m e i . o r g . u k
Curriculum Update
GCSE and A level
Statistics
GCSE Statistics and
A level Statistics are
due to be reformed
for first teaching in
2017. Proposals for
content and
assessment
arrangements are
now out for
consultation. The
deadline for both
consultations is 5
November.
Summary of GCSE
changes from 2015
Ofqual has published
a summary of GCSE
changes from 2015
onwards – this is for
all subjects and lists
the main changes,
when they take place
and links to content
and accredited
specifications.
Postcards outlining
Ofqual’s work
Ofqual has published
a series of
postcards outlining
its work. Subjects
include a summary of
the new GCSE
grading structure and
the national reference
test.
I s s u e
We are delighted to welcome
Dr Hugh Hunt as a guest writer for
M4 magazine. Hugh was awarded
the 2015 Royal Academy of
Engineering Rooke Award for
outstanding contributions to the
public promotion of engineering.
Hugh also
delivered a
plenary:
Bouncing
Bombs and
Boomerangs
at the 2015 MEI
Conference.
Read Hugh’s Views on pages 2-3.
In this issue we are looking at
kinematics, the different terms that
students might encounter and the
distinction between scalar and vector
quantities. There are several reasons
that we think this is an important area to
tackle – not least because it’s
interesting and has many real life
applications!
Looking at current and imminent
curriculum changes, at GCSE level one
-dimensional kinematics is being
introduced in a little more depth than
students have previously encountered,
and some basic two-dimensional
kinematics will become compulsory
within A level Mathematics in due
course. In addition to this, as from
2016, all students will be studying
kinematics within GCSE Science - and
Click here for the MEI
Maths Item of the Month
4 9
S e p t / O c t
2 0 1 5
in somewhat more depth than they will
be studying it in GCSE Mathematics.
One key difference is that in Science,
students will need to understand and be
able to articulate the difference between
scalar and vector quantities.
Looking at examples in a range of
mathematics text books and
assessment materials, it seems that
these distinctions are sometimes
’glossed over’ in order to smooth the
path for students. Terms such as
‘displacement’, ‘distance’ or ‘distance
from station’ are sometimes used
almost interchangeably at GCSE level.
However, with the additional content in
Science, it has to be questioned
whether or not it will be in the best
interests of students to be ambiguous
about terms in Mathematics or to tackle
the issue head on.
In this issue

Curriculum Update

This half term’s focus: Onedimensional kinematics

Hugh’s Views: NEW guest writer
Hugh Hunt

Crash Course: Final edition and
some challenges

Site-seeing with... Simon Clay

KS4/5 Teaching Resource: Onedimensional kinematics
M4 is edited by Sue Owen, MEI’s Marketing Manager.
We’d love your feedback & suggestions!
Disclaimer: This magazine provides links to other Internet sites for the convenience of users. MEI is not responsible for the availability or content of these
external sites, nor does MEI endorse or guarantee the products, services, or information described or offered at these other Internet sites.
Hugh’s Views
Projectiles & parabolas
Dr Hugh Hunt is a
Senior Lecturer in the
Department of
Engineering at
Cambridge University
and a Fellow of Trinity
College. Born and
raised in Melbourne,
Australia, Hugh
gained his first degree
at the University of
Melbourne before
moving to the UK to
study for his PhD in
Engineering at
Cambridge. He has
appeared as an
expert contributor in
several television
programmes,
including Richard
Hammond’s
‘Engineering
Connections’, ‘Fifth
Gear’, and
‘Dambusters: building
the bouncing bomb’.
Hugh is one of the
UK’s leading experts
on the behaviour of
spinning objects, with
a particular love of
gyroscopes and
boomerangs. He uses
these to inspire
students in the study
of Dynamics and
Mechanics.
You can follow
Hugh on
Twitter: @hughhunt
If you throw a ball straight up then it
lands on your head. Throw it
horizontally and it doesn't go very far. If
you just have a go at sketching a graph
of the path of the ball when thrown at
different angles then you will probably
guess about right, that an angle of 45º
gets the ball the furthest distance away.
Funny that. A graph without any maths
at all! If you do the maths then the path
of the ball is a parabola and the answer
for optimal launch angle comes out at
exactly 45º and you feel quite good.
Now try the experiment. On a windy
day? No, of course not. From the side
of a hill? No, that's not right either.
From a plane that's moving at 180mph?
No, the experiment has to be done in a
vacuum from ground level of a perfectly
-flat plane. Now, where will I find one of
those?
dug specially for the gun so that it could
be pointed directly at London – and the
tunnel was dug at an angle of 50º. Why
50º? Well, the projectiles were going
way faster than the speed of sound and
air resistance was really important.
Click to enlarge
(Diagram by Sanders, T.R.B. [Public domain], via
Wikimedia Commons)
The prototype V-3
cannon at Laatzig,
Germany (now
Poland) in 1942.
Bundesarchiv, Bild
146-1981-147-30A
CC-BY-SA 3.0 de
Click here for a
diagram of how the
V-3 worked.
In World War II, guns were all over the
place. None were on flat planes in a
vacuum. So how did the gunners work
out the best angle to shoot their guns?
In northern France Hitler had developed
a mammoth 130-metre-long supergun,
called the V3, buried deep in the chalk
rocks at Mimoyecques, just south of
Calais. It was in a huge inclined tunnel,
The German engineers had done their
sums and drawn their graphs. It was
their best guess, 50º. Was 50º really
right? We'll never know because
fortunately (well, maybe not for the
Germans) the V3 was destroyed by one
of Barnes Wallis's Tallboy earthquake
bombs. The bomb was dropped from a
plane flying high at 20,000ft and at a
speed of 180mph. This bomb impacted
the ground at a speed of 750mph –
faster than the speed of sound. Try
sketching a graph of its path. You'd
start with a parabola, that's good.
Hugh’s Views
Air resistance & arches
New KS4/5
classroom
resource
At the end of the
magazine is a new
teaching and learning
resource:
Kinematics by Carol
Knights. This provides
an introduction to one
-dimensional
kinematics, making it
suitable for those
undertaking the new
GCSE and for those
starting Mechanics at
A level.
The concept of scalar
and vector quantities
is introduced, and
whilst it is not a
specific requirement
within GCSE
Mathematics to know
the terms and
understand the
distinction, it is in
GCSE Science.
Additionally, both
speed & velocity and
displacement &
distance are referred
to within the DfE
objectives for KS4
mathematics and
within several exam
board specifications.
But what about the speed of the
aircraft? And that dreaded air
resistance?
The nose of the Tallboy was
shaped like a parabola. Why?
Well, it had to be very strong to
resist impact so that it would
bury itself deep under the
ground, and then explode.
The Romans built very strong
bridges and they thought that the
best shape for an arch was a
semicircle. Later the Normans
copied the same idea. Then Gothic
arches were pointy. But we know now
that a parabola is the strongest shape
for an arch. Or is it? Well, there is
another curve called a catenary that is
the right shape if the arch is very thin
and carrying just its own weight.
If you sketch a graph of the parabola
and the catenary together they don't
look much different. In fact, even the
semi-circular arch looks quite good.
The real world is very complicated. The
best way to begin is with simple graphs.
Sketch them by hand. Forget air
resistance and sloped ground. Just
enjoy the simplicity of nice clean
graphs, and you learn so much from
them. You might even start to notice
parabolas just about all over the place!
The M4 Editor found plenty of
arches on a recent trip to the USA.
See the MEI Facebook page.
By Mikey from Wythenshawe, Manchester, UK
(Another view of Hulme Arch...) [CC BY 2.0 or
CC BY-SA 2.0], via Wikimedia Commons
By Tagishsimon (Own work) [CC BY-SA 3.0
or GFDL], via Wikimedia Commons
By Iridescent (Own work) [CC BY-SA 3.0 or
GFDL], via Wikimedia Commons
Interpreting and
using graphs
One-dimensional motion
“Many people feel
about graphs the
same way they do
about going to the
dentist, a vague
sense of anxiety and
a strong desire for the
experience to be over
with as quickly as
possible,” says Khan
Academy.
“But position graphs
can be beautiful, and
they are an efficient
way of visually
representing a vast
amount of information
about the motion of
an object in a
conveniently small
space.”
When ‘interpreting
travel graphs’ Mr
Barton cautions
students against
rushing to answer
questions; first look at
the axis, scale,
gradient and read the
question!
“In this tutorial”,
says Khan Academy, “we begin to
explore ideas of velocity and
acceleration. We do exciting things like
throw things off cliffs (far safer on paper
than in real life) and see how high a ball
will fly in the air.” A skill check for onedimensional motion helps determine
what areas to review in onedimensional motion. Following this is
the tutorial Displacement, velocity
and time, covering distance,
displacement, speed and velocity. The
tutorial starts with an Introduction to
vectors and scalars, looking at the
difference between the two, before
moving on to look at Position vs. time
graphs.The 15 minute video looks at
how to interpret graphs using a jet
booster powered turtle as an example
to bring the context to life. What
information can you find from such a
graph?
The video demonstrates how to read
the graphs and calculate the following:






Total displacement
Total distance travelled
Average velocity
Average speed
Instantaneous velocity
Instantaneous speed
On this issue’s Site Seeing page (p.7),
Simon Clay suggests using PhEt’s The
Moving Man simulation (requires free
Java software) to introduce students to
the idea of displacement, velocity and
acceleration-time graphs.
This 11 minute video
demonstrates how to
use Moving Man to draw kinematics
graphs for constant acceleration,
including practice for reading, inferring,
and sketching. Mitch Campbell’s threepart video series (targeted at IB
students) starts with a simple example
of rolling a can up a hill, sketching
graphs by hand, then using Moving
Man to graph displacement, velocity,
acceleration, and finally extracting
information from a travel graph.
Distance-time graphs & speed GCSE Science Shorts Sketch – this 3
minute video was produced for GCSE
science students but gives a good
overview of how distance-time graphs
can be used to calculate speed.
Nrich has some very useful
related resources:
What’s That Graph offers students
the chance to explore functions and
graphs in real-life contexts.
On The Road problem can be
explored using graphing software or
graphical calculators to draw graphs
representing the given information.
Motion Capture - this interactive
environment monitors the motion of
your mouse and produces a
displacement-time graph.
NASA Quest’s FlyBy Math
simulator is an online
visualisation tool that offers multiple
linked dynamic representations to help
students understand distance-rate-time
relationships in the real-world context of
air traffic control.
Classroom Resources
Inside Maths Distance:Time
Graphs
This 14 minute
video by EdChat™
TV is about distancetime graphs using
video clips of sports
activities to give the
graphs a real context.
Originally created for
Teachers TV, the
video demonstrates
how to interpret the
graph and use the
distance-time formula
to calculate speed
(e.g. how an athlete
can be faster than his
opponent but still lose
a race against him).
This 25 minute video
GCSE Maths Distance Time
Graphs - Basic
Introduction for
Foundation GCSE
(Some Higher) by
ukmathsteacher
talks students through
how to answer
questions about travel
graphs, using a calm,
clear approach.
Intel Education Resources
offers a useful interactive
overview of distance-time
graphs as a starting point for further
work on plotting and understanding
these graphs.
The National STEM
Centre eLibrary
houses some useful resources for
teaching about travel graphs:
This interactive Excel
program from The
Virtual Textbook covers distance/time
and velocity/time graphs, including:
1. a distance/time graph made of line
segments with questions relating to
speed for each segment and the time
when velocity is zero.
2. the journeys of two people.
3. a velocity/time graph made of line
segments with tasks to find either the
acceleration or the distance travelled.
4. a more realistic velocity/time graph
and students need to use the trapezium
rule to calculate an estimate for the
distance travelled.
The resource also has seven sheets of
printable sets of questions which may
be suitable for use within the
classroom.
This Interpreting
Distance-Time
Graphs with a Computer resource is
part of the DfE Standards Unit, and is
designed to enable learners to interpret
linear and non-linear distance–time
graphs, using the computer
programme Traffic.
“This program provides a simple yet
powerful way of helping learners to
visualise distance–time graphs from
first principles. The program generates
situations involving traffic moving up
and down a straight section of road. It
then allows the user to take
‘photographs’ of this situation at onesecond intervals, places these side-byside, and then gradually transforms this
sequence of pictures into a distance–
time graph. In this way, direct
correspondences between speeds and
gradients are obtained.”
Using the DfE Standards Unit
Interpreting Distance – Time Graphs
resource students learn to interpret and
construct distance–time graphs, relating
speeds to gradients of the graphs and
accelerations to changes in these
speeds.
“Students have often constructed
distance–time graphs before. However,
experience shows that many still
interpret them as if they are pictures of
situations rather than abstract
representations... they also find it
difficult to interpret the significance of
the gradients of these graphs.”
National STEM Centre Maths Specialist
Steve Lyon comments: “I have found
the fact that there is not a unique
solution to this exercise generates a
great deal of discussion between
students.”
Have you seen this poster
Could you make the jump? by The
Further Mathematic Support
Programme’s Phil Chaffe, looking at
the car jump in Fast and Furious 7?
Crash Course:
final edition
A maths and
computing puzzle
column written by
Richard Lissaman
1. Write a program that prints the coordinates of those points (a, b) with 1 < a <
10 and 1 < b < 10, a and b integers, which are inside the circle centred at (4,5)
with radius 3.
2. Assuming a, b, c and d are real numbers with a ≠ c, write a program that takes
inputs of a, b, c, d and t and prints to the screen the y-coordinate of the point
on the straight line joining (a,b) and (c, d) with x-coordinate of t.
3. You can invest £1000 for one year in any of the following banks:
This column provides
an introduction to the
programming
language Python
using maths puzzles
as motivation to learn
code!
This is the final edition
of Crash Course. In
the column you’ve
learnt about variables,
print, functions, if/
else, while, for loops
and arrays.
All of the problems
opposite draw from
ideas in A level
Mathematics and can
be solved with only
the commands listed
above. For more
problems like this see
mei.org.uk/coding.
The solutions appear
on the Monthly
Maths web page.

Bank 1 pays you 100% interest once, at the end of the year.

Bank 2 pays you 50% interest after six months, and then a further 50%
interest after the second sixth months.

Bank 3 pays you 33.3333…% interest after 4 months, then 33.3333…%
after another 4 months and the final 33.3333…% after the last four
months. And so on…
Write a function which takes input of a positive integer n and returns the
amount in your account at Bank n after one year should you invest your
£1000 pounds there. What is the smallest value of n such that bank n returns
more than £2700 after one year?

4.
1
3
r
r 1
 0.5 How many terms, n, are needed in
n
1
3
r 1
r
so that its value
differs from 0.5 by less than a) 0.1, b) 0.01, c) 0.001?
5. This question is related to definition of differentiation (‘first principles’).
Here you’ll find an approximation to the derivative of f(x) = x2 at x = 3.
Starting with h = 1, calculate
3  h
2
 32
h
Then continually halve h and recalculate. Stop doing this when the distance
between two successive results is less than 0.00001 and print the value of the
latest calculation to the screen.
6. Write a function that takes a, b, n (a positive integer) as inputs, prints the
b
estimate to
 x dx using the trapezium rule with n trapezia and then prints the
2
a
difference between this value and
b3 a 3

3 3
What is the smallest value of n such that the difference between the estimate
to
2
2
 x dx using n trapezia and
1
23 13 is less than 0.00001?

3 3
Site seeing with…
Simon Clay
Simon Clay is the
MEI Teaching
Advanced
Mathematics (TAM)
Coordinator.
Inquiry Maths is a
website which gives
mathematical statements
(prompts) designed to
spark the interest of students and help
encourage them to regulate their own
activity. The approach advocated is
very much student-centred and allows
them to ask their own questions,
develop the direction of their learning
and explore mathematics.
After gaining a BSc in
Mathematics, Simon
completed his PGCE
in Secondary
Mathematics in 2000.
Simon taught
Mathematics for 7
An Inquiry I particularly like is Surds
years in an 11-18
Inquiry.
The prompt is simply the
school. He then
surprising statement shown below:
worked as Head of
Mathematics in a Sixth
Form College for 5
years before joining
MEI in 2012.
Simon is an NCETM
Level 3 Mathematics
Professional
Development
Accredited Lead.
Simon presents the
TAM course, the
Introduction to
Mechanics course
and the Head of
Mathematics course.
Whatever your initial reaction to this
prompt is, you hopefully want to
discover whether it is true or not. Once
this initial statement has been proved or
disproved there is then a rich vein of
inquiry available for students.
The prompts come with supporting
materials such as descriptions of what
happened when the inquiry was used
with a group of students, mathematical
notes, prompt sheets, interactive
whiteboard files and alternative
prompts.
The site helpfully categorises prompts
in the broad areas of Number Prompts,
You can follow Algebra Prompts, Geometry Prompts
Simon on
and Statistics Prompts. It also describes
Twitter at
the Inquiry approach and provides
@simonclay_mei
helpful articles and support for
introducing this approach into your
classroom.
PhET Interactive
Simulations are a free
resource provided by
the University of Colorado. They are
designed for High School Science and
Math(!) and I have found them useful in
the teaching of basic Mechanics. They
run from a web browser using Java and
are extremely user-friendly.
Simulations can be a powerful way of
exploring mathematical models. They
can help students to visualise what is
happening in a given scenario, address
misconceptions and discuss modelling
assumptions. I have found the following
three simulations effective, all of which
can be found in the Physics section:
The
Moving
Man works
very well
on an
interactive
whiteboard where students can be
introduced to the idea of displacement,
velocity and acceleration-time graphs.
Features such as being able to display
1, 2 or 3 of the graphs at a given time is
helpful in order to be able to draw
attention to the various aspects of the
graphs. It is also nice to be able to
replay the motion of the ‘Moving Man’
and pause at interesting points in the
journey. Of course challenges such as
‘Can you create a journey that will
generate a given graph?’ naturally
follow for students.
Other simulations from the site worth
exploring are Projectile Motion and
The Collision Lab.
Words and meanings
In maths, words can be very important and
sometimes have a more specific meaning than
we first think.
For example, if we talk about ‘doing a sum’,
many people think this means the same as a
‘doing a calculation’, but ‘sum’ means
‘addition’, so 7-3=4 is not strictly a ‘sum’ at all.
You will meet other words that are sometimes
misused in maths and science during these
activities.
Scalar and vector quantities
When talking about certain measures, there
are two types: scalars and vectors.
• A scalar quantity has magnitude (size)
• A vector quantity has magnitude and
direction
An example: If I start from home and walk at
5km per hour, how far from home am I after an
hour?
Scalar and vector quantities
Surely I must be 5km from home…
…but what if I turned around after half an
hour?
…what if the road isn’t a perfectly straight
one?
Scalar and vector quantities
If we assume that the road is perfectly
straight:
• distance travelled (a scalar quantity)
is how far I’ve walked, regardless of
whether I’ve turned around or not
• displacement (a vector quantity) is
how far I am along the road from my
starting point – in this case, home
Scalar and vector quantities
Vector quantities also have
direction, so if I walked in the
opposite direction along the road
from my house, it would be a
negative displacement.
Would the distance travelled also
be negative?
Scalar and vector quantities
We also sometimes use just ‘distance’
or ‘distance from xxxxxx’.
This is a scalar quantity and shows how
far from a certain object something is,
but takes no notice of direction.
Can you see that I can be
in two different positions
and still be the same
distance from the house?
Displacement
A displacement
- time graph
could look like
this:
What would the
distance-time
graph look like?
Displacement & Distance
Does one of the
graphs give you
a bit more
information
than the other?
Displacement & Distance
What would the
corresponding
distance
travelled-time
graph look like?
Displacement & Distance
Which of these is
most informative?
Displacement and distance
Which of the displacement-time graphs
on the next slide match with this
distance travelled-time one?
1
4
2
5
3
6
Displacement and distance
Which other pair of the displacementtime graphs would have the same
distance travelled-time graphs as each
other?
What would the distance travelled-time
graph for the third one look like?
3
1
4
Position
Another term used is ‘position’, this is
always relative to a specific object – in
this case the house.
Think about the two scenarios on the
next slide. For each one sketch:
• a position-time graph
• a displacement-time graph
• and ‘distance from the house’-time
graph
Position
1. I start from the house and walk in the
direction of the arrow at a steady
pace for 5 seconds, stop for 2
seconds, turn round and walk back
at a quicker pace for 5 seconds
2. I start from the red dot and walk in
the direction of the arrow at the
same steady pace, stop for 2
seconds, turn round and walk back
at the quicker pace for 5 seconds
Position
What do you notice about the graphs?
You should have noticed that the
displacement-time graphs are identical.
The position-time graphs have the same
shape as each other, and the same
shape as the displacement-time graphs,
but translated a little in each case.
Position
The ‘distance from the house’-time
graphs are similar to the others initially,
but when the walker gets to the other
side of the house, the graph is different
as it stays in the positive section of the
page (because it’s a scalar measure).
Speed and velocity
Speed and velocity are another pair of related
quantities:
• speed is a scalar quantity
• velocity is a vector quantity
Speed and velocity
A car travelling at a constant speed of 30km/h can
be going in any direction, whereas a car travelling
with a constant velocity of 30km/h means that the
car is moving in a specific direction.
Can speed, velocity or both
be negative?
Speed and velocity
Speed and velocity are both ‘rates of change’
which means they refer to how quickly
something is changing.
• Speed is the rate of change of distance
• Velocity is the rate of change of displacement
Speed and velocity
From these definitions we can infer that:
• the gradient of a distance travelled-time graph
is speed,
• the gradient of a displacement-time graph is
velocity.
Speed and velocity
Why would there be an issue with using the
gradient to work out speed from the ‘distance
from home’- time graph below?
Average speed and velocity
Average
speed =
Total distance travelled
Time
Average
velocity =
Displacement
(from start to finish)
Time
Are they the same?
Always?
Sketch a few graphs to convince
a partner.
Average speed and velocity
• Look at this
displacement-time graph.
• What is the displacement
from start to finish?
• What is the total distance
travelled?
• Work out the average
speed and the average
velocity.
Velocity, displacement and
distance travelled
A set of cards – copied on the next slide has 4 displacement-time graphs together
with the corresponding:
• Velocity-time graphs,
• Distance travelled
• Average speed
Match the sets and fill in the blanks
Average velocity is -1m/s
Average velocity is _______
Average velocity is 1.33m/s
Average velocity is 0m/s
Distance travelled is ________
Distance travelled is 12m
Distance travelled is 14m
Distance travelled is 14m
Average speed is _______
Average speed is 2m/s
Average speed is _______
Average speed is_________
Teacher notes: Kinematics
This edition looks at an introduction to 1 dimensional kinematics,
making it suitable for those undertaking the new GCSE and for those
starting Mechanics at A level.
The concept of scalar and vector quantities is introduced, and whilst it
is not a specific requirement within GCSE Mathematics to know the
terms and understand the distinction, it is in GCSE Science.
Additionally, both speed & velocity and displacement & distance are
referred to within the DfE objectives for KS4 mathematics and within
several exam board specifications.
Making references to both without explaining the difference to students
could cause confusion, particularly if they are encountering them in
Science, so parts of this activity address this issue.
Teacher notes: symbols
An opportunity for students to discuss
something in pairs and then feed back to the
class.
Students to write something down or work
something out.
A suggestion in the teacher notes of a way to
make an activity more ‘girl friendly’ in order to
increase the confidence of girls in class.
Teacher notes: Scalar and vector quantities
Slides 3 & 4: If I’ve walked 5km, I could
be anything from 0km to 5km from home.
We usually make assumptions in maths to
help simplify things, but these assumptions
are often not shared with students. With
‘distance-time’ work, our underlying
assumption is often that the road or path or
train track is a straight one.
Slide 6: Distance travelled is always
positive. It is cumulative and so can never
‘drop back down’ (have a negative gradient).
Make it ‘girl friendly’:
Ask students to
discuss it with a friend
before giving an answer
Teacher notes: Displacement and distance
Slides 10 & 11: It’s really worth ensuring
that students understand the difference
between the 3 terms and appreciate how
the graphs correspond to each other.
Ensure that students realise that
distance travelled is cumulative.
Distance and distance travelled are
always positive quantities; displacement
can be positive or negative
Slides 12 - 15: An A4 sheet of 9
matching cards (Distance and
Displacement graphs) is available as an
alternative to using the slides.
Make it ‘girl friendly’:
Print out the matching
cards and ask students to
work in pairs.
Teacher notes: Distance and Displacement
Answers:
Slides 12 & 13: 2, 5 and 6
Slides 14 & 15: 1 & 3 have the same
distance time graph (below); the second
one is for displacement graph 4
Matching cards answers:
A with E, H and J
B with D and F
C has no match
• can you draw one? (Yes)
• Is there more than once
answer for this? (Yes,
infinite possibilities).
G also has no match:
• can you draw one?
(Yes).
• Is there more than one
answer for this? (No: this
graph only).
Teacher notes: Speed and velocity
Slide 21 : Speed is always positive, velocity can be positive or negative.
Slide 24: The gradient of the last part is negative, but since speed is a
scalar, it can’t be negative. This is a big issue with ‘distance from’ – time
graphs, which are often used.
Slide 25 :It can make a difference, sometimes the graphs will look the same
and the values will be the same, often they’re not.
• When are they the same?
Slide 26: An example of when the values are
different.
Slide 28: Either show the slide, use the cards or
print out as a worksheet. Cards would be easier
for students as they will be able to annotate
them. Answers on final slide.
Make it ‘girl
friendly’:
Cut out the cards and
work with a partner.
Average velocity is 0m/s
Average velocity is1.33m/s
Average velocity is -1m/s
Average velocity is -1m/s
Distance travelled is 12m
Distance travelled is 14m
Distance travelled is 14m
Distance travelled is 16m
Average speed is 2m/s
Average speed is 2.33m/s
Average speed is 2.33m/s
Average speed is 2.66m/s