A card sort activity for pupils to sort into groups based on the most suitable mental strategy for answering the question. Of course pupils can then answer questions (answers are provided on the second sheet). Just for clarity in the terminology, the strategies given are as follows: Compensating - adding or subtracting a value near the one suggested and then compensating for the change, i.e. calculating 34 - 19 by doing 34 - 20 + 1 Near doubles or halves - adding two numbers that are near each other by doubling a number and the adjusting as necessary, or subtracting one number that is nearly half the other in a similar way i.e. 34 + 35 = 35 x 2 - 1 (or 34 x 2 + 1); 45 - 23 = 46/2 - 1 = 22. Reordering - Reversing numbers in a sum to make use of bonds i.e. 28 + 36 + 22 = 28 + 22 + 36 = 50 + 36 Multiply then move - Separating a multiplication where one of the values is a multiple of 10, 100 etc so that a multiplication is done, followed by the moving of a number in columns i.e. 23 x 30 = 23 x 3 x 10 = 69 x 10 Move then divide - Similar to above, when dividing by a multiple of 10, 100 etc, move the number first and then divide by what is left i.e. 44 x 5 = 44 x 10/2 = 440/2 = 220. Steps of division - Completing a division in multiple steps i.e. 120 ÷ 8 = 120 ÷ 2 (=60) ÷ 2 (= 30) ÷ 2 = 15 or 30 ÷ 20 = 30 ÷ 10 (=3) ÷ 2 = 1.5. 'Over divide' then multiply - when dividing by a factor of 10, 100 etc, divide by 10, 100, etc then multiply by the complementary factor; i.e. 420 ÷ 25 = 420 ÷ 100 x 4 = 4.2 x 4 = 16.8

Linked to the defining vectors activity, using the vectors defined in the image to prove standard results like ratios of line segments, whether points lie on straight lines, etc. For extra challenge take out the image with the pre-defined vectors and add the image from my vector definition activity so that pupils have to define the vectors before using them. Answers can be found on the prezi at link https://prezi.com/lenmenrpi1li/vector-proof/

Can you complete the 9 squares using each of the numbers from 1 to 9 only once, so that the factors of the pairs of numbers are correct? Comes with one solution - is it the only one?!?

A RAG (Red, Amber, Green) worksheet around identifying invariant points on different transformations, incorporating a CLOZE activity (fill in the blanks), a matching activity, and a Venn Diagram activity

Adapted from an image in Back to Back activities, 2 vectors are defined as a and b and the activity asks how many further vectors can be defined in terms of a and b. The image gives all of the other lines defined as vectors in terms of a and b.

An exam style question linking volume, surface area and expanding and simplifying products of 2 or 3 binomials. Ideal for new GCSE topic.

Use of Venn Diagrams to find LCM, with three grades of challenge (RAG) moving from given multiples, to identifying multiples of 2 numbers, to identifying multiples of 3 numbers - inspired by Craig Barton's love of Venn Diagrams.

Given a vector picture, can you identify the vectors that either match, or are multiples of, the given vector a? A nice alternative vector introduction, or way of introducing the ideas of scalar multiple (including negative of a vector)

A three way matching card resource in the Standards Unit style - the first cards have images of two vectors labelled either a and b or a and -b, the second set of cards give the column vectors of a and b to match to the pictures (note b is given even when the picture shows -b for added difficulty) and then the third set has the result of the vector addition/subtraction to match to the previous two. There are 6 additions and 6 subtractions altogether. Use an alternative resource to introduce or revise column vectors or adding and subtracting with vectors at GCSE or A-Level.

An exam style question combining using ratio to find lengths with calculating the area of a compound shape.

A UKMT inspired 'shuttle' style challenge; pupils complete one question at a time and bring it to the front to try and 'unlock' the next question. If they get it right first time they get three points, if not they get 1 point provided they subsequently get it right. They don't get the next question until they get the previous one right. Works best in groups of 3 or 4, be prepared to have kids running!

A series of 3 worksheets using the BBC news coverage of the European migrant/refugee crisis in the mediterranean and graphs/statistics from their website.

A couple of Venn Diagram exam style questions which both bring in areas of maths that are not probability.

Looking at different real life situations that give rise to listing outcomes, how does the situation effect the probability? Can go as far as multiplicative counting introduction.

Nice early composite function problem, is Harry doing it right?

Given 5 recurrence relations, which of them produce straight line graphs? Which don't?

Given 3 lengths and 3 perpendiculars, which length is incorrect? If working with non-right-angled trigonometry can also bring in cosine rule and area to check by calculating areas from given lengths. Possibly also some Pythagoras links with the perpendiculars? Is there more than one possible answer?

Solving a problem with surface area in the new GCSE style, with assumptions made and justified.

Solving a proportionality problem and then having to discuss the assumptions made in solving the problem.

Using expanding brackets with rectangles in a cloze style activity broken down to support entry level problem solving.