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2017 Investigations on Facebook

On the NZAMT facebook page there will be an investigation posted each week thanks to Gillian Frankcom. Check out the NZAMT Facebook page and follow us. Below is the first Facebook Investigation post for 2017

circles

I aim to put an investigation every week on this page, and I would be very glad if anyone wanted to have discussions with me.


Starting at the beginning of the year, I have decided that the Six Circles activity from Lighting Mathematical Fires by Holton and Lovitt (1998), is an excellent place to start as you begin with your new classes. The lovely thing about this mini-investigation is that there is more than one answer, and how students know there are no more answers is an excellent thinking activity. And because these students may be new to investigations, you could ask them what they could change to investigate (A What If....) and let them have a go, but if you feel the need to give them one, then a great one is, What if there was a similar triangle with 4 circles on each side?

The Six Circles
Six circles are placed symmetrically along the sides of an equilateral triangle as shown. Place the numbers 1 to 6 inclusive in each of the circles so that the total of each row have the same sum. How many ways can it be done?