- PD Planning
If you are thinking about professional development for next year, or even to round off this year, we're here if you would like to chat. Email doug@blackdouglas.com.au or ring 0401 177 775 to talk over your objectives.
- Half day ... full day ... many days.
- Staff teams ... whole staff ... clusters of schools ... education systems
- Any place. Any time.
- Always practical.
- Always classroom based.
- Always consistent with curriculum requirements.
And always viewing curriculum through the lens of learning to work like a mathematician in happy, healthy, cheerful, productive, inspiring classrooms.
- Get to Know a Cameo
Task 120, Nim
Easy to state and easy to start, Nim is a logic challenge with links to odd and even numbers and spatial perception. The game begins with four rows of counters arranged as 1, 3, 5, 7. Players take turns to remove any number of counters from any one row. The person who has to take the last counter loses. The objective is to find a winning strategy and doing so depends on first finding positions from which you can win. In a neat twist which simplifies the analysis of the problem, counters currently in play in each row are show as a set of four numbers. Working backwards is a key investigation strategy in this problem.
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In the eTask Package this task is in the 'easy to make' set because it only needs 16 counters.
Task 188, Arithmagons 1 & Task 194, Arithmagons 2
Arithmagons 2 can be thought of as an extension of Arithmagons 1 through the questions 'What happens if we change the shape?'. Two for the price of one this time.
Both work in the same way. Corner circles large enough to fit the numbered discs are arranged in a triangle, or, if we change the shape, a square. The main difference is that each task has a different set of numbers to work with: 1 to 10 for Arithmagons 1 and 0 - 20 for Arithmagons 2. In either case the rules are the same. Any line joining a pair of corner circles displays the total of the discs at each end. Given the totals, work out the discs which must be in each corner to make the totals true. Is there more than one solution in each case?
Then, just when you think you have worked how to find the right discs every time, you are further challenged with the question: What happens if a line total is missing?.
The tasks can be approached through number sense, organised search and algebra, so a wide range of learners will find success and know that they could return to the task at a later date and learn more. A task is only ever finished 'for now'. Another question can always come along and open it up again.
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From The Classroom in the Arithmagons 1 cameo, contributed by Matt Skoss, confirms this and at the same time provides evidence for Ulla's comment above that "...there are, in every class, students who think smarter than we do!".
In the eTask Package these tasks are in the 'easy to make' set because each task only needs one set of numbered discs.
Keep smiling,
Doug.
Link List
- Did you miss the Previous News?
If so you missed information about:
- Engineering 'aha' Moments in Algebra
- Mathematics Education is not an Enigma
- Origami Sphinx Tiles
- Get to Know a Cameo
... Pythagoras 2 & Triangles & Colours
- ...and more...
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