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APPLIED Maths in the New NC
[Modelling is …] model simple describe relationships in bivariate data … interpolate and extrapolate trends.
contextual and subject-based problems algebraically model situations or procedures by translating them into algebraic expressions or formulae
[Modelling … precise] solve growth and decay problems, such as financial mathematics problems with compound
interest
[Modelling … imprecise] understand and use the concepts of instantaneous and average rate of change in graphical
representations (chords and tangents), including with velocity and acceleration … including piece-wise linear solve velocity and acceleration problems … velocity/time graphs, and mechanics problems,
such as those involving collisions and momentum.
24.1 Mathematical Modelling
• Use of assumptions in simplifying reality. – Candidates are expected to use mathematical models to solve
problems. • Mathematical analysis of models.
– Modelling will include the appreciation that: • it is appropriate at times to treat relatively large moving bodies as point
masses; • the friction law FR is experimental.
• Interpretation and validity of models. – Candidates should be able to comment on the modelling
assumptions made when using terms such as particle, light, inextensible string, smooth surface and motion under gravity.
• Refinement and extension of models.
Map, Narrative, Orientation
Make a collection of phenomena that we may wish to model with the principles of mechanics
Map, Narrative, Orientation
Which principles in Physics are used to model these? • What are the models (relationships = formulae)? • What are the variables?• What mathematical principles and procedures are
needed?• Accurately list the details: units, notations,
diagram conventions…
(You can) limit yourselves to M1 and M2
Map, Narrative, Orientation
• Generate a map for the content of M1 and M2 showing the interconnections of the elements.
• Make clear any necessary ordering.• Put the principles of mathematical modelling
where they belong.• Work in sub groups of 4 to produces an A3
map.
Map, Narrative, Orientation
• Choose one section from the M1 or M2 syllabus.
• In prose, construct a (longish) paragraph which would describe to a learner what they learn in studying this section. (NOT a list!)
Walking the Line understand and use the
concepts of instantaneous and average rate of change in graphical representations (chords and tangents), including with velocity and acceleration
… including piece-wise linear solve velocity and acceleration
problems … velocity/time graphs, and mechanics problems, such as those involving collisions and momentum.
Getting a feeling for Projectiles
We know for a projectile:The horizontal equation of motion is The vertical equation is
Map, Narrative, OrientationIn subgroups of 4 (including one Engineer or PwM)• Construct an activity that
will give learners a feel for one of the ideas that they are being apprenticed into.
• Translate the practical activity into a workable problem-to-be-solved
TASK:1. Devise an activity in
which learners experience the idea
2. Create a ‘text-book’ problem and solve it the same as your activity
3. Share out the labour … use your experts …
4. ‘Teach’ your second subgroup by engaging them in your activity.