# Monthly Archives: February 2016

# World Book Day

See updated page – **World Book Day**.

# Mathematics Proof Resources

Following a Twitter **#mathscpdchat** I thought a quick post noting some resources for proof would be useful. The chat is summarised on NCETM **here**.

From **Mark Greenaway**‘s **Suffolk Maths** site comes **this excellent and varied set of resources on Mathematical Proof**

From CIMT who are one of my favourite sites for a reason – see this **GCSE additional unit on Proof**. A favourite site because if you are ever short of examples it is highly likely you will find something on CIMT who have everything from **resources for little people** to **Advanced Level** and **everything in between**!

Nrich have this collection **Reasoning, Justifying, Convincing and Proof** for Lower Secondary. A search on **Nrich on Proof **returns a wonderful selection for all ages and stages. We have tasks to introduce **ideas of proof to younger children** through to **preparation for STEP** examinations.

**Jo Morgan** (**Resourceaholic**) alerted us to a very interesting resource from the Institute of Education, University of London, **a proof survey** with some great questions for Year 10. Looking for more information about this, I found **another for Year 9**!

This was a lively chat with many contributions giving ideas and resources – the chat is clearly summarised as mentioned above on the **NCETM website**.

# Statistics

Following last week’s post on **Probability**, time to check the Statistics content for the new GCSE specification. To start at the beginning again we can look at the **Mathematics GCSE subject content and assessment objectives** for Statistics; we should also check the **Key Stage 3 content **to see what we should have done already!

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 Statistics. 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.

There are some changes in content for Statistics if you have been teaching the old specifications; note we have lost specific reference to the Data Handling Cycle as well as Stem and Leaf diagrams. Also missing, I see no reference to stratified sampling for example. We have gained tables and line graphs for Time Series data.

**The DfE Key Changes to GCSE Maths document** explains ‘No mention of statistical problem solving / data handling cycle’ by saying that it is ’embedded into other subjects such as science and geography where it is explored experimentally’. (I find the phrase no mention of statistical problem solving puzzling).

Looking for further clues on Time Series data, AQA’s Teaching Guidance states that students should be able to:

- understand that a time series is a series of data points typically spaced over uniform time

intervals - plot and interpret time-series graphs
- use a time-series graph to predict a subsequent value

The **sample available **(the** **full document is available to registered members of All About Maths) of AQA’s excellent **Teaching Guidance document** is in fact the section on Statistics.

We can also see some **questions from Edexcel** via Just Maths.

From OCR, the very useful series of **Check in tests** (select link and scroll down the page) includes **Interpreting and Representing Data** and **Analysing Data**. OCR’s collection of GCSE Teaching and Learning resources also includes a (provisional) **Delivery Guide for Statistics **which includes suggestions for activities and resources in teaching Statistics.

From **Nrich** see the short problems on **Handling Data** which are based on the UKMT Junior and Intermediate Maths Challenges; problems are available on **Processing and Representing Data** and there a small number of short problems on **Interpreting Data**. Longer problems are available in both categories, see **Processing and Representing Data** and **Interpreting Data**. As always from Nrich these are excellent resources to get your students thinking, see **M, M & M** for example, accessible to all and a great example for demonstrating the need for being systematic. Note the follow on problem, **Unequal Averages** to extend thinking on averages.

The outstanding **Standards Unit** resources which really help understanding includes some excellent Statistics activities, see **S4, S5 and S6. **I have often used S4 on **Understanding** **Mean, Media, Mode and Range**.

Note the above link includes a PowerPoint to introduce the activity and also gives the solutions. I used the associated software to generate the images for the solutions.

There are numerous examples of Statistics resources in various **posts and pages on this blog**. David Millward’s PowerPoint collection includes **presentations on Statistics**.

….and to finish, **some games**!

# 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.

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.

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.

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, from TES, see **Frequency Trees **and **Prize Giving **from Nrich, note the **Frequency Tree** representation.

Further resources follow:

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**.

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

**Probability Stage 3 – Short Problems****Probability Stage 4 – Short Problems****Probability – Stage 3****Probability – Stage 4**

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.