News

• Each task has a story to tell about mathematics education.
• A library of tasks tells just about every story that needs to be told about mathematics education.

That's because a Task Library is supported by over 40 years of teacher wisdom collected and retold through Mathematics Centre. Just as with a book library, the more you research your Task Library the more you learn. The more you learn, the more your students learn.

Scrutinise the collection through any education lens and the library can respond with a story about content or teaching craft or curriculum planning or research or... which could inspire you to move your curriculum from where it is now to where you want it to be.

That's why the eTask Package is presented as a self-directed professional development package. You work with your team (which might include parents and students) to build your Task Library over time. With the guidance in the eTask Maker Manual and the eTask Workshop notes you can easily prepare a significant starter set of tasks in just one day. It grows from there. You schedule on-going professional learning driven by your classroom experiences with your tasks.

The eTask Package was released in June 2017. It is already being used by schools in every Australian state and the ACT plus 3 schools in New Zealand, 2 in USA and 1 in Thailand.

• The eTask Package is a professional learning opportunity.
• Is it a professional learning opportunity for you?

See Link List below.

Picture Puzzles are full screen PDF slide shows built around one screen, two learners, concrete materials and a challenge.

• That already sounds like a different form of digital learning.
• Could they provide an additional stimulus in the digital learning component of your mathematics curriculum?

Each Picture Puzzle is in fact an unfolding sequence of challenges which open on any device that supports PDF - that's pretty much anything.

• Users are in total control of the pace of the display and are able to move backwards and forwards through the slides to review data and check hypotheses.
• Picture Puzzles, like tasks, are designed to be used by pairs but they can also be used to guide whole class investigations where all students work concurrently on the same Picture Puzzle.
• All Picture Puzzles support learning to work like a mathematician.

Features likely to encourage learning include:

• Context - working like a mathematician
• Use of technology to deliver challenges
• Visual learning - more pictures than words
• Kinaesthetic learning - concrete materials dependent
• Mathematical conversation - peer support
• Supporting thinking and discussion - move backwards and forwards through screens at will
• Recording mathematics - student access to a journal (which may be electronic) is assumed
• Student ownership - choice from a menu
• Concept focus - mathematics is presented as concrete, visual and making sense
• Easy to start
• Multiple exit points
• Differentiation for ability and experience
• Inclusive
• Non-threatening
• Skill development in context

Some Picture Puzzles are designed as Investigation Guides to present and extend challenges from the Task Library. Others are designed to support the development of specific content and skills.

• There are 36 Picture Puzzles in the current collection - all with teaching notes.
• Two Picture Puzzles and 2 sets of teaching notes are freely available.
• (Editor's Note: From June 2018 all teaching notes for all Picture Puzzles are freely available.)

The current collection of Picture Puzzles is shown here by title slide. Each one is part of a menu of puzzles with similar content. See Link List below for more information.

Investigation Guides

Pattern & Algebra A ... Years 4-12 (Square Numbers and all the teaching notes for this menu are available as Free Tour.) Square and Triangle Numbers leading into generalisation, symbolic notation and other special challenges, including the difference between two squares.

Pattern & Algebra B ... Years 4-10 Exploring and generalising patterns in words and symbols. Seeing the patterns from different points of view leads to equivalent algebraic expressions. Substitution and solution.

Shape & Measurement A ... Years 2-10 (Sphinx Shapes and all the teaching notes for this menu are available as Free Tour.) Concepts of perimeter and area using unit squares and unit triangles as the measures. Includes 2D shape puzzles, tessellation and polyiamonds.

Shape & Space A ... Years 2-11 Representing 3D objects in 2D. Plan (looking down), elevation (side) and isometric views in the context of 3D puzzles.

Concept Learning & Skill Development

Number & Computation A ... Years 2-6 (8) Based on an array model of multiplication students experience how to know the answers to their times tables. Uncover Counting is used to reveal the...

Number & Computation B ... Years 2-6 (8) Students choose their own time limit to complete 20 Times Tables Torture questions. Using array images they correct their work and find two ways of knowing each table.

Number & Computation C ... Years 2-8 Students build Rod Mats and explore relationships between rows of rods the same length. Natural language drives the investigation of fraction equivalence and operations.

Task 8, Addition Totals

The task is easy to state. Choose a whole number. Now find all the whole number pairs that sum to it. How many are there? How do you know when you have found them all? Exploring in an organised way with a sequence of starting numbers, suggest there is a pattern ... but it seems to have two parts depending on whether the starting number is odd or even. How do we express that in words? ...in symbols? ...Is it possible to create a formula which gives the correct result for both odd and even?

This cameo includes an outline a the companion Maths300 lesson to give those who are not yet members the opportunity 'to get a feel of' how a Maths300 whole class investigation is structured. The cameo also includes a contribution from a Year 5/6 class where a student suggested including negative whole numbers. See Link List below for the Addition Totals cameo.

In the eTask Package, this task is in the 'Easy To Make' category because you only need a few counters or square tiles or wooden cubes and a permanent marking pen. ('Nice' handwriting would be a bonus). The card is designed to print in colour on white simply to add a little more visual interest to the set.

Task 181, Pointy Fences

This is a visual algebra problem in three dimensions. The first challenge is really to interpret the 2D diagram on the card and create the 3D object it is representing; hence interconnecting mathematics content areas. The challenge for the Sharp-As-A-Tack company workers is to be able to work out the number of squares and triangles needed to make any length of fence that may be ordered. Exploration leads to a pattern which needs to be explained. That might be in words, drawings or symbols.

The cameo reveals at least five ways that pattern can be described and symbolised. Extension challenges enter the realms of substitution in and solution of equations, equivalent algebraic expressions, domain and range, linear algebra, graphing, gradient and intercepts. As formal as all that might sound, in context it is not so difficult, which makes the task accessible from Year 4 onwards. See Link List below for the Pointy Fences cameo.

In the eTask Package, this task is in the 'Special Equipment' category because to make you need a few 3d Geoshape or Geofix shapes to make it. However many schools do have this equipment so it immediately moves to the 'Easy' category because the card only needs to printed and packaged with 10 squares and 8 triangles.