## Who is this Sequence for?

This lesson is designed for students who are consolidating ideas of proportional reasoning. The related calculations require fractions. Percentages and/or ratios are useful. There are opportunities to describe the sharing procedures using algebra, but this is not required.

## Summary of learning goals

Students devise mathematical strategies to reflect a real world criterion (in this case fairness) that needs to be operationalised mathematically. Students discover that multiple solutions to the same problem often exist and that different solutions can be justified as the optimal solution depending on perspective. Students develop mathematical communication as an important component of argument and in verification of personal beliefs.

## Rationale for this sequence

The concept of fairness is flexible and dependant on the environment and, most importantly, the individual making the decision. This lesson engages students with the notion of “*when is fair actually fair?” *using number operations and three Australian Curriculum General Capabilities:

- Critical and Creative Thinking;
- Personal and Social Capability;
- Ethical Understanding.

The very important concept of proportional reasoning is fundamental in all the scenarios considered.

### reSolve Mathematics is Purposeful

Fluency – Students develop alternate mathematically correct solutions using a variety of operations and strategies; specifically those with rates and ratios.

Reasoning – Students participate in the process of making informed personal decisions based on the mathematical calculations they have made; what is considered fair by one student may not be considered fair by another. Various mathematical models which operationalise the criteria for fairness are created and evaluated.

### reSolve Tasks are Challenging Yet Accessible

Using a scenario with which students are familiar provides access for all students. Justifying one of the variety of possible solutions challenges students to think about the context as well as the mathematics.

### reSolve Classrooms Have a Knowledge Building Culture

Students are encouraged to adopt alternative positions and debate the pros and cons of different strategies. They will be active in their engagement with tasks and have the opportunity to discuss why particular solutions are more, or less, fair than other options. Formative assessment opportunities will arise through student discussions reflecting reasoned mathematical and personal decisions.