Investigation: Conduct experiments
Introduction
Experiment or trial are the words used to describe the event or action of doing something and recording results. For example, the act of drawing cards from a deck, tossing a coin, rolling a dice, watching the weather, asking questions in a survey or counting cars in a parking lot could all be examples of experiments or trials.
Some experiments are small, meaning the event is only repeated a small number of times (e.g. we may flip a coin 10 times). Here is a small experiment for us to try.
Colorful spinners - small experiment
Objectives:
- To determine what makes a spinner fair.
- To compare theoretical probability and experimental probability.
Materials:
- Cardboard
- Colored pencils.
- Sharp pencil
Exploration
Procedure:
- Cut out a square of cardboard and color it in so there's an equal chance of the spinner landing on red, yellow, blue and green. Then stick your pencil point through the center.
- Create a table like the one below. You can draw it or make a table on your computer.
Color Tally Frequency Red Yellow Blue Green - Spin your spinner 20 times by twisting the pencil. Record the color closest to you each time in the tally. After 20 spins, calculate the frequency.
- As a class, create a new table like the one above, but with the results from the entire class combined. You may use a calculator to add up all of the frequencies.
Discussion questions:
- What is the theoretical probability of a spinner landing on each color?
- What was the experimental probability of landing on each question?
- Is this different to the theoretical probability?
- Were the results of the entire class similar to yours or different? Explain some similarities and some differences.
- Which was closer to the theoretical probabilities, your individual results or the whole class? Why do you think that was?
- Was one color more common that the others?
- Were the frequencies more or less even than your individual results?
- How could you change your spinners to make the experiment biased?
Race to win - Large Experiment
Some experiments are large, meaning the event is repeated a large number of times (e.g. we may flip a coin 100 times). Some experiments may involve hundreds or even thousands of trials. Here is a larger experiment for you to try.
Objectives:
- To determine the modal sum of two dice (This means that we're asking what number will be the most common (modal) number when we add the scores of the two dice together)
Materials:
- Two dice (labeled 1-6)
- Printed Race to Win leaderboard (below)
Exploration
Procedure:
- Split the class up into groups of three. Each group should choose a number between 0 and 12 which they think will be the most common sum of the dice. Each group must pick a different number.
- Groups take turns rolling the two dice, adding the scores together and recording the answers on the leaderboard - put an X in the next available box above the sum
- The first group to fill their chosen column on the leader board wins.
Discussion questions:
- Why are some numbers more likely to be rolled than others? Draw a table on the computer like the one below, two values are already filled in. What patterns do you notice in their sums?
+ 1 2 3 4 5 6 1 2 2 3 3 4 5 6 - Use your table to help you create a table of the theoretical probabilities.
- How could this game be changed to make the chances of winning more fair?