at the meaning, but a literal interpretation is difficult!!!

    Liked by 1 person

    • Looking at the exemplification examples, it seems to be as we expect, ie the greater the number of trials in an experiment, the more reliable the results. AQA also refer to the settling down of a relative frequency distribution. There are plenty of past paper questions on that from the old specifications.

      Liked by 1 person

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