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  • Introduction – scenario

    1. Read the following scenario:  
      • Bilby is in urgent need of a new playing field and all the adult citizens have been asked to contribute $2,000 to the project. There are 200 adult citizens in Bilby. The playing field is expected to cost $400,000.
    2. Ask:  
      • Should all the citizens contribute $2,000 to the project? Why?
    3. Record student thinking as the discussion progresses. (Yes, No and why)

    Teacher tip

    Adjust the values according to student ability. For instance, to simplify the problem, divide the values by 10 so the required contribution is $200, Jervis earns $1,000 and Ernabella earns $10,000. Or, values could be increased to present further challenge.

    Unequal contribution – modelling

    This activity may contribute to student portfolios.

    1. Explain that you are going to show how Bilby’s funding proposal will affect two different citizens – Jervis and Ernabella.    
      • Jervis earns $10,000 a year
      • Ernabella earns $100,000 a year.
    2. Explain that playing cards will be used to represent their income. Each playing card represents $2,000.
    3. Ask:    
      • How many cards out of a full deck of 52 will I need to represent Jervis’s income? (5 cards)
      • How many cards do I have left in the deck? (47)
      • Do I have enough cards left in the deck to represent Ernabella’s income? (no)
      • How many cards do I need to add? (3 cards)
    4. Add three cards to the deck.
    5. Invite a student to:    
      • remove the appropriate number of cards to represent Jervis’s contribution to the Bilby council
      • remove Ernabella’s contribution.
    6. Lay the 2 piles side by side.
    7. Ask:     
      • Is this fair?
      • What words could you use to describe how much each person has?
      • What words could you use to describe the difference between each pile?
      • Can both Jervis and Ernabella equally afford to contribute $2,000?
      • Should both Jervis and Ernabella contribute $2,000?

    Teacher tip

    Encourage both mathematical and descriptive language (eg 10 times as much, a huge pile, a big difference, unfair).

    1. Students represent proportion using fractions, decimals and percentages (Resource 1–- PDF, 146KBExternal Link).
    2. Ask:    
      • Is paying a fixed contribution of $2,000 fair? Why? Why not?

    Teacher tip

    Students could be asked to model their thinking in different ways to vary the challenge of a task; number sentences, concrete materials, a word story are examples.

    Fair contribution – problem solving

    1. Community Planning Groups collaborate to find a solution to make the contributions fairer.
    2. Groups consider why their solution is fair and show their mathematical thinking.
    3. Groups share their solution to the Bilby scenario. Throughout the sharing, guide students to evaluate whether their solution is a fair one.
    4. Discuss:    
      • Was it easy or difficult for you to find a fairer solution? Why?
      • In this example [show an example of student solution], Jervis and Ernabella both pay the same proportion of their income. Is it fairer than the original scenario?
      • In this example [show an example of student solution], Jervis and Ernabella pay a different proportion of their income. Is this a fair solution? Is it fairer than the original scenario?
      • Why is it our responsibility to contribute to community projects?
      • In our daily life, do we have a system that allows all citizens to make a fair financial contribution to community projects. What is this called? (taxation system).

    Tax models – worksheet and discussion

    This activity may contribute to student portfolios.

    1. Explain
      The citizens of Bilby are being asked to pay a tax to fund a community resource. In Australia, everyone has a responsibility to pay tax. For example:  
      • businesses pay company tax on their profits
      • individuals pay a goods and services tax (GST) on what they buy
      • individuals who earn an income pay income tax.
    2. Display the slide on tax models (Resource 2: tax models (text version) or PDF (78KB)External Link) and explain each model.

    Teacher tip

    When explaining different tax models, draw on student solutions from Activity 3, if appropriate.

    1. Individual students complete the different tax models worksheet – Resource 3: different tax models worksheet (text version) or PDF (127KB)External Link.
    2. Invite students to share their answers on whether the tax models were fair in each scenario. Encourage them to explain their reasoning.

    Creating our ideal community – group planning

    This activity may contribute to student portfolios.

    1. Students individually complete ‘Planning our ideal community, Part 3’ –Resource 4: creating our ideal community – part 3 (text version) or PDF (78KB)External Link.
    2. Each Community Planning Group discusses individual responses and agrees on a model for their ideal community and the models they will use for each taxable item (Encourage groups to collaboratively complete Resource 4).

    Reflection – I used to think

    • Invite students to complete the sentence: 'I used to think… but now I think…'

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      Last modified: 28 Feb 2020QC 61307