Author: Denis Kelly and Aisling Twohill
CLASS
Sixth Class
STRAND
Data and Chance
LEARNING OUTCOME LABEL
Chance
Goals of this activity
- Use probability to make informed decisions and predictions.
- Represent and express probability in different forms.
- Uses data to predict how likely an event is to happen in the future (j). (Understanding and Connecting)
- Explores how the greater the number of trials brings the experimental [actual] outcomes closer to the theoretical [expected] outcomes (j). (Understanding and Connecting)
- Examines the range of variability in small samples (Useful to explain the law of small numbers) (j). (Understanding and Connecting)
- Represents probability using values from the range of 0 to 1. [With 0 being impossible/never and 1 being always/ certain] (j) (Communicating)
- Represents all possible outcomes of an experiment using a sample space [A sample space is a set of all possible outcomes in an experiment]. (j) (Communicating)
- Deduces through investigation, how the number of repetitions of a probability experiment can affect the conclusions drawn (i).(Reasoning)
- Uses games to carry out blind experiments and predict whether they are fair or unfair (j). (Applying and Problem-Solving)
- Uses previous data to evaluate whether you can use patterns to make informed decisions about future events (j).
(Applying and Problem-Solving)
Key Mathematical Ideas
- Probability can be represented on a scale between 0 – 1.
- The experimental probability of an event occurring may not always match the theoretical probability.
- The probability that a specific outcome will occur can be represented as a fraction, decimal or percentage.
- A sample space contains all possible outcomes of an experiment.
Lesson Introduction
Key Questions
Introduce the game to the children. You have 4 prisoners and you place them wherever you like on the grid. You take turns to roll 2 dice and add them together. You can release one prisoner from the grid of the number you get. Don’t release your opponent’s prisoners.
Now look at the grid and decide where you want to place them.
Do you use strategies when you’re playing board games? Are some strategies useful?
Development
Key Questions:
What do you think? Are some numbers better than others? Are there any that you can’t get? Which ones do you think are better? Why?
Is there a mathematical way to find out which numbers are the best?
Let children play again, and encourage them to play strategically.
Now, what do you think? Which numbers are more likely?
When a child says there’s more ways to make a 7, or more ways to make a 6 or 8, ask them to try to list all the totals they can make from the two dice.
Share examples of groups who are being systematic for others to follow.
When circulating, teacher asks children:
- What happens if you forget some numbers.
- Do you need to list every possible pair and total? Why ?
Whole class discussion:
When we want to find the likelihood of something, it can be useful to list all the possible outcomes, which is what you just did, or started to do. We call this the sample space. As you saw, it’s important to make sure you have all of the outcomes so there are ways to help you to be systematic about this.
Teacher introduces the table showing how it takes an outcome from dice 1 and adds every possible outcome to it; then takes another and does the same, etc.
Question:
From the table of all the possible outcomes, how would you work out the probability of getting a 7? Think, pair, share
If no child suggests that there are “more ways to make” certain numbers, ask, “well, do you think it matters how many ways you can make, e.g. 2 compared to 6?”
How many outcomes altogether?
How many 7s?
Students say we didn’t get more 6s, 7,s or 8s. Teacher responds with why is that? Can probability tell you what will definitely happen? When are predictions more reliable?
Closure/Review
Playing again – which numbers would you not choose?
Which was the most likely number?
Was it very likely? Do you think it would be a good idea to put all of the prisoners in cell no 7?
Anticipated Children’s Responses
0 and 1 because they’re not in the sample space.