News

To date this month, 16 eTask Packages have been placed in schools in Queensland, New South Wales, Victoria and Tasmania. The nominated teacher receives an email with a link to their download page and sometimes they respond with a special comments such as these:

Thank you so much! We have already been talking about where to start so we can plan for effective implementation next year. Your guide is excellent!
Leanne Hoogsteyns, Deputy Principal
Kimberley Park State School, QLD

I have been wanting to set this up for many years but not had the chance. When I worked at Tara Girls school many years ago we had a room set up with all of the tasks. I am hoping to establish something similar where I am now.
Luke Bracks,
Kinross Wolaroi School, NSW

We think the eTask Package provides a hands-on, classroom-based, professional development context for addressing many of the issues in mathematics education:

• reasoning and problem solving
• mixed ability classes
• alternative assessment opportunities
• technology in classrooms
• differentiation
• communicating mathematics
• multiple entry and exit points
• ...in fact all of the issues represented in the Lesson Features list in the Link List below.

The eTask Package provides that service for a teacher who purchases for themselves. The service is richer when a staff works together on the package as an on-going professional learning program, sharing experience and skills as they construct and implement their Task Library.

How much richer again is the professional development likely to be if 10 schools work on creating their Task Library in the context of a cluster professional development experience over time? For now that question may be rhetorical, but down the track perhaps we will have an answer.

The Department of Education Tasmania has just placed an eTask Package in each of 10 secondary schools in the Hellyer Mathematics Project under the guidance of Paul Tabart, Principal Education Officer Numeracy.

We look forward to hearing about their work in the future.

• Can we support your cluster, district or system in a similar way?

We have added Kembo Cuisenaire to the list of suppliers we recommend. Many of the eTasks require 2cm wooden cubes, some need Cuisenaire Rods and a couple use MAB blocks of various sizes. Kembo makes high quality materials.

Choose the Wooden Cubes & Rods link in the Resources Index in the Link List below.

Museum of Cadiz, Spain ... Circa 3000 B.C.

Doona Cover, Australia ... Circa 2016

Real Alcázar de Sevilla, Spain ... 14th century But these shapes aren't quadrilaterals? Why do they tessellate? When you know why you will be able to design your own tessellating shape with measuring tools or software.

Mattress, Australia ... 21st century

Al Alhambra de Granada, Spain ... 14th century Real Alcázar de Sevilla, Spain ... 14th century

Driveway, Australia ... 21st century   This last design is a bit complex. Perhaps you could break the problem into smaller parts and start with the white shape or the black shape. Does either one remind you of any mathematical shape?

• For more on tessellations and the mathematical operations they involve see Wallpaper Patterns below.
• Perhaps in school we should include more of this sort of mathematics now and then?

Task 52, Which Floor?

The context is perhaps one that many children have been attracted to; getting into a lift and pressing any buttons to go up and down just for the fun of it. The card tells of Bronwyn's three step journey like this and tells us the floor on which she exits the lift. But on which floor did she enter the elevator? A closed question to start with which encourages strategies of drawing a diagram, acting out, guess and check, working backwards and writing an equation. Good; when the mathematician asks 'Can I check this another way?', other strategies are evident. However, the start prepares students for What happens if...? questions.

• The journey could stay the same, but the exit floor could change.
• The exit floor could stay the same, but the journey could change.
• The journey could have a different number of steps.
• The building could be a different size.
• ...

Lots to explore in this one, all of which helps to address the problem solving and reasoning proficiencies required by the curriculum. In the eTask Package this task is in the 'easy to make' set because the only concrete material it needs is one block, or toy figure or other object to represent Bronwyn.

Task 169, Wallpaper Patterns

It seemed appropriate to expose this task in an eNews issue that highlights mathematical designs. Wallpaper often has repeated tile patterns (although the 'grout' between the tiles usually isn't shown) and mathematical operations in space (translation, reflection, rotation which are as important as any operation in arithmetic) are often used to create different designs from the same tile. Sometimes the design on the tile also has a mathematical basis. In this activity the starting point tile is provided. It has some mathematical aspects but some detail is present just because the designer thought it was artistic.

(Actually there are two different tiles, but the students have to discover that for themselves.) What creates strikingly different wallpaper patterns is repeating the starting element using mathematical transformations. (Repetition is a creation tool in art as well as mathematics - for example see work from Joana Vasoncelos.)

The extension notes and Investigation Guide provided in this cameo make it incredibly rich just using the tiles provided. Add in the challenge to design your own tile and create wallpaper from it and you have a unit of work, which might include computer design and digital cameras, likely to produce stunning visual outcomes. Mathematics, art, design and technology all in one unit related to 'the real world'!

Task 96, Networks (see Link List below) adds even more opportunities to a study of tessellations and tiling patterns.

In the eTask Package this task is grouped with those requiring 'more work' to create. However, this is simply because of the extra few minutes involved in printing laminating and guillotining a set of cards. Only one set is needed for the task, but from the master supplied in the Package a class set can be made when required.