Engaging weaker students in
D1
Nick Thorpe
5th July 2008
Prior Knowledge
D1 is very accessible; it requires very little
prior knowledge
Algebra
• Plotting straight lines
• Solving Simultaneous Equations
• Proportionality
However
Questions tend to contain a lot of
information and students will need to
practice extracting the necessary
information.
This means that students with English as a
second language in particular can find
interpreting questions challenging.
Do not brush over terminology
Students need to understand the definitions
of the key terms, they will not be able to
interpret questions without it.
Definitions Jigsaw
Rigour
In the exam, students will be given no credit
if they do not follow the specified algorithm
Do not let students feel that they can get
away with skipping steps even if they can
see the solution!
Decision Maths is used
in the Real World!
• Business: Scheduling using Critical Path
analysis
• Nutrition: optimal mix of ingredients to
ensure adequate nutrition for minimum
cost
• Logistics: transporting goods efficiently
(shortest distance, minimum costs etc)
• Finance: Lowest bid - electronic auction
• Health: Nurse scheduling, reducing
queuing times
Decision Maths is used
in the Real World!
Seeing the real world application of the
techniques will help students to remember
and apply them
Cabling
application
History of LP and
In fact, most exam questions are related to
the real world.
Powerpoints
There are some excellent powerpoint
presentations in the MEI online resources.
Activity Networks
Bin Packing 1 Bin Packing 2
Dijkstra
Coloured Pens
This can be very useful for tracing the steps
of any process.
What are the variables?
Leone gets to choose how much of
her garden to devote to lawn and
flower beds.
Define the variables:
•Let x be the area of lawn
•Let y be the area of flowerbeds
What to optimize?
Leone wants the maintenance to be cheap!
Maintenance costs: 0.15x+0.25y
What are the constraints?
Total area:
x + y ≥ 1000
Costs:
0.8x + 0.4y ≤ 500
Preference:
y ≥ 2x
Positive solution: x ≥ 0, y ≥ 0
Write on Sheets
Do not waste lesson time getting students
copying diagrams!
Group work, Discussion
and Problem Solving
Open Questions:
• Create a problem where the first fit
algorithm does not produce an optimal
solution
• Create an LP problem where the optimal
solution occurs when x=20 and y=30.
• Create a matrix where Prim’s algorithm,
starting at A, connects C, B then D.
• What is the worst case for Dijkstra's
algorithm.
Presentations
Each of the different topics are ideal for
setting students real world problems, to
which they can present their solutions to
the class.
E.G
• Dijkstra on a roadmap
• Critical Path for planning a party/meal
• Linear Programming for Diets
• Any interesting algorithm
Look online!
There are many applets which apply the
algorithms in an interactive manner
Which Algorithm?!
Interesting Problems!!
The String Problem:
MacDiet!
Diet 1
Solution:
1.3 Big Macs
70.5 Tomato Ketchups
Cost £1.30
Diet 2
1 Big Mac
2 French Fries
4 Tomato Ketchup
3 Banana Milkshakes
Cost £4.83
Diet 3
Solution:
2 Scrambled Eggs+Muffin
3 French Fries
6 Tomato Ketchup
2 Banana Milkshakes
Cost £5.23
Diet 4
Solution:
1 Cheeseburger
1 MacChicken Sandwich
2 French Fries
4 Tomato KEtchu[p
2 Banana Milkshake
1 Hot Chocolate
1 Orange Juice
COST £5.99
With your class...
• Ask each student to bring in the nutritional
content for their favourite food, and the
price per portion. Or look up online.
• Start off in pairs looking for cheap diets
with basic nutritional needs satisfied,
constraints on quantity etc.
• Then try putting in 3’s – maybe using
online LP solvers e.g.
LP solver
Algorithms
Theseus VS Minotaur
Sheet
www.logicmazes.com/theseus.html
Day of the week algorithm
Sheet
www.travelfurther.net/dates/datesrus.asp
Random Walks
A random walk starts at zero, and moves
either left or right with equal probability. It
is easy to implement in excel. Random
Walk
After n steps, the expected distance
travelled approaches
2π
n
We can use simulation to approximate π!
www.mathworld.wolfram.com/RandomWalk1-dimensional.com
Traversibility extension
A graph is said to be traversable if it is
possible to find a path which uses all of
the edges of the graph without repetition.
If the path starts and ends at the same point
it is Eulerian, and is good for paperboys!
But what if the graph is directed?!
Thanks!
All the activities in this PowerPoint are
referenced either on the MEI resources
website or are online.
You can get free access by registering with
your local Further Maths Centre
This PowerPoint will soon be available on
www.mei.org.uk