Authentic Tasks authentic tasks

Authentic tasks are designed to help students see mathematics as worthwhile and important. When students understand the purpose of a given problem in mathematics, they are more likely to persist when challenged. Authentic tasks generally have an ‘open middle’ which means that students can use different representations and solutions to communicate their knowledge and reasoning.

These curated links provide MAV members with access to nine authentic tasks from some of our primary consultants’ favourite resources. The 11 criteria provide MAV members with a research-informed context to consider each task’s potential impact on student thinking, ways of working, attitudes towards mathematics, their knowledge and understanding.

The following criteria was used to select the tasks based on their potential:

Criteria Elaboration

Intriguing contexts capture the students’ interests and curiosities

An opportunity for students to relate learning to their own lives and communities. High student motivation/enjoyment and sense of purpose can be anticipated or observed.

Problem solving is required to overcome obstacles

Exploring non-routine questions, real life challenges, posing problems and designing investigations. There are obstacles that students have to overcome in order to succeed.

Low entry/ high ceiling, and an open-middle encourages different strategies

Caters for a range of student abilities. Open-middle allows for different possibilities, strategies, materials and products to emerge. Task may adapt depending on student progress.

Opportunities for creative thinking and or visualising

Students invent, discover and imagine new ways to solve a problem. Students make connections and see relationships by visualising the problem or representing solutions visually.     

Encourages reasoning and critical thinking

Logical, rational and critical thinking. eg: estimating, hypothesising, justifying, generalising, comparing, explaining, interpreting and looking back.

Opportunity to collaborate and see others working mathematically

Students challenge each other, the computer, the teacher etc and observe how they work mathematically. Make decisions in groups to communicate findings, engage with different ideas, monitor and regulate each other's thinking.

Opportunities for students to develop fluency

Estimating, collecting and interpreting data, using mathematical language, continuing patterns, choosing appropriate unit of measurement, recalling factual knowledge and concepts readily.

Promotes feedback and metacognition.

Self and peer reflection targeted at specific aspects of the work. eg: knowledge; how your thinking is changed as a result of lesson. Affective traits eg: problem solving attitude, collaborative skills.

Extends knowledge or applies knowledge in new contexts

Provides students with access to forms of knowledge beyond what they can pick up in everyday life or via the Internet.

Promotes an understanding of the ‘why’ and ‘how’ of mathematics

Seeing patterns, connecting related ideas based on previously constructed knowledge. Represent concepts (big Ideas) in different ways eg: developing number sense, place value.

Guides future learning

Provides data on student growth to guide future direction. eg: identifies patterns or errors, level of progress towards goal. Makes suggestions for future learning.

Used with Permission © Martin Holt Educational Consultant 2017

If you would like to learn more about this approach to assessing or using tasks contact us at office@mav.vic.edu.au

Statistics and probability

NRICH problem solving task: Three Block Towers

Maths 300 investigation: Win at the Fair

Scootle lesson sequence: Dice Don't have Brains

Target Level: F - 2

Target Level: 3-6

Target Level: 1-6

Why we love this task:

  • Problem solving based
  • Low entry, open middle and high ceiling
  • Critical thinking and reasoning
  • Extends knowledge
  • Connects ideas to enhance understanding

Why we love this task:

  • Intriguing context
  • Critical thinking and reasoning
  • Develops fluency
  • Connects ideas to enhance understanding
  • Guides future learning

Why we love this task:

  • Problem solving based
  • Low entry, open middle and high ceiling
  • Collaborative
  • Extends knowledge
  • Connects ideas to enhance understanding

Measurement and Geometry

Wildmaths interactive game: Approaching Midnight

Teach Engineering investigation: How Tall are we?

National Literacy & Numeracy Week lesson sequence: Which Way?

Target Level: 2-4

Target Level: F-2

Target Level: F-6+

Why we love this task:

  • Intriguing context
  • Problem solving based
  • Low entry, open middle and high ceiling
  • Critical thinking and reasoning
  • Develops fluency

Why we love this task:

  • Problem solving based
  • Creative thinking and visualising
  • Collaborative
  • Develops fluency
  • Guides future learning

Why we love this task:

  • Low entry, open middle and high ceiling
  • Creative thinking and visualising
  • Collaborative
  • Develops fluency
  • Connects ideas to enhance understanding

Number & Algebra

NZMaths lesson sequence: Six Circles

MAV problem solving task: The 1,2,3,4 Problem

ReSolve Maths by Inquiry lesson sequence: Bakery Challenge

Target Level: 5-6

Target Level: 1-6

Target Level: 5-6

Why we love this task:

  • Problem solving based
  • Critical thinking and reasoning
  • Extends knowledge
  • Connects ideas to enhance understanding
  • Guides future learning

Why we love this task:

  • Problem solving based
  • Low entry, open middle and high ceiling
  • Collaborative
  • Develops fluency
  • Connects ideas to enhance understanding

Why we love this task:

  • Intriguing context
  • Low entry, open middle and high ceiling
  • Creative thinking and visualising
  • Develops fluency
  • Connects ideas to enhance understanding