Throwing a Six

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Introduction to the Starter Pack

This Starter Pack is intended to be the first unit of the course and serves as a bridge between GCSE and Core Maths. Most of the topics covered in this first Pathway are from the Higher GCSE syllabus and so will be vaguely familiar to most of your students. The big difference being that throughout this course we will be trying to make the activities more “thought provoking” by setting them in problem-solving context. The intention is to make the questions themselves “intriguing” and hence “worth solving”. Wherever possible we intend to make use of, or generate, “real data”. But using “real data” will often presents two new problems for your students:

  •          Is the data worth studying?
  •          Real data tends to be “messy”.

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Using real data – Why bother?

Step Zero - Before the Beginning

In this course we firmly believe that when studying data, students must work with real data.  After all if the data is made up, who cares if there are patterns, outliers or other oddities, for we can simply change the data and remove our problems? Why bother to decipher what the data says, if the data has no message?

Most stories (real or made up) start with "Once upon a time”, or "In the beginning" but when we come to data handling this is already too late!

In data analysis:

Step one is usually one variable statistics - extracting information from a single variable like population, size or growth rate.

Step two is usually two variable statistics (the relation between two variables).

But before any of this we need Step Zero, "no variables", the step before the analysis. Step Zero is to ask whether the data is worthy of your time, whether it is trustworthy, whether it is pertinent. 

So in Core Maths:

  •          before you analyse real data
  •          before you try to explain anything
  •          before you compute a single average or look at a single fact

you need to establish: Who, What, Where, Why, When, and How?

Which means, establish the context.

So before you get involved with the detail, ask questions:

  •          Who collected the data?
  •          What are the data about?
  •          What was it collected - if that is important?
  •          Why was it collected?
  •          When was it collected - if that is important?
  •          How was it collected?

You don't need to use a checklist – just ask questions.Think of this as Step Zero. The thing you do before you do anything else!

Just remember - always ask: Who, What, Where, Why, When, and How?

Real data tends to be messy

Unlike textbook questions and exam questions, real data tends to be messy and there is often a lot of it. Consequently, summary statistics rarely work out to be “nice” numbers and calculations can be difficult. So before long your students will need to understand the whys and wherefores of sampling.

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Real data tends to be messy

Unlike textbook questions and exam questions, real data tends to be messy and
there is often a lot of it. Consequently summary statistics rarely work out to be
“nice” numbers and calculations can be difficult. So before long your students will
need to understand the whys and wherefores of sampling.

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Sampling

Simple random sampling is the basic sampling technique a group of subjects (a sample) for study from a larger group (a population). Each individual is chosen entirely by chance and each member of the population has an equal chance of being included in the sample. Every possible sample of a given size has the same chance of selection; i.e. each member of the population is equally likely to be chosen at any stage in the sampling process.

Curiously, a carefully drawn sample of a population can give more accurate results than an attempt to look at the entire population. The reason is a matter of cost and realism because generating data is time consuming and costly.

In activity 2, students will be given a gentle introduction to simple random sampling and for this they will be asked to use random numbers. Consequently each student will need a set of random numbers and a basic understanding of how these tables are used in practice. There are, of course, other ways of generating random numbers but, at least in part, this activity is about using random number tables.  An explanation of how random number tables are used together with a random number table can be downloaded at http://www.nist.gov/pml/wmd/pubs/upload/AppenB-HB133-05-Z.pdf

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Documents supplied in Starter Pack

For each activity you will receive a set of draft documents which will be refined as we progress through the course. These documents will include the “story” of the lesson to help you understand how the lesson might flow as well as a Notebook file (Smartboard) and a Power Point file. There will also be any necessary student handouts and advice on anything you need to prepare.

Activity 1 Shockwheat

Documents included

Description

Shockwheat_LS.doc

Shockwheat_LS.pdf

The story of the lesson

Monster collection.docx

Monster collection.pdf

A set of monsters for making the “Free Gift” cards.

Monster2.docx

Monster2.pdf

Poster for the box

Shockwheat.notebook

A Notebook file

Shockwheat.ppt

A Power Point file

 

Activity 2 Jelly Blubbers

Documents included

Description

JellyBlubbers_LS.doc

JellyBlubbers_LS.pdf

The story of the lesson

Jellyblubbers.notebook

A notebook file

Jellyblubbers.ppt

Power Point file

Jellyblubbers_data.docx

Jellyblubbers_data.pdf

Page 1 is for the teacher

Page 2 is the student handout

 

Activity 3 Throwing a Six

Documents included

Description

Throwing a six_LS.doc

Throwing a six _LS.pdf

The story of the lesson

Throwing a six.

Notebook file (Smartboard)

Throwing a six.ppt

Power Point file

Matching histograms and boxplots.docx

Matching histograms and boxplots.pdf

A student worksheet

 

Activity 4 How do you know you are really unwell?

Documents included

Description

Bodytemperature_LS.doc

Bodytemperature_LS.pdf

The story of the lesson

Bodytemperature.notebook

Notebook file (Smartboard)

Bodytemperature.ppt

Power Point file

Body temperature_data2.docx

Body temperature_data2.pdf

Student handout

 

Activity 5 Practice Time

Documents included

Description

Practice_time.notebook

Practice_time 1.ppxt

Practice questions (Smartboard)

PowerPoint file

Practice time.docx

Student handout