Suggested Learning Intentions

- To design questions that can be answered using statistics
- To investigate how data can be used to solve real world problems
- To describe data using numbers; these are called statistics

Sample Success Criteria

- I can design a question to investigate that can be answered using statistics
- I can collect, analyse, and interpret data to address a real-world problem
- I can model data using a variety of manipulatives
- I can describe data using statistics

In this stage students will use an investigative approach to address a school-based problem. Using the data investigation framework, they learn to pose a question, collect data, represent the data graphically and analyse, interpret, and communicate the results. The context for the investigation presented here is a classroom waste audit, but you may wish to use the framework to investigate an issue more relevant to your school community.

Begin by introducing the question: *‘How can data be used to solve problems in the real world?’*

Prompt student thinking by showing them the ‘Great Australian Garbage Map’ article. Display the image only (*note that you may need to increase the size of the map so that the legend is not visible on the screen*).

Guide students through a See, Think, Wonder process prior to explaining what the map shows:

1) Students write about what they notice or see.

2) Students make inferences as to what they think is happening.

3) Students write their wonderings about the image.

**Enable** students requiring further support by asking prompting questions such as ‘Where are the shapes located? Where aren't they located? What might be similar about the places where the shapes are located? What do you think the shapes might represent? What are some things that the shapes probably don't represent?’

**Extend **students by asking them to predict what each blue shape represents.

Invite students to share their thinking.

Read the article aloud and make comparisons between student predictions and the actual data.

Draw students’ attention to the bar graph showing Beach clean-ups: items by category, and prompt them to describe what can be learned from this graph. Next, facilitate a maths talk to compare and contrast the two different graphical representations in the article and how it affects how well the data are understood. You might also choose to focus on the statistics used in the article and graphs and how statistics are used to build the argument in the article.

It is recommended that students work in pairs or small groups on this investigation.

**Set the context**

Set the context for the whole-class data investigation.

The context will depend on your school. To engage students, you might provide statistics on how much waste is being disposed of by the school each week, or express concern about bins overflowing and polluting the playground. You could even ask a guest speaker from a local environmental group to talk to students about the damaging effects of waste pollution.

Students may take inspiration from watching these primary school students attempting to wipe out waste in their school.

Prompt students’ thinking by asking:

*‘What is the problem we are trying to solve?’*

*‘What questions will help us find out?’*

*‘What data will we need to collect to help us understand the problem?’*

Brainstorm and write responses on the board. For example, the problem might be that the school bins are overflowing with rubbish and that students want to find ways of reducing the amount of rubbish going to landfill.

The questions students might ask to gather information could include *'Which rubbish bins are most/least full? What types of rubbish are found in the bins?'*

Note that the questions students design need to be able to be answered using statistics, should include variability and students must be able to gather data for them. Once students have developed questions, it would be useful to sort these questions into examples and non-examples. That is, which questions can be answered using statistics and which cannot? For example, the question ‘Which rubbish is the most harmful to the environment?’ is not statistical in nature but could be adapted with a more specific focus on what is meant by harmful.

To help understand the problem, it may be helpful to conduct an investigation of school rubbish bins to find out what and how much is being thrown away**. **This could include conducting a school waste audit and surveying students about their use of non-reusable (such as single-use plastics) and reusable products, and the amount of compostable food waste that is being thrown away.

**Data investigation: Conduct a waste audit**

Use the Data Investigation Framework to lead students through the four steps of a data investigation.

1) Formulate the question

2) Collect the data

3) Analyse the data

4) Interpret the data

Depending on your students’ responses, you might support students to complete a classroom waste audit using the sample student task sheets referred to in the Framework, which are available in the Materials and texts section above. This is an opportunity for students to revisit the process of collecting, sorting and classifying their data, and representing data in a column and pie graph as well as describing the data using numbers (statistics).

**Enable** students requiring further support by providing a worked example of the support materials so that they can describe the data using statistics. For example ⁷/₁₀ pieces of rubbish were plastic = 0.7 or 70%.

**Extend **students by requiring them to use spreadsheet software to present the information in digital form. Instructions for using Excel to create graphs are available here. Also encourage students to use statistics to describe their data such as fractions, decimals and percentages. Students can explore other graph types such as stem-and-leaf plots to illustrate their data and evaluate the usefulness to other forms of graphical representation.

Once students have constructed their graphs, they should write about their graph.

Ask:

*What does your graph show? *

*Why did you select that type of graph to represent the data? *

*Did you use words and numbers to describe the data? *

*What statements might you make about your graph?*

**Taking action**

Students could use the data from the waste audit to educate other students and their families about waste and recycling. They could campaign for recycling and compost bins, promote rubbish-free lunches or even get involved in local Clean Up Australia projects.

**Areas for further exploration**

Now that students have a framework for conducting a data investigation, they may wish to investigate other school-based issues. For example, they could use data to encourage more students to walk or ride to school; suggest improvements to the playground; or examine Student Attitudes to School survey responses (e.g. student voice and agency).

You could extend student learning about data concepts by:

- Collecting observational data in the playground to find out who/how many students are recycling.
- Using a digital survey tool to find out what families know about waste and recycling.

Lead a class discussion about the findings from the investigation. Prompt discussion by using both task-specific questions, where the answers are evident in the data, and big picture questions that require students to think more deeply about the Big understandings and Learning Intentions of the sequence. Questions that support meaningful discussion on data interpretation include:

- Which graph was more useful to represent and understand the data?
- Were there any unusual results? How might you explain this?
- Do you think the data would have been different if we gathered data from another school (i.e. change the sample/population)? Why/why not?
- What do our graphs not tell us? What might we infer?
- Do you have new questions that arise from these data?

Formative assessment of student learning at this stage of the sequence could include:

- Reviewing student work samples
- Noting whether students select an appropriate graph to represent the data. Did they provide a good justification for their selection? Have they used statistics to describe the data? What inferences can they make from the data to help them solve the problem/answer their question?
- Asking students to explain the steps of a data investigation in their own words in their data journals. They might describe how they approached the investigation, and what they learned.

9 Story Media Group, 2013. *If the World Were a Village - Promo. *[Online]

Available at: https://www.youtube.com/watch?v=XUHA2-YRtKA

[Accessed 15 March 2022].

ABC News, 2017. *Census 2016: This is Australia as 100 people. *[Online]

Available at: https://www.abc.net.au/news/2017-06-27/census-australia-as-100-people/8634318?nw=0 28 June, 2017

[Accessed 15 March 2022].

Central Intelligence Agency (CIA), 2020. *World Factbook: Australia. *[Online]

Available at: https://www.cia.gov/the-world-factbook/countries/australia/

[Accessed 15 March 2022].

Gapminder, 2020. *Play with the Data. *[Online]

Available at: https://www.gapminder.org/tools/#$chart-type=bubbles

[Accessed 15 March 2022].

Global Change Data Lab, 2020. *Our World in Data: World Population Growth. *[Online]

Available at: https://ourworldindata.org/world-population-growth

[Accessed 15 March 2022].

Good Magazine, 2016. *Good Data: If the World were 100 People. *[Online]

Available at: https://www.youtube.com/watch?v=QFrqTFRy-LU 14

[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].

Kahoot, 2013. *Kahoot. *[Online]

Available at: www.kahoot.com/

[Accessed 11 May 2020].

Plickers Inc, 2019. *Plickers. *[Online]

Available at: https://get.plickers.com/ 2019

[Accessed 15 March 2022].

Smith, D. J., 2020. *If the World Were a Village: A Book about the World's People. *2 ed. Toronto: Kids Can Press Ltd..

Toby Ng Design, 2020. *The World of 100. *[Online]

Available at: https://www.toby-ng.com/works/the-world-of-100/

[Accessed 15 March 2022].

University of Cambridge, n.d. *NRICH: If the World Were a Village. *[Online]

Available at: https://nrich.maths.org/7725

[Accessed 15 March 2022].

Walle, V. d., Bay-Williams, J., Lovin, L. & Karp, K., 2018. *Teaching Student-Centered Mathematics. Developmentally appropriate instruction for grades 6-8. *3 ed. New York: Pearson Education.

Worldometer, 2020. *World Population Clock. *[Online]

Available at: https://www.worldometers.info/world-population/

[Accessed 15 March 2022].

Other stages

1. Class Statistics

EXPLORESuggested Learning Intentions

- To gather and organise data to answer questions about our world
- To explore various graphic techniques and explain how they provide a different picture of the shape of the data

Sample Success Criteria

- I can gather and organise my data to answer questions about the sample population the data came from
- I can demonstrate my solution and thinking using a variety of manipulatives
- I can describe key features of graphs
- I can construct graphs in ways that help me represent and understand data

3. Demographic Diversity

EXPLORESuggested Learning Intentions

- I can design a question to investigate that can be answered using statistics
- I can collect, analyse, and interpret data to address a real-world problem
- I can describe data using statistics

Sample Success Criteria

- I can design a question to investigate that can be answered using statistics
- I can collect, analyse, and interpret data to address a real-world problem
- I can describe data using statistics
- I can model data using a variety of manipulatives and use this to analyse the data

4. Welcome to the Global Village

EXPLORESuggested Learning Intentions

- I can design a question to investigate that can be answered using statistics
- I can collect, analyse, and interpret data to address a real-world problem
- I can describe data using statistics

Sample Success Criteria

- I can explain how populations differ using statistics and graphic techniques
- I can model data using manipulatives
- I can justify my choices of how I represent data visually or with statistics
- I can communicate my findings effectively