Playing with positive and negative integers

​One team of Year 6 teachers was interested in developing a Guided Inquiry for exploring positive and negative integers with their students. They wanted the inquiry to involve investigating everyday situations that use integers and to generate an authentic need for locating and representing these numbers on a number line (ACMNA125). What better way to engage students with learning about integers in Year 6, than with their inquiry, What is the best game that you can create to model positive and negative integers? If you would like to try this inquiry in your own classroom then please see the four phases of the 4D framework (Allmond, Wells & Makar, 2010) outlined below:

Discover
To start the inquiry, investigate the use of integers in everyday contexts. A game that includes positive and negative numbers on a number line (vertical or horizontal) can create an authentic context for modelling positive and negative numbers. You might like to consider the Elevator Challenge developed by re(Solve): Maths by Inquiry. Introduce the inquiry question and reflect on the challenge of the inquiry.

Devise
In this phase, have students collaborate to design their own games to model positive and negative integers. Guide the co-construction of a class set of criteria to define ‘best’ in this context. Use content from the Australian Curriculum and the Proficiencies described for Year 6 to inform this criteria e.g. the ‘best’ game needs to give players lots of chances to represent positive and negative numbers on a number line as well as opportunities to formulate and solve authentic problems involving positive and negative integers.  Encourage students to share their ideas and provide feedback on planning ideas. 

Develop
Provide time for students to make their games based on their planning and ideas in the previous phases. Have students play games other students have made to generate feedback on challenges to game designs, and on improvements and innovations that can be made. In this phase, have students prepare the mathematical evidence they will need to Defend their solution to the inquiry question.

Defend
Students now get to play the games designed by others and reflect to Defend how a game ‘best’ models positive and negative integers. Have students consider the mathematical evidence generated in games they play and focus learning on the many opportunities to problem solve as they play – locating and representing positive and negative integers on a number line. 

In all phases of the inquiry, Checkpoints can be used to share interim ideas and challenges. You can download the Authentic Problems Teachers’ Guide from the re(Solve): Maths by Inquiry website to find more information on this Guided Inquiry process. 

The Year 6 teachers who designed this unit were also interested in using the information about their students’ learning, generated through the inquiry, as summative assessment information. This assessment information would contribute to their current assessment schedule. The team here at Inquiry Maths Pedagogy in Action (IMPACT) worked with the Year 6 teachers to develop possible formative and summative assessment opportunities that could complement the Guided Inquiry, What is the best game that you can create to model positive and negative integers? (Now available from the Members section of this website). Part of this required the students to apply ideas gained from playing games with integers to an unfamiliar context to demonstrate transfer to cartesian planes. If you wish to use Our Marking Guide and suggested summative assessment questions in your own classroom, then you will need to ensure you do not explore games involving locating and representing positive and negative integers on a cartesian plane, such as in Battleships, prior to the assessment.

Our Marking Guide - ​available from the Members section of this website

If you decide to give this inquiry a try then we hope your class enjoys finding out What is the best game that you can create to model positive and negative numbers? You can use Our Marking Guide as well as the suggestions for assessment to generate assessable information about your students. We hope you find this useful and welcome your feedback (Contact).