Six maths "spiders" designed to test whether students can substitute in to formulae correctly. The spiders get increasingly difficult and are designed so that they have to think and possibly discuss their answers rather get on a "substitution treadmill". I know people use these for starters/plenaries and I have used them as tasks in lessons.

Clive is tackling a bit of substitution but making mistakes again. Your students' task is to help Clive sort out his errors and explain to him what he's done so that he doesn't make the same mistakes in the future. Ideal for starter or plenaries and encourages discussion.

Clive is having a go at simplifying expressions, without complete success. Your task (or more accurately, your class' task) is to help Clive correct his homework and explain where he's gone wrong. Good for starters or plenaries and encourages discussion.

There are four "explosions" for students to deal with, each covering different types of algebraic fraction. The first slide involves simple indices and simplifying, the second involves adding and subtracting (find a common denominator), the third has algebraic expressions as denominators and the fourth involves factorising quadratics. These are designed to stop students getting in a rut of doing the same thing over and over again, plus they should (hopefully!) generate good mathematical discussions.

Erica is struggling with iteration and Newton-Raphson, as it's on the new "Pure 2" syllabus. Can you help her sort out her homework answers and explain what she's done wrong?

Clive is doing some homework involving error in measurement and is getting a bit confused. He has made some mistakes that you need to correct and explain to him where he's gone wrong; the homework contains just stating bounds as well as calculations that require thinking more carefully about. This really makes students check their explanations and generates good academic discussion in my experience as well as allowing students to demonstrate the depth of their knowledge.

A set of six spiders which encourage students to show every stage of their calculations as they tackle increasingly difficult questions. There are also some question where the answer is given and the workings shown so that students can work backwards; this is designed to avoid students getting stuck in a rut and not thinking about what they are doing in each case.

This idea is from Craig Barton and is an excellent one (check them out his at website); essentially it is four questions based on the same information. There are four here which use ratio, Pythagoras, time, fractions, probability, percentages and measures as well as other topics. This really should create discussion and a deeper understanding of the topics covered on top of ensuring that students actually read the question. I hope these are worthy! I will be using these as starters or plenaries.

This idea is from Craig Barton and is an excellent one (check them out his at website); essentially it is four questions based on the same information. There are four here which use volume, ratio, Pythagoras, bearings, measures, area and perimeter, speed, percentages and bounds as well as other topics. This really should create discussion and a deeper understanding of the topics covered on top of ensuring that students actually read the question. I hope these are worthy! I will be using these as starters or plenaries.

This is designed to get students thinking rather than just blindly following a mathematical recipe. There a four sets of 4 problems which all have the same answer (given in the centre of the screen). Each question has a blank for the students to fill in and sometimes there is more than one answer for the blank. This particular one covers probability,fractions, ratio, angles in polygons, solving equations, sequences, area and other topics. I will be using these as starters to get students thinking. One error corrected in the answers! (I need to read the question.)

This takes students through the skills required to answer vectors questions and some vectors questions from adding vectors to describing routes to proof.

This takes students through the skills required to solve differentiation problems at GCSE and IGCSE level.

This takes you through basic indices then on to fractional and negative indices covering all the skills required allowing students to understand how they all link up to reach the most challenging question types.

This goes through straightforward conversions to compound measure (speed and density).

Working up from simple fraction of a number to adding/subtracting/multiplying/dividing mixed numbers with everything in between, including a “Show that” question which always seems to confuse some.

This takes students through the basics of rounding (hundreds, units, dp, sf etc)through to estimation and bounds, including bounds calculations.

Working its way up from symmetry to negative and fractional scale factor enlargements; the diagrams are as big as I can make them in the format so sorry if they are a bit small.

Another one of these, although I have not included probability scales or tree diagrams specifically (there are a couple of questions where a tree diagram could be designed to help with a solution); this is due to lack of space in the main.

Complete the pyramids to figure out the punchline to a lame joke. This involves simplifying indices and could be used as a plenary or starter, although that is clearly up to you.

This is designed to encourage students to explain their working rather than just read out an answer at the end. I have given an example of solutions but these are not the only solutions for each. This should encourage discussion too.