This is a level 4 measurement strand activity from the Figure It Out series.
A PDF of the student activity is included.
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use a graph to show height and diameter of a cylinder
interpret a graph
FIO, Level 4+, Measurement, Book Two, Cylinder Collection, page 16
In this activity, students visually interpret the relationship between the height, diameter, and volume of a collection of cylinders. They graph the relationship and then use the information to draw a conclusion.
You could introduce this activity by bringing a collection of cylinders to the classroom and asking the students to sort them first by height, then by diameter, and then (on a large table) by both height and diameter. They could then measure each cylinder and accurately plot them on a graph similar to the one in the students' book but with the axes marked in centimetres.
In question 1, there are no units marked on the axes, so the students need to compare each cylinder with G, which is already plotted. Is it thinner or fatter than G, shorter or taller than G? Points are then plotted for the other cyclinders by comparing them with ones already on the graph.
It is possible that some students may realise that they can be quite precise about the position of each point by using the method in this diagram.
Similarly, they could measure the height and diameter of each cylinder in the illustration in their book and use these measurements to mark the location of each point on the graph. However, this method removes the need to make comparisons, which is the main point of the activity.
In question 2, the students work in reverse, from plotted point to cylinder, and in question 3, they show they understand the finished graph by explaining where to look for the cylinders with the greatest volume. They should be able to justify their answer.
Answers to Activity
3. In the top right-hand area of the graph