the Further Mathematics network
the Further Mathematics network
www.fmnetwork.org.uk
www.fmnetwork.org.uk
Additional Maths
Additional Maths (MEI Conference)
Welcome!!
3rd July 2008
Let Maths take you Further…
FSMQ Additional Mathematics
FSMQ Additional Mathematics
Hello, my name is Tim…
And you are…
What is Additional Maths?
„
„
„
I have just completed my second year teaching
Additional Maths to students from four different
schools, through the Further Mathematics Network
Lessons took place at the University of Warwick on
Thursdays after school, 4pm-5.30pm
I come from a University background and taught
alongside someone with a school background. This
worked well
„
„
„
Extension to GCSE mathematics
Aimed at able year 11 students
Level 3 qualification
FSMQ Additional Mathematics
FSMQ Additional Mathematics
The content of Additional Maths
How many students did we have?
4 strands of Pure Maths each followed by an
application
1.
2.
3.
4.
Algebra – The binomial distribution
Co-ordinate geometry – Linear programming
Trigonometry – 3D Trigonometry
Calculus – Kinematics
First year:
„ At first we had getting on for thirty!
„ They all seemed to enjoy the lessons, but sadly a lot
dropped off (reasons: perhaps after school, too
hard, largely though problems with schools
arranging taxis)
„ We finished with about twelve
Second year:
„ Similar but better!
1
FSMQ Additional Mathematics
Why did students join our classes?
„
„
„
NOT everyone joined our classes to sit the exam
Even people who weren’t too confident for the
Additional Mathematics exam still recognised that
the lessons had improved their confidence in GCSE
no end, and had prepared them brilliantly for A Level
Our ‘success story’ was a student who was keen but
not one of the best in the class. Over the course of
the year he became a top student in his GCSE
lessons. The school now wants to send 10+
students to Additional Mathematics next year
continued
„
„
One student even used Additional Mathematics to
improve his confidence in his Core A Level
Mathematics (and the improvements have been very
noticeable)
This year we had two Year 10 students sit the exam
The feedback
FSMQ Additional Mathematics
Homeworks/Independent Study?
„
„
„
„
All students had access to the Online Resources
Homework was set though some of the students
weren’t very motivated for independent study. It was
hard to push this when they were doing this as an
extra subject (I’ll be harder next year! [A year on: “I
could still be harder!!”])
We could cover the course content across the
year… but only just!
Please ask me any questions at any stage of this
hour… or afterwards!
"Thanks for all of your help, I know [student's name] didn't take
the exam with you but she had a lot more confidence after
attending your classes, I think you opened her eyes to a different
way of looking at maths, she's chosen to take Maths at AS level
this year at school."
"Thanks for all your help - we wouldn't have got those results
without you."
"You have been a really great help in helping me to understand
Maths a lot better.“
[We had a presentation to parents before the start of the course].
FSMQ Additional Mathematics
FSMQ Additional Mathematics
Models of delivery used by schools
Resources
„
„
Complete GCSE Maths in year 10 or by
January of year 11, then study Add Maths
Study alongside GCSE Maths in year 11 (or
across Years 10 and 11)
‰
‰
Whole group
Selected students from a group
„
„
„
„
Textbook
Online resources –
www.addmaths.mei.org.uk
Past papers – www.mei.org.uk
Handwritten solutions and Powerpoint
solutions
It is preferable if the decision to enter the students
for the exam is delayed for as long as possible
2
FSMQ Additional Mathematics
Professional Development
„
‰
‰
Useful URLs
„
2-day CPD courses
‰
FSMQ Additional Mathematics
Day 1: introduction to the big ideas in Add Maths
In-between: consolidation based on web-resources and
textbook
Day 2: teaching approaches, student misconceptions and
extension work
„
„
„
The Further Mathematics Network:
www.fmnetwork.org.uk
Online resources:
www.addmaths.mei.org.uk
Past papers and CPD information www.mei.org.uk
Specification
www.ocr.org.uk
see http://www.mei.org.uk/cpd/alevel.shtml
FSMQ Additional Mathematics
UCAS tariff points
FSMQ
A level
120
A
100
B
80
C
60
D
AS level
A
50
E
C
30
D
A
20
E
B
17
C
13
D
10
E
7
FSMQ Additional Mathematics
Additional Mathematics Statistics
2003
2004
2005
2006
2007
2342
3466
3936
4381
5500
A
Grade
Points
A
45
B
40
C
35
D
30
E
25
B
40
candidates
FSMQ Additional Mathematics
Performance table points
B
C
D
E
77
67
57
48
39
29.10%
44.50%
58.00%
67.40%
76.40%
70
61
52
43
34
27.50%
40.30%
52.70%
63.30%
73.10%
71
61
51
41
32
27.80%
38.30%
47.60%
57.20%
66.40%
79
67
56
45
34
35.2%
48.1%
57.3%
65.7%
75.3%
??
??
??
??
??
28.8%
38.6%
48.1%
57.5%
66.8%
What the examiners have said
„
„
“Many candidates not only failed to
demonstrate any understanding of the
extension material but failed to demonstrate
… understanding of some Higher Tier topics”
[2003]
“There were a distressing number of
candidates scoring very low marks… This
cannot have been a positive experience for
them” [2004]
There were some very good comments too!
3
continued
„
„
the Further Mathematics network
www.fmnetwork.org.uk
“… it is still true to say that there are a significant
number of candidates who appear to have been
entered for a qualification that is not suited to their
abilities” [2005]
“However, it is still disappointing to find a number of
centres for which this specification is clearly not
appropriate. The specification clearly states that…
[it]… is suitable for those gaining a good grade at
GCSE – typically A*, A or B.[It]… is designed to be
an enrichment for Higher Tier students” [2006]
Additional Maths Revision Day
11th June 2007
University of Warwick
Outline of Topics
the Further Mathematics network
www.fmnetwork.org.uk
Welcome!
Algebra I - Review
1. Algebra I - Review
2. Algebra II - Techniques
3. Algebra III - Polynomials
4. Algebra IV - Applications
5. Co-ordinate Geometry I
6. Co-ordinate geometry II – Applications
7. Trigonometry I
8. Trigonometry II – Applications
9. Calculus I – differentiation
10. Calculus II – Integration
11. Calculus III – Applications to Kinematics
AM 13th June 2003
Question 1
I.
II.
III.
IV.
V.
VI.
VII.
Linear Expressions
Solving Linear Equations
Changing the subject of an equation
Quadratic expressions
Solving a quadratic equation that factorises
Completing the square
Simultaneous equations
4
Algebra II - Techniques
AM 15th June 2006
Question 5
I.
II.
III.
IV.
V.
Linear Inequalities
Solving quadratic inequalities
Simplifying algebraic fractions
Solving equations involving fractions
Simplifying expressions containing square roots
AM 21st June 2004
AM 13th June 2003
Question 6
Question 13
Algebra III - Polynomials
AM 13th June 2003
Question 9
I.
II.
III.
Operations with polynomials
The factor theorem
The remainder theorem
5
AM 15th June 2006
AM 20th June 2005
Question 9
Question 2
Algebra IV - Applications
AM 21st June 2004
Question 10
I.
II.
The binomial expansion
The binomial distribution
AM 20th June 2005
AM 13th June 2003
Question 6
Question 6
6
AM 15th June 2006
AM 20th June 2005
Question 11
Question 5
AM 13th June 2003
AM 21st June 2004
Question 12
Question 9
Co-ordinate geometry I
AM 15th June 2006
Question 10
I.
II.
III.
IV.
V.
VI.
VII.
VIII.
IX.
X.
Co-ordinates
The gradient of a line
Parallel and perpendicular lines
The distance between two points
The midpoint of a line joining two points
The equation of a straight line
Drawing a line given its equation
Finding the equation of a line
The intersection of two lines
The circle
7
AM 21st June 2004
AM 15th June 2006
Question 7
Question 7
AM 21st June 2004
AM 15th June 2006
Question 1
Question 4
AM 21st June 2004
Co-ordinate geometry II - Applications
Question 12
I.
II.
III.
Inequalities
Using inequalities for problem solving
Linear Programming
8
AM 15th June 2006
AM 13th June 2003
Question 8
Question 5
AM 20th June 2005
AM 21st June 2004
Question 11
Question 11
Trigonometry I
I.
II.
III.
IV.
V.
VI.
VII.
VIII.
IX.
X.
Using trigonometry in right-angled triangles
Trigonometric functions for angles of any size
The sine and cosine graphs
The tangent graph
Solution of equations using graphs of trigonometric
functions
Identities involving sin θ, cos θ, and tan θ
Using trigonemetric identities to solve equations
The sine rule
The cosine rule
Using the sine and cosine rule together
AM 20th June 2005
Question 12
9
AM 13th June 2003
AM 20th June 2005
Question 4
Question 4
AM 15th June 2006
AM 21st June 2004
Question 3
Question 5
AM 20th June 2005
AM 13th June 2003
Question 9
Question 7
10
AM 20th June 2005
AM 21st June 2004
Question 3
Question 8
AM 15th June 2006
AM 13th June 2003
Question 2
Question 14 (Part One)
Trigonometry II- Applications
AM 13th June 2003
Question 14 (Part Two)
I.
II.
Working in three dimensions
Lines and planes in three dimensions
11
AM 21st June 2004
AM 13th June 2003
Question 3
Question 8
AM 15th June 2006
AM 15th June 2006
Question 13 (Part One)
Question 13 (Part Two)
Calculus I - Differentiation
AM 20th June 2005
Question 1
I.
II.
III.
IV.
V.
The gradient of a curve
Finding the gradient of a curve
Differentiation using standard results
Tangents and normals
Stationary points
12
AM 13th June 2003
AM 21st June 2004
Question 2
Question 4
AM 20th June 2005
AM 15th June 2006
Question 10
Question 14 (Part One)
Calculus II - Integration
AM 15th June 2006
Question 14 (Part Two)
I.
II.
III.
Reversing differentiation
Definite integrals
The area between two curves
13
AM 15th June 2006
AM 13th June 2003
Question 1
Question 3
dy
AM 15th June 2006
AM 20th June 2005
Question 6
Question 7
AM 21st June 2004
AM 13th June 2003
Question 2
Question 11 (Part One)
14
AM 13th June 2003
AM 20th June 2005
Question 11 (Part Two)
Question 13 (Part One)
AM 20th June 2005
Calculus III – Applications to kinematics
Question 13 (Part Two)
I.
II.
III.
IV.
Motion in a straight line
The constant acceleration formulae
Motion with variable acceleration: the general case
Finding displacement from velocity and velocity from
acceleration
AM 13th June 2003
AM 20th June 2005
Question 10
Question 8
15
AM 15th June 2006
AM 21st June 2004
Question 12
Question 14
AM 21st June 2004
Question 13
The End
Here’s looking at you kids…
FSMQ Additional Mathematics
This is a Conference so we’ve got to have
a few funnies…
Reminder to me…
Show Bob Francis’ Powerpoint
exam solutions!!
16
FSMQ Additional Mathematics
This is a Conference so we’ve got to have
a few funnies…
17