In this edition of the News you will find:
New Cube Tube Videos
Remind Yourself About Pymble
Tasks of the Month
Task 218, Guessing Colours Game
Task 219, The Hole In The Triangle
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- Ashburton Succeeding
Do you remember me?
It's more than a year since we last visited Ashburton Primary School. You can read about the earlier visits in the Link List below.
Yes, answers one Year 5, you're the Task Box Man.
No, corrects another, you're a mathematician.
Yes, I reply, just like you and everyone else here.
From Year 4 the school uses Tasks on a regular basis as part of their Working Like A Mathematician curriculum. Sometimes the students are using the tasks as an invitation to work like a mathematician. Sometimes the teachers are using one task as the stimulus for a whole class investigation through which they can model what it means to work like a mathematician. Task Cameos and the school's Maths300 membership support this 'life' of a task.
On this occasion we were involved in Discussion Lessons based around using Tasks with two Year 4 classes (team taught) - new to the program this year - and a Year 5, who were in their second year. The teachers are doing a wonderful job. Students were easily able to articulate what it means to work like a mathematician, were enthusiastic, considerate of each other and orderly in selecting their Task for the session and automatically used their journal to record what they were working on and what they found out and thought. This purposeful activity can only happen through well planned and executed teaching with clear objectives.
Five classes use the task resource at various times, so it is located in the corner of a central connecting space, along with folders containing multiple copies of worksheets needed for some tasks. Teachers make no particular rules about who partners whom, so the pairs are fluid from session to session.
When asked, students simply disappeared from the room to the collect a Task - sometimes with one choosing the task and the other finding their journals - and within 3 minutes everyone was settling to their investigation. To be precise, according to the camera date stamp, this photo was taken 2 minutes and 16 seconds after the one above.
(Clicking on the journal photos in this article will reveal them in larger size. In this case it will show that these students needed assistance in learning how to use isometric dot paper to create 3D drawings like the ones on the card. A few moments with the pair and that was sorted.)
Task 103, Four Cube Houses
From here the session continued enthusiastically and purposefully until it was time to return the task boxes and debrief. Before journals were closed students were asked to ensure that they had recorded all they needed to about their investigation so far and to use a 'thought bubble' or just a comment to point towards how they could continue next time. See more from this class in the new Cube Tube videos, below.
These photos are from near the end of the Year 5 class later in the day. The extra year of experience working like a mathematician is producing some quite detailed recording and explanation.
Hamish & Niro have worked out the first 23 moves
of Task 142, Tower of Hanoi. Their recording shows
exactly where to start next time to continue the challenge.
Gemm and Lana have been working out all the possibilities
for Task 183, Pizza Toppings. They have been very
orderly and think they have them all. Do you?
Kyla & Lexy have worked created a code to record
the moves in Task 173, Crossing The River 1.
Will it help them find a pattern?
Faster and harder? Perhaps more neatly so you realise the insight displayed in these drawings. Showing the object, the mirror and the reflected image in these solutions for Task 100, Mirror Patterns 1 takes considerable skill.
See Link List below for links to the Cameos for these tasks.
- New Cube Tube Videos
Nick and Owen, Year 4, Ashburton Primary School, made three videos about Task 143, Hearts & Loops.
- In the first, Nick shows he can disconnect the pieces.
- In the second, Owen shows he can reconnect the pieces.
- In the third, they teach the teacher how do to it - with their hands behind their back!
See the Cube Tube link in the Link List below.
- Remind Yourself About Pymble
Years 7 - 10, Pymble Ladies' College, Sydney, is one secondary school using Tasks, Maths300 and more in rich and captivating ways to build the curriculum around learning to work like a mathematician. Glenn Dudley, Head of Department, wrote a couple of short articles about their work in 2014 after presenting at the British Congress of Mathematics Education. These pieces have been edited into a story recently added to our Research & Stories link. See Link List below.
- Tasks of the Month
Two new cameos this month.
The Task Cameo Content Finder has been updated to include these tasks.
- Guessing Colours Game Count a total number of discs (in this case 15) using five colours and any number of each to make the total. Hide them in an opaque bag. Students take turns to select a disc from the bag, but first they each have to guess which colour will come out. A points scoring system is involved and a running total of points is kept for each player until all the discs are removed. The game involves simple addition and subtraction, may include negative numbers and is an excellent experience of chance events and sample space.
- The Hole In The Triangle appears to make the same size triangle in two different ways with the same pieces. The twist is that one of the triangles clearly has an area one square bigger than the other. It just can't be, but only mathematics can help us understand how we are being tricked and why the apparent difference is exactly one square unit of area.
Click a photo to access its cameo, or access all current cameos through the Link List below.
August 2015, July 2015, June 2015, May 2015, April 2015, February 2015
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Continue exploring our history back to July 1992 through the Sense of History link.