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This problem offers students the chance to explore functions and graphs in real-life contexts. There is an opportunity for students to use their scientific understanding as they are invited to suggest plausible processes for each graph.
Hand out this worksheet with copies of the eight graphs, and ask students to discuss in pairs what physical processes they could represent. Make it clear that there are a lot of possible answers:
After students have had time to come up with processes for each graph, invite them to share their suggested processes and justifications. Encourage the class to be critical of the suggestions.
Next, reveal that the graphs were actually generated from the processes listed on this worksheet. Hand out the worksheet, and ask students to work in pairs to match the processes (and equations if appropriate) to the graphs.
To ensure that students think critically about matching the processes to the graphs, students could be required to present their solutions on a poster with each graph and process (and equation if appropriate) accompanied by a short sentence explaining WHY they match.
What are the key features of each graph?
Where might the axes be placed on the graphs? What scale might you put on the axes?
Start by giving students the processes and ask them to discuss and sketch what the graphs might look like first. Clarify the appropriate labels for each of the axes.
Ask students to suggest realistic values for the constants A, B and C in the equations of the graphs.
If a is the radius of the axle, b the radius of each ball-bearing, and c the radius of the hub, why does the number of ball bearings n determine the ratio c/a? Find a formula for c/a in terms of n.
An observer is on top of a lighthouse. How far from the foot of the lighthouse is the horizon that the observer can see?
Find the distance of the shortest air route at an altitude of 6000 metres between London and Cape Town given the latitudes and longitudes. A simple application of scalar products of vectors.