1. Investigations MATHEMATICS Years 1 to 10

2. Investigations  exemplify a teaching approach that supports thinking, reasoning and working mathematically  use real-life and lifelike contexts  illustrate how learning, teaching and assessing may be sequenced.

3. Investigations May be framed as:  a problem to be solved  a question to be answered  a significant task to be completed  an issue to be explored.

4. Investigations  are open-ended  provide opportunities for students to use multiple pathways when investigating problems, issues, situations or questions.

5. Why use investigations? Engaging in open-ended investigations:  promotes a higher level of thinking  encourages students to think, learn, analyse, criticise, solve unfamiliar problems  asks for more than recall of facts or the replication of procedures.

6. Investigations  develop students’ abilities to think, reason and work mathematically  develop students’ abilities to know about mathematics, know how to do mathematics and know when and where to use mathematics  may be developed using the model for planning investigations or units of work illustrated in the Planning PowerPoint.

7. Investigations or units of work, may combine learning outcomes from:  within a strand of the key learning area  across strands within the key learning area  across levels within the key learning area  across key learning areas.

8. Select learning outcomes on which to focus Consider:  prior learning, needs and interests of students  the core learning outcomes at the levels most likely to progress student learning  the strands and topics and the relationship among them.

9. Choose or negotiate the context(s) for learning  Identify a life-like context in which students can develop the knowledge, procedures and strategies needed to demonstrate their learning.  Use an investigative approach to provide a focus or context for learning.

10. Contexts for learning may be drawn from  students’ interests  the local community or environment  current events or issues  topics being explored in other key learning areas.

11. Sample investigation  The editor of a travel magazine wants to include an article about the best countries in which to live. Your job is to present information that compares the standard of living in Australia with that of three other countries on three different continents. Use a variety of methods including data displays, data analyses and maps to support your conclusion.

12. Investigations  may be organised in three phases: 1. Identifying and describing 2. Understanding and applying 3. Communicating and justifying.

13. Identifying and describing Is exemplified by students:  describing an investigation in their own words  linking an investigation to known mathematics  identifying situations that required similar thinking and mathematics  identifying the mathematics required for an investigation  revising and clarifying knowledge, procedures and strategies  identifying and negotiating possible pathways through an investigation.

14. Identifying and describing

15. Understanding and applying Is exemplified by students:  representing problems using objects, pictures, symbols or mathematical models  applying previously learned mathematics to progress through an investigation  developing new mathematical knowledge, procedures and strategies appropriate to an investigation  generating possible solutions  considering the reasonableness of solutions  validating their findings by observation, trial or experimentation  exhibiting some self-correcting behaviour.

16. Understanding and applying

17. Communicating and justifying Is exemplified by students:  presenting findings or conclusions  recounting the pathway through an investigation  evaluating thinking and reasoning  making connections between prior and new learning  making generalisations  describing new learning  evaluating strategies and procedures used  reflecting on new knowledge  posing similar investigations or problems.

18. Communicating and justifying

19. QSA sample investigations  To view sample investigations go to the QSA website.  Click on the ‘Yrs 1 to 10’ tab then ‘Mathematics’  Click on ‘Support materials’ then ‘Planning’.

20. Contact us Queensland Studies Authority PO Box 307 Spring Hill Queensland 4004 Australia Phone: +61 7 3864 0299 Fax: + 61 7 3221 2553 Visit the QSA website at www.qsa.qld.edu.au www.qsa.qld.edu.au