Hello, and welcome to the third teachmathematics newsletter. We aim to share with you 10 brilliant ideas for the secondary mathematics classroom. We hope you enjoy it and find it useful.
10 Great Ideas
1. Virtual Manipulatives of the Month
There are some fantasic virtual manipulatives to help us visualise factors and primes. Here are a few we've come across recently
Number trees - http://www.ventrella.com/numbertree
Primitives - http://www.ptolemy.co.uk/primitives/primitives-application
Prime Number Simulator - http://www.numbersimulation.com
So how to exploit these in the classroom? One lovely activity is to get students to try to produce some factor diagrams of their own. We've got some beautiful primitive-type diagrams adorning the walls of the classroom. A useful visual reminder of the proerties of numbers.
Craig Barton Recommends Teachmathematics
It's always nice to know that other mathematics teachers appreciate and make use of the site so it was a proud moment for us to get a glowing testimony from Craig Barton AKA MrBartonmaths and the main man behind mathematics resources in the TES. Here's Craig's short video
In his video Craig recommends 3 different activities:
Age: 15+ Time 1 hr. This set of games asks students to find the correct equation of the parabola in order to hit the pig! Three set of coordinates are given and students are required to calculate the equation of the parabola. They will be required to understand the equation of a quadratic, in particular the form y=a(x - p)(x - q) would be helpful. Great fun!
Age: 12+ Time 1h The aim of this resource is to develop student’s association of nets, hence surface area, with 3D solids, hence volume. The activity starts with a matching activity, nets and solids, some of which work, some don’t, students can cut and fold to check. Two virtual manipulative websites are then used, one aimed at inspiring them with a wide, and unusual range of 3D shapes.
Age: 11+ Time: 1h Roll, roll, roll… This carefully structured activity aims to get students to discover that experimental probability approaches theoretical probability as we increase the number of trials. We often overlook the importance of carrying out games of chance to build up an intuition for probability. In this case we roll a dice then use a lifelike simulator on Excel to produce up to 2000 rolls.
Here are four of the newest activities from the teachmathatics site:
Watch this video to get a quick overview of the activitiy
Age: 14+ Time: 1h+ This activity will challenge high achieving students to learn about the properties of transformations of functions using exponential graphs. Interactive applets and quizzes get the students to discover the properties for themselves then there are a couple of games to challenge them to 'copy the function'. Watch the short video below for a quick overview.
Age: 14+ Time:1-2 hrs. Use this fun, fictional set of results on a number of levels! Processing data, calculating averages, quartiles, ranges and more. Most importantly this resource is great for comparing distributions. The data is full of surprises and two sets might have some things in common and other things really quite different!
Age: 14+ Time:1-2 hrs. This activity is based around a set of transitive dice (invented by James Grime) which have a rather surprising set of properties. They are NOT the classic 6-faced dice with numbers one through six on each face - they are far more interesting! Played against each other, rather like paper, rock scissors, there is no dominant dice (red dice beats blue dice, blue beats green yet green beats red). Students find them fascinating to play with (you will not reveal this fact beforehand) and this provides the motivation to analyse the probabilities behind them. You will easily be able to transform a set of normal dice into transitive dice or you may wish to make use of a digital simulation provided. Students are free to solve the problems with whatever probability techniques they have built up, although knowledge of possibility spaces and/or tree diagrams would certainly be helpful. Full solutions for the teacher as well as instructions how best to exploit the dice are provided.
Here's a quick video overview of the activity
Age 13+ Time: 1-2hrs This is a very practical activity to help students develop a sense of volume/capacity and how to calculate it for prisms. Through pouring sand or water into and between a range of millimetre precise relational prisms, students discover that the volumes of prisms are proportional to the areas of their cross-sections! Plenty of hands-on challenge for all abilities.
Here are a couple of activities that we look forward to teaching when the mensuration topic comes around (as it just has!). They are practical activities that help derive formulae for the volume of a pyramid and the surface area of a cone. Discovery based learning at its best!
Age: 13+ Time 2 hrs This is a lovely practical activity to help students visualise and derive the formula for the volume of a pyramid. By constructing square based pyramids (10cm by 10cm) with height 5cm then fitting six of them together to make a cube of edge 10cm they realise the volume of the pyramid is 1000/6cm². The activity is supported with videos and practice questions.
Age: 15+ Time: 1 hr Explore cones by making one! This activity helps students understand where the formula for the surface area of a cone comes from and play with the associated mathematics. A great practical task that seems easy and works out to be more of a challenge. In making the cone students will confront some great mathematical reasoning and maybe even some algebraic proof!
That’s it for now. Have a great term!
Oliver Bowles, Jim Noble & Richard Wade
If any of you have resources, comments or suggestions that you would like to share with other subscribers, please send them to me and I will try to include them in the next newsletter.