Hot Under the Collar
The Redhill Academy
Hot Under the Collar
Date. Time and place of research lesson
Time: 8.45 – 9.45
Date: 13 November 2013
Place: The Redhill Academy, Arnold, Nottingham
Target Class
This class is a higher GCSE group currently studying foundation topics. They are a set 2 out of 5 who
began their GCSE curriculum last academic year. They have target grades of A, B or C with the vast
majority being B.
Mathematical Goals
Key Processes applied to the task:
Interpreting and evaluating:
 Interpret their tables and graphs to solve the problem, relating their findings to the original
context.
 Form convincing arguments based on findings and make general statements
 Consider the assumptions made and the appropriateness and accuracy of results and
conclusions
Communicating and reflecting:
 Communicate their reasoning and findings clearly.
 Consider the elegance and efficiency of alternative solutions
Research Question
 How can Neriage be used to support student progress in the process skills?
 Do students have a better understanding of what makes good mathematical communication by
the end of the lesson?
 What impact do the changes made from the original lesson have?
Link to Case Study or other Bowland Materials
This lesson is inspired by the Hot Under the Collar assessment task.
Introduction
 Students were asked the following question without any input or prompts in the previous lesson:
“In your own words, what is good mathematical communication?”
 Individuals attempted the task as a plenary to the previous lesson. They were given20 minutes.
 Students are sat in groups of 4 based on a seating plan that is unrelated to the task.
 At the start of the lesson, outcomes will be shared as well as a literacy based guide on how to
make progress in mathematical communication.
 In this lesson they will work in pairs to produce a joint solution. A few groups will be asked to
share their solutions and these solutions will be compared and contrasted.
 The lesson will finish with the students being asked the same question: “In your own words, what
is good mathematical communication?”
Feedback from previous lesson, plain A4 paper, graph paper, 1cm squared paper, calculators, rulers, PC
and projector.
Time needed
1 hour
© 2012 Bowland Charitable Trust
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Hot Under the Collar
The Redhill Academy
Before the lesson
Ask students the following question in a previous lesson and collect their responses in to review them.
“In your own words, what is good mathematical communication?”
Students should attempt the task individually, in silence, in a lesson a day or more before the research
lesson.
Collect in this work and prepare questions that will move student thinking forwards. Some anticipated
common issues are detailed below to help you with this.
Anticipated issues with the task
Anticipated Issue
No indication is given as to whether they think
Anne’s model is appropriate
For example they calculate lots of different values
to compare but draw no conclusion from them.
Evidence is presented in a way that does not
aid comparison
For example they calculate values but on different
sides of a piece of paper or do not summaries
them from within their working out
Not enough evidence is considered
For example they only consider a few different
temperature values.
Considers temperatures out of a realistic range
of values
For example they produce a table of values from 0
up to 100 degrees Celsius.
Does not consider negative temperatures
Assumes that Anne’s method must give exactly
the same value as John’s For example they
calculate for 5oC giving 40oF for Anne and 41oF for
John and use this to conclude that Anne’s model is
not appropriate.
Their assumptions regarding an allowable
variation in the two models is too tight or two
slack
Eg they allow a temperature difference of 10 oF or
similar. They insist in a difference of less than 2 oF
No reasoning is given as to their assumption of
what is suitable and what is not
For example, they provide evidence and make a
simple statement about their opinion regarding
Anne’s model without explaining how they have
arrived at that conclusion. Eg. Anne’s model is
suitable.
Suggested questions and prompts
Have you answered the question: Is Anne’s idea
suitable for all situations?
What conclusion have you come to?
How could you set out your findings more clearly?
Does the way your findings are set out make it
easy to draw a conclusion?
Is this enough evidence to make a decision about
ALL situations?
What temperature is outside today? When was the
last time you can remember it being this
temperature?
Does Anne need to be able to talk to the viewers
about all these temperatures?
Are all these temperatures realistic for a weather
report?
Have you considered temperatures below zero?
Do we ever get any temperatures that are different
to these ones?
Is it really important that Anne’s model gives the
exact same value as John’s?
Is it only SUITABLE if Anne’s method gives
EXACTLY the same value as John’s?
Would a difference of 1 oF effect for example
whether or not you wore a coat?
Would a difference of ???oF effect for example
whether or not you wore a coat?
How have you decided if it is suitable or not?
Would someone that was not in our lesson be able
to fully understand your reasoning?
© 2012 Bowland Charitable Trust
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Hot Under the Collar
The Redhill Academy
Research Lesson Outline
Introducing the lesson (5 to 10 mins)
Have the students returned work set out on desks as they come in but instruct them not to look at them
yet.
Do you remember the problem I asked you to do last time? I have had a look at your work and I
have put some questions on it for you.
Without talking I would like you to read the comments I have made and think about what they
mean.
Give the students a minute or two to read and think about the comments.
Select a few students to read out the comments on their work, taking care to ensure you get a range of
different prompts.
Today you are going to work together to improve your initial attempts.
You will have time to work in a pair to produce a better solution.
Before you begin though, can you remember the question I asked you: “In your own words, what is
good mathematical communication?” Today’s lesson is about trying to improve your understanding
of mathematical communication so you can answer that question better.
Share the learning outcomes with students and refer them to the progress assessment grid and the
cross-curricular links of the PEE structure and how it can become EEP for Maths. Encourage them to
refer to this throughout the lesson to ensure their solutions are of the best possible quality they can be.
Collaborative activity: Producing a joint solution (20 to 25 mins)
Organise the class into pairs and give them access to a range of resources including graph paper,
squared paper, rulers and calculators. Ask students to try the task again, this time combining their ideas.
I want you to work in pairs now. You only need to produce one solution between you.
First, take some time each to share your solutions with each other.
Now, put your individual work aside.
Your task now is to produce a solution that is better than your individual solutions.
Try to produce a joint solution to the problem.
Remember to refer to the communication progress grid as you work. Think about each strand of
this EEP structure.
Circulate the room whilst students are working. Try to stay away from helping them directly and try
instead to pose questions that will move their thinking on and allow them to get past any barriers they
have reached.
Use the same questions from the anticipated issues above to help them find a solution.
Your role is also to seek out (from students) the main ideas to share in the whole class discussion and
which groups you feel it will be interesting to have share their presentation with the class for comparison.
Self-assessment, comparing Student Work and Whole class discussion (Neriage)(15 to 20 mins)
Use a visualiser or digital camera to capture examples that allow discussion. Find a pair of solutions to
compare and contrast each of the three strands of the EEP structure.
Lead a whole class discussion comparing and contrasting the pieces of work.
Can you find some similarities in the solutions?
What differences are there?
How could each have improved their solutions?
Have they included elements from each of the strands on the EEP assessment grid?
How could they have communicated their solution more effectively?
Summarising and reflecting
Summarises the findings from the groups, and helps students to identify the important ideas and make
generalisations.
Return their attempts from the previous lesson and ask them to once again answer the same question:
“In your own words, what is good mathematical communication?”
© 2012 Bowland Charitable Trust
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Hot Under the Collar
The Redhill Academy
Lesson Handout: Task
Name:
Hot Under the Collar
© 2012 Bowland Charitable Trust
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Hot Under the Collar
The Redhill Academy
Progress assessment grid
Communication
 Progress 
Evidence
Explain
Point
Their solution
includes evidence to
back up their
conclusion
Their solution
explains their
evidence and
assumptions
Their solution
indicates a conclusion
Shows some evidence but it
contains errors
No reasoning given
No conclusion given
Shows some evidence clearly
that helps draw a conclusion.
May contain a few errors
Some reasoning given
Their solution indicates a
conclusion
Shows enough clear evidence
that helps draw a conclusion
Clear reasoning given and
assumptions stated
Their solution clearly indicates
a conclusion
Shows full evidence clearly
and succinctly that allows a
conclusion to be drawn
Detailed and clear reasoning
given. Assumptions are stated
and justified
Their solution clearly indicates
a more complicated
conclusion
© 2012 Bowland Charitable Trust
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Hot Under the Collar
The Redhill Academy
Sample response: Declan (individual attempt)
Observations:
 A variety of temperatures considered
 Some inappropriate temperatures considered
 No negative temperatures considered
 Presentation of evidence not easy to access
 No conclusion reached due to incomplete solution (time restricted)
Sample response: Dan (individual attempt)
Observations:
 A variety of temperatures considered
 No negative temperatures considered
 Presentation of evidence clearly summarised
 No conclusion drawn
© 2012 Bowland Charitable Trust
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Hot Under the Collar
The Redhill Academy
Sample response: Connor (individual attempt)
Observations
 No negative temperatures considered
 No indication of which model is being used
 No clearly set out
 Incorrect use of mathematical notation
 Conclusion not precise enough
Sample response: Chloe (Joint solution)
Observations:
 A variety of temperatures considered
 No negative temperatures considered
 Presentation of evidence clearly summarised
 Sensible conclusion reached
© 2012 Bowland Charitable Trust
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