There are varied descriptions of what makes for a rich or engaging task, most of the literature agrees on three criteria: that it has the potential to stimulate interest, provide challenge and extend the knowledge of all students (Sullivan & Lilburn; 1997, Sullivan et al, 2013; Ferguson, 2012; Clarke et al, 2014). Each of the criteria below extends from one or more of these fundamental ideas.

No | Criterion | Description & Scholarly Support |

1 | Builds student understanding of the | The task requires students to think about and represent mathematical concepts, (big ideas that are transferable, timeless, abstract and universal such as |

2 | Develops fluency. | The task promotes the development of flexible strategies over rote methods and automaticity. Fluency occurs as students “recognise robust ways of answering questions.” (Kilpatrick, Stafford & Findell, 2001). It includes “..performing calculations, collecting & interpreting data, using mathematical language, continuing patterns, choosing appropriate unit of measurement, recalling factual knowledge and concepts readily.” (Australian curriculum / mathematics / KeyIdeas). |

3 | Presents obstacles that require patient problem-solving. | A truly problematic task provides obstacles that students do not automatically know how to overcome. "When no such obstacle exists all you are doing is providing an activity." (Cai & Lester, 2010). Tasks can be in the context of exploring non-routine questions, real life challenges or posing problems where students can be moving, designing, constructing and actively solving problems in the physical space. The goal is to equip students with with skills that enable them to apply and communicate mathematics in relation to the solving of problems in their world.” (Stillman, Brown, & Galbraith, 2010). |

4 | Promotes reasoning and critical thinking. | The task challenges students to “engage in thinking about the various patterns, techniques and strategies available to them” (Polya,1965), look for reasons and draw conclusions (Stacey, 2010), convince others and evaluate the thinking of their peers (Boaler, 2016). Reasoning includes "estimating, hypothesising, justifying, generalising, explaining, interpreting and looking back.” (Australian curriculum / mathematics / KeyIdeas). |

5 | Presents opportunities for visualising and/or promotes creative thinking. | The task invites the student to “create, invent, discover and imagine new ways to solve a problem.” (Paivio, 2006). It has a visual component, requiring the student to draw the problem, picture an idea in their head, sketch or colour code to make connections and “see” relationships. (Tunks & Weller, 2009). When a task “requires the student to visualise or draw ideas, I always find higher levels of engagement and opportunities to understand the mathematical ideas that are not present without the visuals.” (Boaler, 2016). “Imagery leads to intuitive ideas, inference and possibilities.” (Munro, 2016). Pictorial models “stimulate development of algebraic thinking.” (Carter, Ferrucci & Yeap, 2002). |

6 | Extends knowledge in new contexts. | The task has the potential to “solidify and extend" what students know (Cai and Lester, 2010), provides "access to forms of knowledge beyond what [students] can pick up in everyday life or via the internet" (Yates, 2016) and aide the development of a knowledge-building community whereby "all individuals legitimately contribute to the advancement of knowledge in the classroom." (ReSolve: Maths By Inquiry). |

7 | Provides multiple entry and exit points. | The task caters for a range of student abilities. An open-middle means that different possibilities, strategies, use of materials and products can emerge. It may adapt depending on student progress. “Tasks with open goals can engage students in productive exploration.” (Christiansen and Walther, 1986). |

8 | Encourages collaboration and discourse. | The task creates room for students to show initiative and make decisions in groups, engage with each other's ideas, monitor and regulate thinking, see other ways of knowing and communicate their findings (ACARA, 2016; Goos, Galbraith & Renshaw, 2002). The task gives students opportunities to develop their personal & social capabilities by building positive relationships, handling challenging situations constructively and developing leadership skills. |

9 | Stimulates curiosity and imagination. | The task has the potential to "foster positive student motivation" (Ames, 1992) and “capture [student] interests and curiosity.” (Cai and Lester, 2010). It might tell a story, offer a challenge, play a game, connect to an authentic daily life context, utilise technology, offer student choice or deviate from traditional ways of 'doing maths' ie by prioritising kinaesthetic learning, outdoor learning, multi-age or transdisciplinary learning. |

10 | Supports formative assessment practices. | The task encourages self, peer and teacher assessment designed to give feedback about an aspect of the work, e.g. to identify patterns or errors, reflection on what they have learnt, show progress towards goal and/or makes suggestions for future learning. “When feedback focuses not on the person, but on the strengths and weaknesses of the particular piece of work and what needs to be done to improve, performance is enhanced.” (Hodgen & William, 2006). “We learn so much from errors and from the feedback that then accrues from going in the wrong direction or not going sufficiently in the right direction. (Hattie, 2008) “It is what you learn after you have solved the problem that really counts.” (Wilson, Fernandez, & Hadaway, 1993).” |

Clarke, D., Cheeseman, J., Roche, A., & van der Schans, S. (2014). Teaching Strategies for Building Student Persistence on Challenging Tasks: Insights Emerging from Two Approaches to Teacher Professional Learning. Mathematics Teacher Education and Development, 16(2), 46-70.

Ferguson, S. (2012). Challenges in Responding to Scaffolding Opportunities in the Mathematics Classroom. Mathematics Education Research Group of Australasia.

Sullivan, P., & Lilburn, P. (1997). Open-ended maths activities: Using" good" questions to enhance learning. Oxford University Press.

Sullivan, P., Clarke, D., & Clarke, B. (2013). Teaching with tasks for effective mathematics learning. New York, NY: Springer New York.