At offset glance it appears that calculus features inwards the novel GCSE specification. On closer inspection it turns out that our students volition detect the slope of a fold yesteryear drawing a suitable tangent rather than yesteryear differentiating. And instead of integrating, students volition use the trapezium rule (or similar) to detect the expanse nether a curve. So calculus remains reserved for Key Stage 5, merely our students volition at nowadays endure amend prepared for calculus when they offset consider it. GCSE volition induce got given them a conceptual agreement of charge per unit of measurement of alter in addition to an powerfulness to translate this contextually.This post talks yous through this novel GCSE topic - it tells yous what yous demand to learn in addition to provides links to resources.
Specification in addition to Exam Questions
Here's the relevant extracts from the novel GCSE specification:
This all becomes clearer when nosotros hold off at illustration examination questions. Huge thank yous to Tom Bennison (@DrBennison) for doing the difficult go for me hither - he's been through the sample assessment materials for all examination boards in addition to collated the relevant questions inwards this Subject Knowledge Check. In a typical question, students are given a velocity-time graph in addition to asked to detect the amount distance travelled and/or the acceleration at a specific time.
AQA helpfully provides additional clarification nigh the specification inwards their instructor guide. The extract below is from GCSE Mathematics (8300) Teaching Guidance (available to All About Maths members) which provides a publish of additional illustration questions.
The diagrams below are taken from this extract from a novel GCSE textbook which sets out the measure methods that our students volition use.
Students volition already know how to detect the slope of a straight off line of piece of employment (ie 'rise over run' or equivalent). To guess the slope of a fold they volition induce got to push clitoris a tangent, equally shown here:
To guess the expanse nether a graph, students volition induce got to separate the expanse into sections. The AQA Teaching Guidance says 'the trapezium dominion demand non endure known merely it is recommended equally the most efficient agency of calculating the expanse nether a curve'. Unlike at H5N1 level, they won't endure given the formula inwards the exam.
Motion Graphs
The methods described to a higher house are fairly straightforward. I recollect interpretation powerfulness seek out trickier (eg agreement what motion graphs are showing). Students volition demand to know that speed, acceleration in addition to deceleration are rates of change, in addition to that the expanse nether a velocity-time graph represents distance. There's a lot of novel concepts in addition to vocabulary here.
Bear inwards heed that motion graphs come upward up inwards Physics GCSE too. As shown inwards this extract from the AQA Physics GCSE Specification, it's just the same content:
Other Contexts
I was initially confused yesteryear the nurture of 'graphs inwards fiscal contexts' inwards this department of the specification - I've seen questions inwards which students induce got to interpret fiscal graphs merely cipher involving tangents or areas. Thanks to @DJUdall for sharing the moving painting below (taken from this novel GCSE textbook) which shows an illustration of estimating a charge per unit of measurement of alter inwards a fiscal context.
Instantaneous Rate of Change
Students volition demand to sympathize the departure betwixt an average charge per unit of measurement of alter over a menses of fourth dimension in addition to an instantaneous charge per unit of measurement of change. In my post 'Introducing Differentiation' I talked nigh how to give students an intuitive agreement of the slope of a fold at a point. It's worth reading the department entitled 'An Instantaneous Rate of Change' for ideas, videos in addition to resources (including my worksheet 'Thinking About Gradient' which was designed for H5N1 score merely is at nowadays suitable for GCSE).
Resources
Resources for this topic are listed below. I'll add together these to my library in addition to volition go along to add together novel resources equally I detect them.
I was initially confused yesteryear the nurture of 'graphs inwards fiscal contexts' inwards this department of the specification - I've seen questions inwards which students induce got to interpret fiscal graphs merely cipher involving tangents or areas. Thanks to @DJUdall for sharing the moving painting below (taken from this novel GCSE textbook) which shows an illustration of estimating a charge per unit of measurement of alter inwards a fiscal context.
Could examination questions embrace other contexts, likewise motion in addition to finance? It's possible. In the illustration below from CIMT students are asked to detect the mass of H2O represented yesteryear the shaded area. To sympathize why the expanse nether the graph represents mass nosotros tin consider the units - the units on the horizontal axis are seconds, in addition to the units on the vertical axis are m3/s, in addition to hence when nosotros multiply the 2 together nosotros larn m3.
Resources
Resources for this topic are listed below. I'll add together these to my library in addition to volition go along to add together novel resources equally I detect them.
- @DJUdall has produced this fantabulous graphing activity which covers both tangents in addition to areas nether graphs.
- @jase_wanner has written this super hero activity on distance-time in addition to speed-time graphs to prepare students' agreement of how to translate these graphs.
- Gradient on a curved graph by Owen134866 on TES gives students the chance to exercise drawing graphs in addition to tangents. My worksheet Finding the slope of a fold using a tangent is similar, merely students aren't required to push clitoris the graphs themselves.
- Using Graphs from CIMT covers a broad attain of graph topics. Section 17.2 covers areas nether graphs using the trapezium dominion in addition to Section 17.3 covers tangents to curves. The amount attain of resources for this module are available on TES.
- Nuffield Mathematics provides a Free-Standing Mathematics Activity 'Speed in addition to Distance' which is nigh finding the expanse nether a speed-distance graph. Resources include slides, a student sheet and teacher notes.
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| 'Graphing' by @DJUdall |
I promise this post has been useful inwards helping yous laid upward to learn this novel GCSE topic. Please allow me know if yous induce got whatsoever resources to share.
You powerfulness also detect my other posts nigh novel GCSE topics helpful: Sequences, Inequalities in addition to Quadratic Graphs.
See my New GCSE Support Page for resources in addition to links for all novel GCSE content.
You powerfulness also detect my other posts nigh novel GCSE topics helpful: Sequences, Inequalities in addition to Quadratic Graphs.
See my New GCSE Support Page for resources in addition to links for all novel GCSE content.
