In my first lesson with each class I have been talking to my students about being gritty and green! The green refers to our engagement with learning assessments where we traffic light students green / amber / red for their engagement with their learning. They certainly all listened and understood the message and clearly want to do well.
I have used the name cards I described here; I printed the address of my homework blog on one side for them to see and note and they wrote their name on the other. I find these really helpful, seeing the name beside the student means you can use their name when you talk to them and I already know many names. I collect them in at the end of the class, providing another opportunity to use their name thanking them for returning the card. (The ‘cards’ are actually folded A4 paper.)
I read Tom Sherrington’s post “Empowing students to own their learning solves maths problems“; a great idea to start with a diagram with no labels at all as a way into a problem. I tried this with Year 10 (very able students) in their first lesson, presenting them with only Tom’s diagram and was very pleased indeed with the outcome. I didn’t even give them the question – just the diagram (a small copy each) and we started by deciding what the question might be. We quickly got onto areas as a possibility so then answered Tom’s original question ‘what fraction of the shape is shaded?’. The class happily discussed how to solve the problem and a student asked ‘can we write on the diagram?’ which of course was perfect – absolutely they could write on it. We solved the problem, revising some basics and had the discussion about what to do when you don’t know what to do! I will certainly use diagrams with no labels again.
I tried an Android app I rather like, Numberswhich is similar to Countdown. Use the given numbers to achieve the target. There are over 200 levels. I’m not sure the levels have a lot to do with increasing difficulty – look at level 61 here for example – this is much easier than some of the earlier problems. When I first started playing I didn’t realise you could click on intermediate results as you see in the illustration here and actually managed several levels without doing do! Dave Gale has written a post on the app here. I think I’ll try some of the problems this week with my Year 7 class when we discuss order of operations because we could write out the solution on several lines as in the app but then discuss how we could write the solution with brackets. I really want this on my interactive whiteboard (as well as my tablet and my phone!)
From Desmos we have the outstanding graphing calculator, their Facebook page(youdo not need to be a Facebook user to view this) is also worth keeping an eye on. Some of the photos availablemake ideal starters. See the Think Fast series or perhaps Mental Maths Monday; there are also several probability problems. I think I’ll try some of the Mental Maths Monday series with my sixth form students – look at this for example!
The problem shown in the image could be used with younger students but also with older students who could look at an algebraic proof.
This video from Numberphilemade me think about possible starters / fuller investigations on gaps between primes; something which could be investigated by students of various ages. I like the idea of using it for proof with older students, for example considering which gaps are not possible between primes and why.
and finally… In the news – look how useful mathematics can be! The University Sheffield Mathematics Department have been considering the very serious problem of how to build a perfect scone!You can read the paper here, skip straight to section 4 for the recommendations!