1. EDFGC5713 – Mathematics, Numeracy and Learner Engagement A
Semester One
Lecture Seven – Statistics and Probability
Lecturer - Peter Sellings

2. Learning Intent Consider ways of teaching Statistics & Probability.
Explore the Victorian Curriculum F-10 levels for Statistics & Probability.
Examine how higher order thinking skills can be used in teaching Statistics.

3. Success Criteria
Describe different ways of teaching Statistics & Probability.
Discuss how higher order thinking can be used in teaching statistics.

4. What is Probability?
In general terms, Probability examines how likely it is that a particular event will or will not occur.
Probability is often referred to as Chance.
Chance in the Victorian Curriculum F-10 is normally taught from grades 1-10

5. Activities in Chance Grade 1: Will, Won’t or Might happen. Roll a die:
Even number? 1,2,3,4,5,or 6? 0?

6. Activities in Chance
Grade 2: Likely or Unlikely; Certain or Impossible.
It will rain today.
I will win lotto this weekend, buying just one ticket.
I will roll at least one six if I roll 20 dice.
I will choose a red marble out of a bowl of white marbles.

7. Activities in Chance Grade 3: Conducting experiments.
Roll a die 20 times and record the results.
Toss a coin 30 times and record the results.
Spin a spinner 40 times and record the results.

8. Activities in Chance
Grades 4, 5 & 6: Ordering (4), listing outcomes (5), Technology (6).
4 – Order the chances of events
5 – Listing all possible outcomes using fractions
6 – Conduct chance experiments using digital technology

9. Activity 1 – What are the chances?
Order the following events according to their chance.
You flip a coin and get “tails”
May is followed by January
You will win a trophy for sport this year
You will eat food in the next week
You roll a die and get a 1 or 2

10. Activities in Chance
Grades 7, 8, 9: Sample Spaces (7), Tree diagrams (8), Collect (9).
7 – Write the sample space for two dice being rolled together
8 – Draw tree diagrams for two and three step arrangements
9 – Collect data to estimate probabilities.

11. Activity 2 – How fair? Two dice are rolled and the numbers added.
What are the possible outcomes?
How can these outcomes be shown on a tree diagram?
The teacher chooses 5, 6, 7, 8, & 9 leaving the class the less likely outcomes 2, 3, 4, 10, 11, 12

12. Partial tree Diagram for the event “Two dice are rolled”1 2 3 4 5 6
Sample Space – Two dice rolled
(1,1) (1,2) (1,3) (1,4) (1,5) (1,6)
(2,1) (2,2) (2,3) (2,4) (2,5) (2,6)
(3,1) (3,2) (3,3) (3,4) (3,5) (3,6)
(4,1) (4,2) (4,3) (4,4) (4,5) (4,6)
(5,1) (5,2) (5,3) (5,4) (5,5) (5,6)
(6,1) (6,2) (6,3) (6,4) (6,5) (6,6)

13. Activity 2 – How fair?
Two dice are rolled and the numbers added. The teacher chooses five of the outcomes and gives the students six of the outcomes. First to get 10 of their numbers win.
Is this fair if the teacher chooses the outcomes 5, 6, 7, 8, & 9 leaving the class the outcomes 2, 3, 4, 10, 11, 12?

14. Partial tree Diagram for the event “Two dice are rolled”
Sample Space – Two dice rolled
(1,1) (1,2) (1,3) (1,4) (1,5) (1,6)
(2,1) (2,2) (2,3) (2,4) (2,5) (2,6)
(3,1) (3,2) (3,3) (3,4) (3,5) (3,6)
(4,1) (4,2) (4,3) (4,4) (4,5) (4,6)
(5,1) (5,2) (5,3) (5,4) (5,5) (5,6)
(6,1) (6,2) (6,3) (6,4) (6,5) (6,6)
Partial tree Diagram for the event “Two dice are rolled” 1 2 3 4 5 6

15. Activity 2 – How fair?
From the sample space drawn, it can be seen that the teacher would have a 2/3 (24/36) chance of their numbers coming up, while the students would have a 1/3 (12/36) chance of their numbers coming up.

16. Statistics in schools
In general terms, Statistics is the collection, analysis and display of data.
According to the Victorian Curriculum P-10 data representation and interpretation are normally taught from grades f-10.

17. Statistics in schools Foundation: Collect yes/no responses
Grade 2: Display data in a variety of forms
Grade 3: Compare displayed data
Grade 6: Interpreting data

18. Teaching Statistics
Allow students to create their own survey questions
Use data that interests students (be aware that some data can distress)
Use ICT to get students to display data
Make sure that students are making judgements based on the data, not just expressing their own opinion
Encourage higher order thinking skills when students are interpreting data

19. Activities Circle Time Odds & Evens
Opening Doors (
How Likely?
Misconceptions
Data

20. Let’s recap & Review Success criteria
Can you?
Describe different methods of teaching probability and statistics?
Suggest how higher order thinking skills can be used in teaching statistics.