Picture the process I

How does the temperature of a cup of tea behave over time? What is the radius of a spherical balloon as it is inflated? What is the distance fallen by a parachutist after jumping out of a plane? After sketching graphs for these and other real-world processes, you are offered a selection of equations to match to these graphs and processes.

Exploring and noticing Working systematically Conjecturing and generalising Visualising and representing Reasoning, convincing and proving
Being curious Being resourceful Being resilient Being collaborative

Problem

Image
Powerful Quadratics



This resource is from Underground Mathematics.

Here are descriptions of eight real-world processes.  For each, try to sketch a suitable graph.  If you are not familiar with the background science, then try to use what you do know to reason through what a graph might look like.

You do not need to calculate or plot exact points, just sketch graphs that give the general shape.

As you produce your sketches, make a list of the features that you are considering.

You can download Printable versions of these cards

 

Temperature of a cup of tea over time.Height of the valve on a bicycle tyre as the bicycle moves forwards.
Height of a tennis ball thrown straight up and then caught.Distance fallen by a parachutist jumping out of a plane.
Reading on the odometer (mile counter) of a car driving on a motorway.Radius of a spherical balloon as it is inflated.
Volume of water remaining in a cup as water is sucked out through a straw.Distance along a tape measure measured in inches compared with distance measured in metres.

Once you have sketched graphs for some of the eight processes described, click on the following link to read a further question and move on further.

GRAPHS

EQUATIONS

This is an Underground Mathematics resource.

Underground Mathematics is hosted by Cambridge Mathematics. The project was originally funded by a grant from the UK Department for Education to provide free web-based resources that support the teaching and learning of post-16 mathematics.

Visit the site at undergroundmathematics.org to find more resources, which also offer suggestions, solutions and teacher notes to help with their use in the classroom.