EDFGC5713 – Mathematics, Numeracy and Learner Engagement A 2017 - Semester One Lecture Seven – Statistics and Probability Lecturer - Peter Sellings

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.

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

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

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

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.

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.

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

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

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.

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

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)

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?

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

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.

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.

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

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

Activities Circle Time Odds & Evens Opening Doors (http://stayorswitch.com/) How Likely? Misconceptions Data

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.