News

Here's one more tessellation with non-regular shapes to include with those provided in the September News.
Click the tessellation to reveal a high resolution version.

Calle Caballeros, Marbella, Spain ... 21st century

Google Maps shows the light and dark pattern from above.

See Maths Then and Now in the Previous News link below for teaching thoughts.

Eric The Sheep waiting in a line to be shorn becomes Sneaky Pete queuing for ice cream and provides a teaching craft talking point for your next team meeting. Thanks to Marshall Spooner, Greenwich Country Day School, Connecticut, who shares his many years of experience using Eric The Sheep with Year 8 classes. Open the article in the Link List below, read the background, follow the suggestions with your colleagues ... then consider dropping us a line with a record of your discussion and analysis. Update: Task 111, Square Numbers Square Numbers was featured as a cameo in March 2018 when lesson notes for a whole class investigation were added based on a lesson at Ashburton Primary School. Recently the cameo was revised again as a result of a discussion with teachers at Croydon Primary School. See Link List below. Diagrams of 36 blocks partitioned in various ways are used to suggest justification for the index law a2 x b2 = (a x b)2.

Earlier this year, in preparation for rebuilding, staff at Croydon Primary did a massive clean up. They discovered a box of ready-made tasks in good condition. Principal Julie Gilbert recognised their educational value immediately because she had organised professional development around embedding tasks into the curriculum during her time at Ashburton Primary. (See Link List below for examples of student work from Ashburton.) Julie approached us to provide similar support for her Year 3 - 6 staff and that session was carried out at the beginning of Term 4 when the new buildings were ready to go.

Four staff and two trainee teachers were involved. The structure of the day was:

• Session 1: Introduce tasks to the staff based on the workshop notes in the eTask Package.
• Session 2: Divide Year 5/6 classes into 4 half classes so teachers can try for themselves.
• Session 3: Debrief the experience and plan for a second presentation of the same lesson.
• Session 4: Divide Year 3/4 classes into 4 half classes and repeat the lesson.
• Sessions 5 & 6: Debrief the second lesson, plan for the next step, use one task as an example to workshop the many ways Mathematics Centre supports Reasoning & Problem Solving through the context of learning to work like a mathematician.

Tell the children what school mathematics is and ask what they think a mathematician's work involves.		Use the student responses to restate the mathematician's answer that it begins with an interesting problem ... just like these...

Choose one pair to select a task and with the class gathered around ask them to help you model the expectations of the lesson.		In an ordered way invite other pairs to select a task and start trying it. Within 10 minutes all students are working like mathematicians on the interesting problem they have chosen.

Pause the class when the need to start a journal arises for one group. Briefly discuss why a mathematician needs a journal and encourage key elements such as name of task, date ...		... and that you will be able to explain what your page means the next time you use your journal.

Ten minutes before the end ask children to check they have entered important journal notes and suggest making a 'next time I will' note. Then count the pieces back into the bag. Five minutes before the end gather the class at one table and ask that pair (previously arranged) to 'tell the others about your task without telling the answer'.   Repeat, refine and extend.

The Mathematical Association of Victoria runs what is surely the largest conference for mathematics educators in the southern hemisphere. Teachers from every part of the country and some from overseas, several keynote addresses and scores of seminars, lectures and workshops.

Workshops from Mathematics Centre this year are:

• B12, Picture Puzzles, Y3 - Y10
• C41, 4 Arm Shapes & Other Visual Algebra Experiences, Y5 - Y10
• D41, Working Mathematically with Infants, Y0 - Y2
• E41, Engineering 'aha' Moments in Number, Y3 - Y7
• G16, Taking Tricubes to the Limit, Y2 - Y12
• H41, Fascinating, Captivating and Absorbing Learners, Y0 - Y12
• I6, Learning Fractions With Picture Puzzles, Y2 - Y8
• J4, Get Your Hands On Hand-on Tasks, Y2 - Y10

The 55th annual conference will be at La Trobe University on Thursday 6 and Friday 7 December. On-line registration closes November 23rd, which is not far away. Until that date you can also change sessions for which you have already registered. We hope to see you in at least one of our sessions. See Link List below.

Task 45, Eric The Sheep

Eric is a task that captures the interest of most teachers and students. It can be used from very early primary school through to the end of secondary school. The scenario is that Eric is standing at the end of a line of sheep waiting to be shorn. But he isn't willing to wait his turn and begins sneaking past two sheep each time the shearer takes a new sheep to be shorn from the front of the line. If I tell you any number of sheep in front of Eric can you tell me how many will be shorn before Eric gets to the front? The cameo confirms this task is popular. It includes classroom work from Year 1,

Year 5 and Year 7 classes. The contributions demonstrate every aspect of working like a mathematician and give prominence to both keeping a mathematics journal (even in Year 1) and publishing the results of an investigation. The publishing in this case is as a PowerPoint presentation from a pair of Year 7 students. They also illustrate the three lives of a task - as an invitation for two students to work like a mathematician, as a whole class investigation modelling how to work like a mathematician and as an investigation in either of these ways supported by an Investigation Guide which extends the initial task.

Also linked in the cameo are:

• The Sneaky Pete article above.
• A whole class lesson plan on learning to write a Maths Report which uses Eric as the example.
• A You Tube video from the Association of Teachers of Mathematics (UK) acting out what it means to learn to work like a mathematician, again using Eric as the example.

One further link places Eric in a unit planning model called Menu Maths which gives students a choice about the mathematics problem they investigate.

You may already be quite familiar with Eric The Sheep, but is it time to become more familiar with the collected classroom wisdom in this cameo?

In the eTask Package this task is in the 'easy to make' set because the only concrete material it needs is about 50 counters and one object to be a pretend sheep.

Task 91, Pick A Box

The task uses 15 numbered 'boxes' and 12 different designs, therefore 3 pairs of boxes have the same design. The designs don't actually matter but it does matter which boxes have the same designs and that is specified on the card. Three rules - two that are number based and one that is design based - sort the boxes into three groups. Find the three groups. We know this delightful task captivates many, because solutions in the cameo have been submitted by several students and teachers. We still don't know how many

solutions there are. Perhaps that's part of the attraction of the challenge. But we do know that it takes disciplined application of problem solving strategies to find even one.

The task has a companion Maths300 lesson which places the problem in the context of Santa's elves making gift boxes, sorting them into three groups then accidentally knocking them over. The rules help them get the boxes back in the right groups. Perhaps this is the time to start planning this task for use in its whole class investigation life around the beginning of December. The cameo describes how paper versions of the boxes can be easily made.

In the eTask Package this task is in the More Work category because it supplies a PDF of attractive boxes which has to be printed onto card, laminated and guillotined. Not really that much more work.