Download Word - The Further Mathematics Support Programme

Further Mathematics Support Programme
OCR M2 – Scheme of Work Template - 2016-2017
This template is part of a series designed to assist with planning and delivery of further mathematics courses.
It shows how Integral Resources and Live Interactive Lectures can be used to support students and teachers.
Integral
Resources
Integral
Resources
Live Interactive
Lectures
Teacher-level access to the Integral Resources (integralmaths.org/) for
Further Pure and Applied units is available free of charge to all
schools/colleges that register with the Further Mathematics Support
Programme: www.furthermaths.org.uk/
Student-level access to the Integral Resources and the Live Interactive
Lectures for Further Mathematics is available at a moderate cost via:
www.furthermaths.org.uk/lilfm
Integral Resources include a wide range of resources for both teacher and student use in learning and assessment. A selection of these are suggested in the
template below. Sample resources are available via: http://integralmaths.org/help/info.php.
Live Interactive Lectures are available for individual Further Pure and Applied units and take place in the spring and autumn terms. LIL FM is ideal for
schools/colleges teaching Further Mathematics with small groups and/or limited time allocation. It is also useful to support less experienced teachers of
Further Mathematics. See www.furthermaths.org.uk/lilfm
Scheduling will depend on circumstances, but the template below breaks the module down into 7 sections which may be allocated approximately equal
time. Each section corresponds to one Live Interactive Lecture (LIL) and these take place fortnightly to supplement the teaching and tutorial support in
schools/colleges and students' own independent study. FMSP Area Coordinators will be able to offer additional guidance if needed. See
www.furthermaths.org.uk/regions
OCR M2 – Scheme of Work Template - 2016-2017
Topic
Specification statements
Suggested Integral Resources
Motion of
projectiles
 model the motion of a
projectile as a particle
moving with constant
acceleration and understand
any limitations of this model
 use horizontal and vertical
equations of motion to solve
problems on the motion of
projectiles, including finding
the magnitude and direction
of the velocity at a given
time or position, the range
on a horizontal plane and the
greatest height reached
 derive and use the Cartesian
equation of the trajectory of
a projectile, including
problems in which the initial
speed and/or angle of
projection may be unknown
► OCR_M2
/ ► The motion of projectiles
/ ► The motion of projectiles
1: Introduction
 understand the concept of
the work done by a force,
and calculate the work done
by a constant force when its
point of application
undergoes a displacement
► OCR_M2
/ ► Work, energy and power
/ ► Work, energy and power
1: Introduction
Work, energy and
power
 Projectiles teaching activities
 Additional exercise
Assessment
(Integral
Resources)
Live Interactive
Lecture
Other resources
Motion of
projectiles
PhET simulation:
Projectile motion
nrich: Model
solutions
 Section Test P1
nrich: Dam Busters 1
► OCR_M2
/ ► The motion of projectiles
/ ► The motion of projectiles
2: General equations
 Trajectory teaching activities
 Additional exercise
 Section Test P2
► OCR_M2
/ ► The motion of projectiles
 The motion of projectiles topic assessment
Work, energy and nrich: Powerfully
power
fast
nrich: Go Spaceship
Go




not necessarily parallel to the
force (use of the scalar
product is not required)
understand the concepts of
gravitational potential
energy and kinetic energy,
and use appropriate
formulae
understand and use the
relationship between the
change in energy of a system
and the work done by the
external forces, and use in
appropriate cases the
principle of conservation of
energy
use the definition of power
as the rate at which a force
does work, and use the
relationship between power,
force and velocity for a force
acting in the direction of
motion
solve problems involving, for
example, the instantaneous
acceleration of a car moving
on a hill with resistance
 Energy and power teaching
activities
 Additional exercise
 Section Test W1
► OCR_M2
/ ► Work, energy and power
/ ► Work, energy and power
2: Potential energy
 Energy teaching activities
 Additional exercise
 Section Test W2
► OCR_M2
/ ► Work, energy and power
Rigid bodies 1:
Moments
 calculate the moment of a
force about a point in two
dimensional situations only
(understanding of the vector
► OCR_M2
/ ► Rigid bodies
/ ► Rigid bodies 1: Moments
 Moments teaching activities
 Work, energy and power topic assessment
Rigid bodies 1:
PhET simulation:
Moments
Balancing act
Rigid bodies 2:
Rigid bodies in
equilibrium
Centres of mass
nature of moments is not
required)
 use the principle that, under
the action of coplanar forces,
a rigid body is in equilibrium
if and only if (i) the vector
sum of the forces is zero, and
(ii) the sum of the moments
of the forces about any point
is zero
 solve problems involving the
equilibrium of a single rigid
body under the action of
coplanar forces, including
those involving toppling or
sliding (problems set will not
involve complicated
trigonometry)
 use the result that the effect
of gravity on a rigid body is
equivalent to a single force
acting at the centre of mass
of the body
 identify the position of the
centre of mass of a uniform
body using considerations of
symmetry
 use given information about
the position of the centre of
mass of a triangular lamina
and other simple shapes
 Additional exercise
 Section Test R1
/ ► OCR_M2
/ ► Rigid bodies
/ ► Rigid bodies 2: Rigid
bodies in equilibrium
 Equilibrium teaching
activities
 Additional exercise
/ ► OCR_M2
/ ► Centres of mass
/ ► Centres of mass 1: Finding
the centre of mass
 Centres of mass teaching
activities
 Additional exercise
► OCR_M2
/ ► Centres of mass
/ ► Centres of mass 2: Centres
of mass of special shapes
Rigid bodies 2:
Rigid bodies in
equilibrium
 Section Test R2
► OCR_M2
/ ► Rigid bodies
 Rigid bodies topic assessment
Centres of mass
nrich: Overarch 1
nrich: Overarch 2
 Section Test
CoM1
(including those listed in the
List of Formulae)
 determine the position of the
centre of mass of a
composite rigid body by
considering an equivalent
system of particles (in simple
cases only, e.g. a uniform Lshaped lamina or a
hemisphere abutting a
cylinder)
 Notes and examples
 Section Test
CoM2
► OCR_M2
/ ► Centres of mass
Impulse and
restitution
 recall and use Newton’s
experimental law and the
definition of coefficient of
restitution, the property
0 ≤ 𝑒 ≤ 1 and the meaning
of the terms ‘perfectly
elastic’ (e= 1) and ‘inelastic’
(e=0)
 use Newton’s experimental
law in the course of solving
problems that may be
modelled as the direct
impact of two smooth
spheres or as the direct
impact of a smooth sphere
with a fixed plane surface
 recall and use the definition
of impulse as change of
momentum (in one
dimension only, restricted to
‘instantaneous’ events, so
► OCR_M2
► Impulse and restitution
/ ► Impulse and restitution 1:
Newton's law of impact
 Centres of mass topic assessment
Impulse and
restitution
PhET simulation:
Collision lab
nrich: Whoosh
 Collisions (Geogebra)
 Collisions teaching activities
 Additional exercise
 Section Test I1
that calculations involving
force and time are not
included)
► OCR_M2
/ ► Impulse and restitution
Circular motion
 understand the concept of
angular speed for a particle
moving in a circle, and use
the relation v = rw
 understand that the
acceleration of a particle
moving in a circle with
constant speed is directed
towards the centre of the
circle, and use the formulae
rw2 and v2/r
 solve problems which can be
modelled by the motion of a
particle moving in a
horizontal circle with
constant speed
/ ► OCR_M2
/ ► Circular motion
/ ► Circular motion 1: Motion
in a horizontal circle
 Impulse and restitution topic assessment
Circular motion
PhET simulation:
Ladybug revolution
 Circular motion teaching
activities
 Additional exercise
 Section Test C1
► OCR_M2
/ ► Circular motion
 Circular motion topic assessment
Consolidation and
revision
FMSP - Revision
Videos
The study plans available on Integral Resources refer to Mechanics 2 for OCR (Cambridge Advanced Level Mathematics) (ISBN 9780521549011). Other
textbooks covering this course may be available, and Integral Mathematics Resources does not endorse any particular set of textbooks.