Graphing Data and Making Predictions
In this lesson, students construct and use spinners to gather data, from which they construct circle and bar graphs using their knowledge of fractions and angle measurement. Theoretical predictions and experimental outcomes are explored with an emphasis on confidence levels, sample sizes and probabilities.
The first step is to create a circle graph for a set of relationships like these:
Next, supposing that this circle had a spinner on it, students predict how many times the spinner would land on each color if the spinner were spun 40 times. Then, a paper clip spinner is used to carry out an experiment of 40 spins to test the predictions, and the students construct a circle graph and bar graph showing the results of their experiment. The two graphs are compared, and become a way of discussing theoretical and experimental probabilities. Terms like highly likely, somewhat likely, and unlikely are used to describe various possibilities of outcomes.
Here's a bar graph of some data from a different spinner:
Design some spinners that would be highly likely, somewhat likely, or unlikely to produce the results shown in the bar graph. You can use these shapes for the spinner boards:
Remember that the data shows experimental results, and that the spinner's theoretical probabilities would probably not match the experimental results exactly!