 Hello, my name is Mike Olliton and I'm here to discuss the importance of helping students develop confidence with their mathematics and their competence at being mathematical. A key planning issue is to offer students something that is easily accessible, which they can all make a start on. A strategie I frequently use is to ask either an open question or present an image for them to look at and discuss in pairs for the first two or three minutes. After two or three minutes I shall ask several pairs of students to tell me one thing that they've been discussing. I won't ask for hands up because I'm more interested in just getting a general response from a group of students. So it's just one thing that I want them to tell me about they've been discussing. In response to what they tell me I'm going to try to praise here on the board what they've said. After gathering some information from the students I will then make it kind of an open house where I will say well would any other pair like to say something that hasn't already been talked about or they can build upon something that has been already mentioned. And in this way I'm interested in giving the students some ownership and some direction of where the lesson might be heading. I call this strategy one of drawing upon and drawing out and drawing upon. So having drawn out some information from them I'm going to go a little bit further with my questioning to use what they've told me to go further with their thinking. So I'm drawing upon what they tell me. And again this is about ownership it's about them having a sense that this lesson isn't all done and dusted it's about it's kind of dependent upon what we've already told the teacher. For example a lesson aimed at summing linear sequences with a key stage 2 class. I know that's a key stage 5 topic however I'd been asked to do something on sequences and I thought that's what we'll do. So I started off by asking them to tell me everything they already knew about the word sequences. If you're interested in pursuing this particular line you might read pages 36 and 37 of Mathematics Teaching MT 271. So that's enough talking about pedagogic issues just for now. But in preparation for the next short video I would like you to choose three whole numbers between 0 and 10. I'd then like you to turn them into coordinate pairs where the x-ordinate as far as you're concerned is smaller than the y-ordinate for each pair of the pairs. Having done that I invite you to think about where it might go next, where you might take the lesson next having got the students to create some data and we'll see where that takes us. Hello again. I would love to find out what kind of ideas you came up with with regards to what you might ask the students to do next having gained these three pairs of coordinates. Well obviously we can ask them to plot the coordinates on a square grid. Now plotting coordinates is something that children meet at the beginning of key stage two in year four. It might even be in year three but it won't be a new idea. So plotting coordinates and of course they're all going to recognise that assuming they've plotted them correctly they've ended up with right angle triangles. Depending on the numbers they've chosen some might end up with isosiles right angle triangles and some with scalene right angle triangles and again there's some important vocabulary to be brought out in that simple situation. So mathematics as well as needing to be accessible it needs also to be extendable and so because they're right angle triangles and because they'll have worked on areas of shapes in key stage two then I think a nice extension task for them will be to work out the areas of their triangles. And now there's other things we can do such as instead of plotting the coordinate pairs as x being smaller than y what happens when y is smaller than x when x is greater than y. Well yeah if you plot them you'll find there's a very interesting geometric property to arise and of course why miss out on that opportunity when it's there to be had. Certainly in the lesson where I taught this was a key stage two group the children were noticing different things and this ultimately led me to asking them to work out what would the area be for any three numbers which I'm going to call A, B and C. I thought I'd take a chance but certainly that kind of problem will be will be suitable in year eight year nine maybe sorry I should have said year nine year eight maybe. But what happens if we then have six coordinate pairs and we form a hexagon what will the area of the hexagon be and how does that relate to the three numbers that we started off with. Of course students are going to need some knowledge of Pythagoras' theorem in order to be able to work out the perimeters of the triangles and of the hexagon but it's all there to be had depending upon who we're working with and what knowledge one would expect students to have in order to be able to work on more complex problems. And if you want something for your your A level students and then try turning the three numbers into three dimensional coordinates or coordinates in a three dimensional plane. Do you call coordinates triordinates I'm not sure. Anyway it doesn't matter but what does matter is that there's a cracking problem there for our GCSE A level students which is so plot the six points on a 3D grid. What shape do you get. What will its volume be. What will its surface area be. All kinds of potential developments starting from think of three numbers. Again the triangle problem is written upon in the same article that I referenced in the first video in the first video in MT 271. Okay thank you bye for now.