In this month's News you will find:
Sicherman Dice: a new task
Maths300 ETuTE: a new book
Updates to Maths300
Reflection on Home School Lending
Reflection on Rote Learning
Tasks of the Month
Task 116, Who Owns The Monkey?
Task 118, Ice Cream Flavours
370 tasks placed in schools during September.
326,191 placed since the project began in July 1992.
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- Sicherman Dice
As with all of our work, it keeps developing because teachers keep on contributing. Matthew Reames, St. Edmund's Junior School, England, put us onto this one. He writes:
I have been looking at Sicherman Dice recently. These dice are evidently the only other set of dice using positive, non-zero integers to give the same possible outcomes as a pair of 'normal' cube dice. Rather than being the normal 1 to 6, these are two different dice, one numbered 1, 2, 2, 3, 3, 4 and the other numbered 1, 3, 4, 5, 6, 8.
I used these with Year 6 and 7 classes (aged about 10 and 11 this time of the year). In future lessons I would probably include this in the regular probability things, but this was one of those end-of-term lessons. We talked about the possible outcomes of flipping one coin, of rolling one number cube, then flipping two coins, and finally rolling two normal dice. We made an outcome grid for addition.
So, now we have Sicherman Dice in the collection as an invitation to students to discover their special property. And with Matthew's email you have the outline of a whole class investigation using this task as a model of how to work like a mathematician. It has been listed in the Task Catalogue as Task 241. See Link List below
Then, I asked the class to find another set of dice that would give the same possible outcomes. When allowed to use zero or negative numbers, there are a huge (possibly infinite) number of possibilities. There was a lot of good discussion about this!
The next step was to limit the faces to positive integers only. Though this required a bit more guidance from me (and I eventually had to tell them the final combination), there was good discussion about what they knew some of the numbers had to be (for example, each cube had to have a 1 otherwise they could not make a 2).
All of this was leading up to some further activities on the TI Nspire handhelds we were borrowing. Discussion was about probability distribution and why, for a small number of rolls, the frequency graphs they made were so different but then got more and more identical as they increased the number of rolls.
Anyway, I wasn't sure if you already had a task similar to this or not, but I thought it was worth passing along just in case. My classes certainly had some fun trying to figure it out and there was a lot of excellent maths discussion along the way.
- Updates to Maths300
Two lessons have been re-entered in the Lesson Library. They were somehow 'lost' when the new look site was released. They are:
Lesson 70, Pick A Box, Years 5 - 8
Lesson 95, Domino Trails, Years K - 6
Pick A Box is back just in time for Christmas preparations - yes really! The story shell of the lesson is about the North wind messing up the arrangements of groups of presents and Santa's elves only remembering some of the criteria for resorting them. It is also explored in Maths300 ETuTE, as is Domino Trails, which makes an appearance in that book and the Working Mathematically with Infants kit.
- Reflection on Rote Learning
Elsewhere in the world, Ghana to be precise, Aaron Peeters, is continuing to ponder his teaching craft as he shares the challenges of education in Africa. What he has to say about rote learning, and how he is working with a team of local professional development leaders to bring about supported curriculum shift, has messages for all of us in the privileged first world. See Link List below.
- Tasks of the Month
Two new cameos this month.
- Who Owns The Monkey? is probably our most difficult - and most satisfying - language and logic task. In essence it is a set of clues to help you find the right place for each of 25 cards on a 5x5 grid. The title relates to the clever design of the puzzle which doesn't allow you to find out who does own the monkey until the final few cards are placed.
- Ice Cream Flavours is an adventure in combination theory that begins with simple logic. If there are two items and two places to put them they can only be arranged in this order or that order. Following the opening challenge there are many What happens if...? to explore.
Click a photo to access its cameo, or access all current cameos through the Link List below.
- Did you miss September?
If so you missed information about:
- Maths, maths, Maths With Attitude world
- Professional development developments.
- Upgrade to the Resources & Ordering page
- History of the Maths Mat
- MacMaths revealed
- Maths Not At The Movies ... a new web paper
- Iceberg Information about two Tasks of the Month (Tasks 109, 110)
- ...and more...
Did You Know?
- You can find tasks coded by Year Level and Curriculum Strand in the Task Centre Catalogue (PDF file).
- The Activities link of Calculating Changes offers Content Finder & Year Level Finder tools.
- Our Site Map acts as a Table of Contents to help you find what you need in Mathematics Centre.
- You can search for lessons by Year Level, Curriculum Strand, Lesson Features & Keyword at Maths300.
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