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# News

## July 2021

In this edition of the News you will find:

Get to Know a Cameo
... Farmyard Friends
... Knight Protectors

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• I Moved The Decimal Point

 A non-teacher friend wrote the other day asking me to check his working out of: (6·43 times 10 to the power of 4) divided by (8·01 times 10 to the power of 2) In his explanation of what he had done he wrote: I moved the decimal point... No you didn't mate, I thought. The decimal point is always in the ones column as a marker to indicate where whole numbers end and parts of whole numbers begin. Yep, in the ones column. It doesn't have a column of its own. If it did, our numeration system would lose its beautiful symmetry. Surely no one teaches those rules these days. But do you use the game Calculator Slido to help kids learn what really does happen to the numerals when numbers are made powers of 10 bigger or smaller? See Link List below where are there two links to the activity. The first is in Calculating Changes which is the original source. Here the text is addressed to teachers and includes suggestions for beginning as a whole body involvement activity. The second is to Maths At Home where the text is addressed to self-learners who may be in the classroom, or learning from home as part of remote learning, or maths homework.

• Matt's Maths Mat Continues To Matter

 Article used with permission of The Coonamble Times: https://www.coonambletimes.com.au/ Matt Skoss has been working with the Mathematical Association of NSW (MANSW) in a project to support rural, regional and remote teachers to build local, self-driving, professional development networks which include primary and secondary, government and non-government schools. Matt's Maths Mat has been a fantastic way of getting kids involved in learning activities which also stimulate many layers of teaching craft discussion among participating teachers. Click the photo to reveal the article that surrounds it, then use the zoom tool to make it more readable. See Link List below for the history behind maths mats, example activities and more.

• Maths At Home Update

If you are registered at our Maths At Home site you have already received, and possibly already acted on, the following information. If not, then please take a look. There are now 66 activities in this learners' library.

• Colour Spots on a Number Line (3-7)
Children like colouring and colouring in can be a useful way of illustrating patterns in mathematics. But colouring can also mean more time spent colouring than learning to work like a mathematician. The colouring in this activity is as quick as making a few small spots with a pencil or marker. The act of doing that forces the hand to work in a physical pattern and the mind to ask itself where the next spot will be. The children don't write any numbers on the line, but they are encouraged to imagine which ones are hiding under the colour spots.

The mathematics that results produces, firstly, a visual pattern, then a list of related numbers, then a table connecting numbers used for two purposes. The tables beg the question: If I tell you any ..., can you tell me ...?. Any learner who can make such a prediction has generalised the situation and is already involved in algebra.

The activity goes on to gently lead from oral, to written, to simple symbolic algebra. The latter part of the activity introduces co-ordinate geometry and a little exploration of straight lines in that context.

See Link List below for Maths At Home, then take the Learners link for the activity library. Remember, if you register you will know about new activities the moment they are published.

• Get to Know a Cameo

 It's easy to see how this task works. Five animals have to be placed in five pens. It's only a matter of obeying the rules about which can go where. The joy is that there is more than one answer! The challenge is to find them all and know how you know that you have. A consequence is a desire to fiddle with the clues so that there is only one solution; or perhaps that there are exactly three; or more than one hundred; or... Becoming interested in such questions is the work of mathematicians. So, any student at any age who becomes interested is in fact working like a mathematician - and doesn't have to
know numbers or measurements or algebra or any other text book stuff (important as those things may be in a toolbox) to be able to demonstrate it.

Interestingly though, if you ask the right questions, the Farmyard Friends task that can be tackled successfully from Year 2, can also be used to practise toolbox skills related to selections and arrangements in Years 11 and 12.

In the eTask Package this task is in the 'more work' set because there's an extra sheet of animals to copy, cut and laminate.

 This task another that requires content-free reasoning, thus opening the door to any interested person. Twelve nights have to placed on a chess board so that every square is either protected or occupied. It's something you can get into immediately by placing one of the knights and finding a way of showing and recording what is protected and what remains unprotected. The delight is that the solution turns out to have characteristics of a mathematical transformation. The cameo details, with colourful diagrams, a composite of reasoning that students have been known to use and shows the solution and the transformation.

In the eTask Package this task is in the 'easy' set because, apart from the two cards, it only needs 12 'pretend knights' that fit the grid.

Keep smiling,
Doug.

• Did you miss the Previous News?
If so you missed information about:
1. Introducing Professor Morris
2. Maths At Home Update