Take Ten Cards (I am not sure now where I got it from, but it makes an excellent low floor/high ceiling activity, and is capable of many, many What Ifs...Give students the numbers one to ten from a pack of cards, Ace counts as one. Place those ten cards in this configuration so that no consecutive cards are adjacent to each other, this goes for up-and-down, side-to-side and diagonally. Initially students just skirmish and are happy to find a solution, if you give each student the whole page of 6 solutions they will get the idea that you expect more than one answer. Once many answers are found, ideas develop about which card position(s) is important, and why. If they can articulate this, then you know they have been using algebraic thinking. If they don't automatically say something about how many different solutions are possible, question them - don't give it away.
What If... many students change the configuration of the cards,then test to see if solutions are possible. A lovely twist is to make 10 and 1 "wrap-around" so they are considered as consecutive.
For more investigations like these, please visit the NZAMT Facebook page
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
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?
The training squad for the 58th Olympiad has been announced at the conclusion of the January training camp. The camp took place at University Hall from 8th to 14th January where 24 students spent the week attending lectures and problem sessions in their preparation for the selection test on the Friday. The team will travel to Rio de Janiero, Brazil this July to represent New Zealand.
During the second week of January this year 30 teachers from all over New Zealand gathered together and volunteered their time to create NCEA internal assessment resourcesfor all NZAMT members.
They were based at the Saint Francis Friary and Retreat Centre which is a lovely quiet site situated in Auckland. This allowed them the space and time to let the creativity flow and many resources were produced.
A huge thank you to all involved for your time and efforts. We hope that the resources are found to be useful and that you may be interested in future years to give up some time to assist in this process too.
The resources will be available very soon. If you would like your school to have access, make sure that your HOD has filled in the membership Google form under the Membership tab.