Suggested Learning Intentions

- To analyse data to make predictions, answer questions and make decisions about real-world issues

Sample Success Criteria

- I can analyse and interpret data in context
- I can identify different factors that influence my interpretation of the data
- I can answer questions and make decisions based on data
- I can explain the certainty of my decisions
- I can model and justify my solutions using a range of manipulatives

- Future Foods learning resource

This stage illustrates how probability is used in everyday life to answer questions and make decisions.

Display the following table from the Bureau of Meteorology that display the climate statistics for Cairns, Australia. Facilitate a maths talk about what students notice in the table.

- What might students consider when looking at data? For example, mean, median, mode, range.
- Connect the discussion to experimental probability such as how can we use this data to predict what might happen in the future?
- How can we use this data to make decisions about the best time of the year to go to Cairns?
- What will base our decision on? Focus on the concept of variables and likelihood of events.

This learning task has been inspired by Meat & Livestock Australia’s Future Foods learning resource and is reproduced with permission.

Lead a discussion about the modern practices in sustainable farming and its role in the future of food production. Consider the challenges Australian cattle and sheep farmers’ face and how science can help them to meet the challenge of sustainably feeding the world with a growing population and climate variability.

- What types of questions do you think Australian cattle and sheep farmers might have? Invite students to respond.

Explain to students: *Did you know that the number of people in the world is growing every year. This means we need to be able to produce more and more food. What questions does this raise? How might we find out?*

Lead the discussion towards the following question: *Will there be enough to feed everyone?*

Display the following graph which shows the world population. Invite students to contribute to an I see, I think, I wonder about the graph.

Next, display the table showing how much meat and milk is eaten in different areas of the world. In small groups, invite students to make statements from information in the graph. You might also direct students' attention towards information about the source of publication (i.e., the OECD, who they are and what they do - how does this inform the reliability of the information in the table?)

Pose the following questions to students to brainstorm and record their thinking in pairs or small groups of three.

- What predictions is the graph making about how the world’s population will change over the coming years? (Hint: Which parts of the world will grow the most/least?)
- What predictions is the table making about the amount of beef (cattle) and lamb (sheep) people will be eating in the future? (Hint: Who will be eating more/less?)
- How do you think cattle and sheep farmers might react to this information? (Hint: What might you think about this if you were a cattle or sheep farmer? Is it good/bad news?)
- If the predictions in the graph and table come true, what advice would you give to farmers to help them respond to the growing demand for food?

**Areas for further exploration**

You might also adapt this stage with the alternative topics for exploration such as the Great Barrier Reef. Other tasks include: Investigating Epidemics and Choc Chip Cookies.

Come together as a class to listen to and discuss each group’s answers:

- Did most groups give similar answers to the questions?
- What sort of advice did people have for today’s farmers?
- What reactions did you have to what others have suggested?

Revisit the success criteria of this stage and invite students to add to their Connect, Extend, Challenge thinking tool.

ABC: Behind the News, 2015. *Fire Preparations. *[Online]

Available at: https://www.abc.net.au/btn/classroom/fire-preparations/10525718

[Accessed 15 March 2022].

ABC: Behind the News, 2016. *Coral Bleaching. *[Online]

Available at: https://www.abc.net.au/btn/classroom/coral-bleaching/10524996

[Accessed 15 March 2022].

Black Douglas Professional Education Services, n.d. *Mathematics Task Centre: Chocolate Chip Cookies. *[Online]

Available at: http://mathematicscentre.com/taskcentre/197chocc.htm

[Accessed 15 March 2022].

Commonwealth of Australia , Bureau of Meteorology, 2022. *Climate statistics for Australian locations: Cairns. *[Online]

Available at: https://www.bom.gov.au/climate/averages/tables/cw_031011.shtml

[Accessed 15 March 2022].

Harvard Graduate School of Education, 2019. *Project Zero: Connect, Extend, Challenge. *[Online]

Available at: https://pz.harvard.edu/sites/default/files/Connect%20Extend%20Challenge_0.pdf

[Accessed 15 March 2022].

Harvard Graduate School of Education, 2019. *Project Zero: See, Think, Wonder. *[Online]

Available at: http://www.pz.harvard.edu/resources/see-think-wonder

[Accessed 15 March 2022].

Meat & Livestock Australia, 2014. *Future Foods. *[Online]

Available at: https://www.goodmeat.com.au/globalassets/goodmeat/education/stage-3-future-foods.pdf

[Accessed 15 March 2022].

Reys, R. E. et al., 2020. *Helping Children Learn Mathematics. *Milton: John Wiley & Sons Australia..

Siemon, D. et al., 2015. *Teaching Mathematics: Foundations to Middle Years. *Melbourne: Oxford University Press.

University of Cambridge, n.d. *NRICH: Investigating Epidemics. *[Online]

Available at: https://nrich.maths.org/8336

[Accessed 15 March 2022].

Van de Walle, J. A., Karp, K. S. & Bay-Williams, J. M., 2017. *Elementary and Middle School Mathematics: Teaching Developmentally. *Ninth ed. Harlow`(Essex): Pearson Education Limited.

Other stages

1. Probability of an Event

EXPLORESuggested Learning Intentions

- To describe the probability of an event using words and numbers
- To understand the concepts of randomness and fairness and their impact on determining likelihood of events

Sample Success Criteria

- I can represent probability on a continuum from 0-1
- I can use the language of chance: certain, likely, equal chance, unlikely, impossible
- I can express probabilities using fractions, decimals, and percentages
- I can describe whether the probability of an event is random and/or fair
- I can use manipulatives to model my solution and thinking

2. Theoretical and Experimental Probability

EXPLORESuggested Learning Intentions

- To describe probability in terms of what happened and what might be likely to happen in future events
- To compare the results of small and large trials to determine which provides a more accurate estimate of probability

Sample Success Criteria

- I can analyse a situation and describe probability in terms of what I expect to happen (theoretical)
- I can design and conduct an experiment, and collect and analyse data to determine how likely something will happen in the future (experimental)
- I can explain the ‘law of large numbers’
- I can apply my understanding of fractions and percentages to express probability of events

3. Sample Space and Independence of Events

EXPLORESuggested Learning Intentions

- To analyse probability situations and predict the likelihood of events (independence of events)
- To list and compare all possible outcomes for an experiment or chance situation (sample space)
- To understand the difference between short-term variability and long-term stability (law of large numbers)

Sample Success Criteria

- I can identify dependant and independent events
- I can systematically list and count the possible outcomes in an experiment
- I can record probabilities using tallies, tables, and diagrams
- I can conduct repeated trials of chance experiments to determine the probability
- I can explain the notion of ‘in the long run...’ when determining probability