### Overview:

The disciplines of Mathematics and Science have much in common. Many of the inquiry skills nominated in the Australian Science Curriculum bear close resemblance to skills necessary for students to be competent with Modelling and Problem Solving.

These include:

- Questioning and Predicting
- Planning and Conducting
- Processing and Analysing Data and Information
- Evaluating and Communicating

These inquiry skills can be a very useful starting point for creating engaging activities in Mathematics and for developing students familiarity with the Modelling and Problem Solving criteria found in the QSA Senior syllabi.

The introduction of the Australian Curriculum will inevitably place a renewed focus on content and coverage. This will potentially create more pressure than has been experienced in recent years for teachers and HOD’s to ‘get it all done’. When the ‘breadth of coverage’ takes precedence over the depth, student learning and engagement can be compromised.

This workshop will give teachers the opportunity to explore:

- The benefits of practical based lessons to gain deeper insights
- Expanding the possibilities to consider how students visual literacies can be developed through appropriate activities
- Thinking about ‘the products” students can create
- Experiencing the practical based approach
- Thinking about particular contents e.g. measurement and perspective
- Using communication and data collection technology but keeping it in perspective

Some topics that can be covered include:

*1. **Estimating the mass of the Earth given only the radius: Making Scientific Notation Real*

This integrates components of the content strands: *Number and Algebra*, *Measurement and Geometry* and *Statistics and Probability*. This activity generates important discussion regarding assumptions in the modelling process but also illustrates how simple activities akin to science experiments can improve engagement and lead to deep exploration of how we know things about the Earth.

The technology devices that students carry offer the possibility of students using these tools to communicate more effectively. Photographs taken by students can be utilised to improve the quality of products, by merging these with digital text and tabulation.

Solutions generated provide a platform to discuss the limitation of the modelling and the assumptions made in determining the density and these become apparent when their results will inevitably be out by close to a factor of 10.

2. ** Earth lies on average 180 million km from the sun, using appropriate modelling determine how fast we are travelling**.

Students can be given a good insight into modelling by answering this question: Use of PPT integrated with activity to understand modelling and the limitations of modelling and how to scaffold an enquiry like this.

3. **Measurement and Volume:** ( includes some reference and discussion related to *Researching Your Own Practice: The Discipline of Noticing*” by John Mason (2002)

A number of years ago I ‘noticed’ and recorded an ‘account’ that a group of year 11 Mathematics A students were unable to:

- calculate the volume of a variety of wooden solids when provided a ruler and no instructions
- draw a 3_D representation of their solids
- use appropriate numbers of significant figures in both measuring and recording the volumes calculated once prompted

Are you familiar with this problem? Why did this happen? What was overlooked? When we ask these questions we are on the road to dispelling some of the negative images of our student that we generate from time to time…. and develop insight into what learning and engagement.

In this workshop teachers are invited to do this simple activity and discuss the obstacles that would normally be encountered by students in the middle years. Is this symptomatic of a “text approach” in which students do not get enough “hands on “ activity?.

4. Simple problem solving to encourage engagement. Using the tools you have to solve a problem – The Macgyver Challenge

[youtube]http://www.youtube.com/watch?v=Ym65fYMu5Gs[/youtube]

- Estimate areas of states of Australia given a the total area, map ,scissors and mass scales.
- Determine the thickness of a film of oil given a measuring cylinder, 5ml of oil,