Name:
Linear versus Non-Linear Patterns – “Fill it up!”
(Supplement for first part of Activity 3.1)
Step 1. Predict (Think)
You are going to conduct as experiment in which you pour a predetermined amount of water into a solid (cube, cylinder,
and cone) and measure the height of the water at each stage.
1.) For which shapes, if any, will the height of the water increase by a constant rate of change. Explain your
thinking.
2.) In your own words, describe the difference between a linear pattern and a non-linear pattern.
Step 2. Experiment (Pair)
Steps to follow for each solid:
Step 1. Fill up the measuring cup to 1 cup and pour into the solid using the funnel.
Step 2. Using a ruler, measure the height of the water in inches.
Step 3. Record data in appropriate fields.
Step 4. Repeat steps until all necessary data is collected.
1.) Cube
Stage #
1
2
3
4
5
6
7
Height of water
a.) Do you see a pattern for the data in the table?
Explain.
b.) Looking at the graph, what do you notice about the relationship between the stage number and the height of
the water? Describe the shape of the graph.
2.) Cylinder
Stage #
1
2
3
4
5
6
7
Height of water
a.) Do you see a pattern for the data in the table?
Explain.
b.) Looking at the graph, what do you notice about the relationship between the stage number and the height of
the water? Describe the shape of the graph.
3.) Cone
Stage #
1
2
3
4
5
6
7
Height of water
a.) Do you see a pattern for the data in the table?
Explain.
b.) Looking at the graph, what do you notice about the relationship between the stage number and the height of
the water? Describe the shape of the graph.
Step 3. Conclusion (Share)
Each of the following questions are quickwrites and require 2 to 3 complete sentences to answer.
1.) Explain how the shape of the object affects the rate of change.
2.) If the height of the cylinder and the cone were extended indefinitely, explain how the height of the water
would change as the stage number increased for each solid.
3.) Now that you have completed the experiment, describe the difference between a linear pattern and a nonlinear pattern (you may still agree with your initial description).