Download Real time distance-time graphs

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Stage
Subject
Secondary
mathematics
Year
Term
8
Real time distance-time graphs
Module contents
Module focus
Curriculum focus
Creating, analysing and interpreting real time distance-time graphs.
Learning objectives
By the end of the lesson pupils will:
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know how to generate real-time data and plot a distance-time graph;
be able to identify the function of real-time data and express it as an
equation.
Learning outcomes
Most pupils would be expected to:
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make different simple movements to create sets of data and recognise
what the distance-time graph would look like for each set of data;
suggest a function for a given or generated set of data, plot the graph of
the function and express it as an equation.
Pupils making slower progress will:
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understand the link between a simple movement and the resulting
distance-time graph with support;
express a given function as an equation.
Pupils making faster progress will:
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experiment with making different movements to create sets of data and
suggest what the distance-time graph would look like for each set of data;
suggest functions for a range of given or generated sets of data, plot the
graph for each function and express them as equations.
This document is part of a range of materials designed to help teachers teach using ICT.
For more information, log on to www.teachernet.gov.uk/supportpack
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of the Practical Support Pack website, available at www.teachernet.gov.uk/supportpack/termsandconditions.aspx.
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References
Strategy Framework references
Algebra
Sequences, functions and graphs
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Express simple functions in symbols; represent mappings expressed
algebraically.
Construct linear functions arising from real-life problems and plot their
corresponding graphs; discuss and interpret graphs arising from real
situations.
The Framework for teaching mathematics can be found at:
www.standards.dfes.gov.uk/keystage3/respub/mathsframework/forewo
rd/.
National Curriculum references
Ma2 Number and algebra
Sequences, functions and graphs
Pupils should be taught to:
Functions
f construct linear functions arising from real-life problems and plot their
corresponding graphs; discuss and interpret graphs arising from real
situations [for example,
distance-time graph for an object moving with constant speed]
The National Curriculum programme of study can be found at:
www.nc.uk.net/nc/contents/Ma-3-2-POS.html.
Use of ICT
Teacher use of ICT
This module will give you the opportunity to:
This document is part of a range of materials designed to help teachers teach using ICT.
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
use a data-logger with a whole-class display to produce distance-time
graphs in real time;
use a graphical calculator to produce a scattergraph.
Requirements
Hardware
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A computer
Data projector, large display screen and/or interactive whiteboard (IWB)
Graphical calculator
Data-logger
Software

Word-processing software, such as Microsoft Word
Other

Data-loggers and graphical calculators for pupils (if available)
You can download the viewers needed for these files on the Software
downloads page.
Lesson preparation
A key element of this module is a lesson for you to adopt and adapt to
meet the needs of your class. It is designed to help you evaluate the
impact of using ICT for learning and teaching. Display and discuss the
objectives and key vocabulary for this lesson with the pupils.
Read the lesson plan and familiarise yourself with the resources before
the lesson. Ensure your computer, data logger and large screen
display or IWB are set up before the lesson and that you can access
the resources from your computer. If required, print sufficient copies of
the graphical calculator helpsheet.
Vocabulary
distance-time graph, gradient, intercept, linear function, linear
relationship, slope, steepness, value
Health & Safety
This document is part of a range of materials designed to help teachers teach using ICT.
For more information, log on to www.teachernet.gov.uk/supportpack
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All standard safety procedures with computers need to be in place.
Information can be found at www.ictadvice.org.uk.
ICT skills guidance
The guidance in this section supports the ICT skills described in the
Module contents.
Pupils' prior knowledge and skills
Pupils should already:
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be able to g enerate coordinate pairs that satisfy a simple linear rule and
recognise straight line graphs parallel to the x -axis and y -axis;
know how to represent and interpret data in a graph (e.g. for a
multiplication table);
recognise that equations of the form y = m x + c correspond to straightline graphs.
Starter
Open the file Function machines and select the 'View' menu to adjust
to full screen. You can drag the cards around on screen. Click and type
in the large green box to enter the function in algebra.
Select two machine cards and display them. Ask a pupil to choose an
input number for the function and ask another pupil to find and place
the correct output number. The blank cards can be used to make any
new number cards needed. Ask a third pupil to write or type the
function using algebra.
Ask different pupils to devise similar function machine challenges for
the class.
The cards also may be used to consolidate inverse functions.
Main
Ask pupils questions that focus on some of the key features of straightline graphs to remind them of year 7 work. You might like to ask
questions, such as:
This document is part of a range of materials designed to help teachers teach using ICT.
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Give me an equation that would give a straight line. Does it go through
the origin? How do you know?
Give me the equation of a straight line that does not go through the origin.
What would a sketch of the graph look like? How do you know where to
draw it?
Connect the motion sensor and whole-class display device.
You might like to ask pupils questions, such as the following:
If someone starts one metre away from the sensor and walks at a
steady speed away from it, what shape will the resulting graph be?
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What happens if the person starts in the same place but walks more
quickly? More slowly?
What if they start a different distance from the sensor?
What if they start about five metres away and walk towards the sensor?
Ask pupils to re-enact each of the scenarios and discuss the features of
the resulting graphs.
Establish the scales of the axis and, if the graphs are being projected
onto a whiteboard, annotate the resulting graphs.
With a straight-line graph displayed on the screen, ask pupils:

Can you guess the equation of this line?
Exit the data-logging software and plot the data as a scattergraph on
the graphical calculator. Enter pupils’ suggestions for the equation of a
line through the points. Ask pupils:
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How can you improve the fit of this line?
What do the numbers in the function mean?
Pupils should now work in groups in any of the following ways:
1. If you have sufficient motion sensors ask pupil to walk their own straightline graphs and find equations for the data as above.
2. They could load the data files provided for the lesson into the graphical
calculators and fit their own functions to the data.
3. Pupils could work with the data provided in Fitting functions.
Plenary
Either display one of the sets of data from the data lists given, or
generate a new distance-time graph by asking a pupil to walk at steady
speed in front of the motion sensor. Ask pupils the following:
This document is part of a range of materials designed to help teachers teach using ICT.
For more information, log on to www.teachernet.gov.uk/supportpack
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of the Practical Support Pack website, available at www.teachernet.gov.uk/supportpack/termsandconditions.aspx.
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Suggest a function that might fit this data? How good is the fit? How could
you improve the fit of this function?
What information can we use to help us find a function that is a good fit?
(gradient and intercept)
What is the unit for the scale on the x axis? (seconds)
What is the unit for the scale on the y axis? (metres)
In the equation of the line y = 2x + 3, x is in seconds and y is in metres.
In what unit is the gradient measured? (metres per second)
What do we measure in metres per second? (speed)
Assessment
In assessing for learning you should consider the following points.
1. Ensure objectives are expressed in language that pupils understand.
2. Give pupils clear success criteria related to these objectives.
3. Give pupils opportunities to discuss their successes and challenges
focusing on the objectives.
4. Provide oral and written feedback to pupils.
5. Encourage pupils to explain their thinking and reasoning in a secure
environment.
6. Provide time for pupils to reflect upon what they have learned and
understood and identify any difficulties.
You can find information on assessment for learning at:
www.standards.dfes.gov.uk/keystage3/respub/afl_ws.
Adaptation
All pupils will be able to make the links between the movement and the
resulting graphs by experiencing them first hand. Focus on the
interpretation of graphs relating to simple movements in front of the
data-logger, such as standing still, and walking slowly in one direction.
Lower attaining pupils may need support to interpret the resulting
graphs. If the image is projected onto a large sheet of paper, the axes
can be labelled and the graph annotated. Ask questions such as:
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
If you are standing still, what will the graph look like?
How can you tell how far from the data-logger you are standing?
Higher attaining pupils could explore distance-time graphs produced by
bouncing a ball beneath the sensor. Ask questions such as:
This document is part of a range of materials designed to help teachers teach using ICT.
For more information, log on to www.teachernet.gov.uk/supportpack
Please note - Permission to reproduce, distribute, adapt and use this document is subject to the terms and conditions
of the Practical Support Pack website, available at www.teachernet.gov.uk/supportpack/termsandconditions.aspx.
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

What percentage of the original height does the ball reach on the second
and third bounce?
Is this percentage the same for different types of balls?
Evaluation
Lesson reflection
These prompts are designed to help you reflect on how the use of ICT
affected your teaching and pupils’ learning.
Prompts for reflection:
1. How did the use of ICT:
o
help pupils to make better progress towards achieving the learning
objectives?
o
affect the pace of learning?
o
affect pupils’ motivation, interest and time spent on task?
o
affect your ability to differentiate your teaching and personalise pupils’
learning?
2. What knowledge or skills have you gained and extended in teaching this
lesson?
3. What adaptations would you make to the lesson and its resources to suit
the needs of your class?
You may wish to create a record of your evaluation and save it as
evidence of your professional development. If so, you can download a
template containing these prompts and spaces for your responses.
Materials evaluation
These prompts are designed to help you consider why, how and when
you would incorporate these lesson activities and resources into your
curriculum and teaching plans.
Prompts for evaluation:
1. What are the benefits of using these teaching and learning approaches
and resources to achieve the subject objectives?
2. How do the suggested activities fit with your existing curriculum and
teaching plans?
3. What adaptations would be required to the activities or resources to suit
the needs of your class?
4. Are there any requirements for ICT equipment, other resources, space,
etc. that might limit how and where the lesson is taught?
This document is part of a range of materials designed to help teachers teach using ICT.
For more information, log on to www.teachernet.gov.uk/supportpack
Please note - Permission to reproduce, distribute, adapt and use this document is subject to the terms and conditions
of the Practical Support Pack website, available at www.teachernet.gov.uk/supportpack/termsandconditions.aspx.
www.teachernet.gov.uk/supportpack
You may wish to make a note of your thinking for your own records
and to share with your colleagues. If so, you can download a template
containing these prompts and spaces for your notes.
Download module
Download module
You can download a module pack containing the lesson plan,
resources, supplementary information and extension activities using
the link below. The pack is in a zipped file to minimise file size, but
unless you have a broadband connection, the download may be slow.
To extract the files within the module pack you will need either Winzip
or Microsoft Windows Extraction Wizard. This software is freely
available and can be downloaded from the Software downloads
page.
This document is part of a range of materials designed to help teachers teach using ICT.
For more information, log on to www.teachernet.gov.uk/supportpack
Please note - Permission to reproduce, distribute, adapt and use this document is subject to the terms and conditions
of the Practical Support Pack website, available at www.teachernet.gov.uk/supportpack/termsandconditions.aspx.