The Mathematics Investigation Cycle – poster and cards
Find a poster of the Mathematics Investigation Cycle and accompanying student cards.
About this resource
This page provides information about the Mathematics Investigation Cycle, a poster of the cycle, and accompanying student cards.
The Mathematics Investigation Cycle
Investigating rich tasks and meaningful situations utilises all the mathematical processes, and encourages students to make connections and develop mathematical concepts and understandings.
The Mathematics Investigation Cycle is a structured approach that teachers and students can use through the different stages of an investigation.
The poster for the Mathematics Investigation Cycle guides teachers and students through the different stages of the process. The student cards can be used for a display or as prompts for groups of students as they work through their investigations.
In the accordions below you will find the following information.
Connecting big ideas, concepts, and processes
- The Mathematics Investigation Cycle as it connects to the revised math and stats learning area.
Planning mathematics investigations
-The Mathematics Investigation Cycle as part of a comprehensive teaching and learning programme.
Teaching using the Mathematics Investigation Cycle
-The cycle presents a structured approach to teaching through investigations and rich tasks
Understand: Through mathematics investigations, students see the big ideas in action.
Know: Mathematics investigations provide purpose for the knowledge students develop as they progress along the schooling pathway. All strands of mathematics can be used as contexts for investigations.
Do: In mathematics investigations, students purposefully use all the processes.
Students:
- use a range of representations to make meaning of the situation
- connect concepts and procedures, across and within mathematical strands to solve a mathematical investigative question
- generalise their findings through identifying patterns, regularities, and structures that are observed
- explain and justify their reasoning in order to convince themselves and others that their findings are reasonable and accurate.
The investigation cycle has a place in all types of mathematics lessons:
- relatively short tasks, such as solving a problem as a motivational ‘hook’ to explore and develop conjectures about new concepts
- rich tasks within a lesson to encourage students to apply existing concepts, procedures, and processes to other situations
- complex problems that take place over an extended period of time.
The rich task to be investigated may be:
- a real-world situation, like creating a container to hold popcorn
- a purely mathematical situation, such as investigating magic triangles.
The rich task should allow students to connect with their prior learning and progress understanding of their year level’s mathematical concepts and processes.
To develop confidence and support positive relationships with maths, make tasks accessible to all students by:
- using low floor, high ceiling tasks,
- encouraging persistence and providing prompts and scaffolds,
- providing opportunities for all to experience success.
The mathematics investigation cycle is a tool to prompt and support students’ decision making. Students can move backwards and forwards through the cycle to investigate meaningful situations using mathematics.
Use explicit teaching throughout:
- to teach the concepts, procedures, and processes students need to carry out their investigation
- as targeted small group teaching for students who need support
- to demonstrate representations and the use of tools
- to highlight connections and generalisations.
Teachers notice and recognise students’ progress throughout the investigation and can step in to respond with explicit teaching and feedback ‘in the moment’.
Enhance communication skills by supporting students to share and explain their reasoning and collaborate with others.
Further resources to help use the revised mathematics and statistics learning area
Other resources to help you use the revised mathematics and statistics learning area
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4 of 7PLD for structured approaches to maths
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5 of 7PLD days activities for mathematics and statistics
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6 of 7Using materials in years 0-8 maths teaching – Video library
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7 of 7
