A short, snappy starter which refreshes pupil’s mental arithmetic skills and provides a healthy mix of challenge and competition. This starter is suitable for all maths classes in secondary school and those in KS2. The task is this: Using digits from 1-9, make an addition with two 3 digit numbers to make another 3 digit number. Each digit from 1-9 can only be used once (carrying is allowed). . This could be done as a competition to encourage group work where pupils (in teams) are set a certain amount of time and must come up with as many different additions as they can. This starter is also useful for generating discussions as the pupils may notice certain patterns in the answers (i.e. the digits of the final answer always add up to 18) and the commutative law of addition (3 + 5 = 5 + 3).

A set of sample learning objectives for teaching a Year 10 GCSE Maths class about Surface Area of 2-D Shapes (drawing and interpreting). Differentiated objectives/outcomes are shown for the topic, literacy links, real world applications of the topic are displayed so that pupils can see the relevance of what they are learning as well as homework, merits and lesson questions pupils should be able to answer. This is an easily adaptable resource which can be changed and formatted to display any topic in the KS3 and GCSE Maths curriculum.

A set of sample learning objectives for teaching a Year 8 KS3 Maths class about Polygons (Classifying and Properties of). Differentiated objectives/outcomes are shown for the topic, literacy links, real world applications of the topic are displayed so that pupils can see the relevance of what they are learning as well as homework, merits and lesson questions pupils should be able to answer. This is an easily adaptable resource which can be changed and formatted to display any topic in the KS3 and GCSE Maths curriculum.

A teaching sheet on ratio which defines what ratio is and provides worked examples of cancelling down ratios, representing them in the form 1:n and n:1 and answering questions which require the student to share a quantity (money, number of sweets etc.) between people in a given ratio. This teaching sheet is very accessible and presented in a simple, consistent easy-to-understand manner. Methods to answer each question are structured very clearly and are explained. It could be used to introduce a topic of ratios or provide worked examples to assist students in tackling questions on the topic. It will be of general use to students in Years 8-10 but may also assist Year 11 students who are aiming for a grade 5 in Mathematics.

A handy glossary of terms (separated by each of the 4 strands of Mathematics: Number, Shape, Handling Data and Algebra) which will be very useful for pupils for revision purposes and act as a reminder for when they forget the meaning of key terminology. Suitable for both KS3 students or those studying foundation at KS4. Links excellently with Literacy and promotes the use of this within Mathematics.

A handy resource with 3 separate diagrams of circles showing each part clearly labelled as well as diagrams of basic 2-D shapes and their area formulae. Although mainly suitable for students at KS3 Maths, this resource would also specifically those pupils in KS4 studying Foundation. It is especially useful for those pupils who struggle to retain information and acts as a handy prompt to remember key formulae.

A simple resource demonstrating how to calculate the area and circumference of a circle with worked examples clearly illustrating the methods behind answering the question. At the beginning of the resource, children are reminded of the precise definitions of Circumference, Diameter and Radius. Students can use this resource to help them with working out the area and circumference of a circle and and also for revision too. Primarily this resource should be aimed at those pupils in KS3 Maths, though older pupils may benefit from this as a refresher of some basic skills.

This is a great revision source for KS3 and KS4 pupils on triangular numbers. The resource includes a definition and explanation, patterns which can be found in the sequence, how to find the nth term of the sequence and worked examples of exam questions involving triangular numbers. Depending on the ability of the class, you may wish to differentiate; the opening part of the resource is suitable for less able learners whilst the later part of the resource should stretch more able students. Other topics linked with this resource include finding the nth term of quadratic sequences, generating sequences and properties of numbers.

This is an interesting investigation which mainly covers the topics of rearranging formulae, expanding brackets and simplifying expressions. However, there are some links to ICT as the words input and output are introduced to students. The pupils are asked to think of a domino and using all the possible digits on the domino as input (if the numbers on the domino were 1 and 6: A=1 and B=6) into a given algorithm find an output. The pupils are then asked to find a formula which connects the input and output. This investigation is very logical and gets students to see patterns, but there is also a very logical, satisfying solution to the problem which is sequential and hopefully gets students to appreciate the rigor of mathematics.

An investigation (including teacher notes and worksheets) into the origins of square numbers which guides students to generate the square numbers sequence and observe the patterns within it. This investigation would be suitable for a wide variety of age groups including KS2, KS3 and GCSE. In terms of differentiation, earlier stages of the investigation (looking at the patterns in the square numbers) may be more suitable for lower ability learners whereas the latter stages of the investigation (finding the nth term of a quadratic sequence) should stretch higher ability students. Topics covered in this resource are mental arithmetic, properties of numbers, nth term (quadratic) and sequences.

A useful revision aid on all the 2-D shapes whom students will encounter in the KS3/GCSE Mathematics curriculum, with notes on their properties and different types of shapes. Also includes a section on polygons for higher ability learners.

Teacher notes on an investigation on areas of triangles, also covering topics such as simplifying surds, Pythagoras’ Theorem, congruency and algebraic formulae. The problem the students must solve is ‘When the perimeter of a triangle is 20 cm and it is an isosceles triangle, how many possible triangles can there be?’. Students find this out through working out the area of each possible triangle and seeing a pattern. An extension is also included in this resource which gets pupils to work out the total possible number of any triangle (not just isosceles) with a perimeter of 20 cm. Students then work to find a link between the base length of the triangle and the number of possible triangles which can be drawn with that base length. A worksheet is included for each activity as well as notes and guidance on how to conduct the investigation with pupils.

A useful resource for student Maths Teachers to self-assess and audit their subject knowledge of all topics in the curriculum. Topics are categorised by area and learner specification, with trainees able to easily use this resource to determine their own subject and pedagogical knowledge, whilst tracking the actions they’ve taken to improve their knowledge and when they’ve taught certain topics to pupils. This is also a really useful document for students to use as evidence to prove they are meeting the standards required to achieve Qualified Teacher Status (QTS)…

This is an investigation (including teacher notes and worksheets) which is suitable for GCSE maths students, though higher ability KS3 students should be able to complete it. The problem students have to answer is ‘Can you find a formula to find out the total possible number of half-time scores if you know the full-time score of a football match?’ Probability is the main topic covered (listing outcomes, formula for total number of outcomes) as well as algebra topics such as expanding brackets, sequences, factorising and generalising formulae. Pupils can probably work on this independently with some teacher input in setting up the investigation and prompting pupils.

This is a short maths test aimed at pupils in KS3. It could be used as a baseline assessment to determine their level at the start of a year as it covers the majority of the basic skills- working out the area and perimeter of a shape, ordering decimals, simplifying fractions and so forth needed to succeed at Mathematics.

This investigation is an effective way of introducing triangular numbers for those in KS3 and gets students to explore the sequence of triangular numbers through shapes and their properties. Pupils could build the triangular numbers using mutli-link cubes or something similar and gives students a visual representation of them. Others topics touched by this resource are formulae, properties of number and volume of 3-D shapes.

This resource gets students to investigate how to find a formula for the triangular numbers through the investigating the number of football teams play each other in a round robin. This resource is suitable for GCSE students and more able KS3 students. Students are then guided through an investigation to see a step-by-step derivation for the algebraic nth term for the sequence of triangular numbers. This would be an excellent way of introducing how to find the nth term of quadratic sequences as pupils will be familiar with the triangular numbers sequence.

This resource handily introduces compound interest to more able KS3 groups and GCSE in the form of adding interest to a bank account. Other topics covered include percentages and decimal multipliers. This resource is an investigation (with teacher notes and accompanying worksheets) which gets students to investigate whether how often interest is added to a bank account effects the total amount of interest. The problem is so: I invest £1,000 in a savings account at an interest rate of 3.1% p.a. for one year. What interval at which the interest is paid will get me the most money? The students can then be guided to calculating the total amount of interest when it is added, daily montly etc. before being guided to an overall formula to solve the problem.

A comprehensive Powerpoint for a whole lesson on constructing and solving linear equations for KS3 and GCSE foundation groups. Depending on the ability of the class, there is enough material on the Powerpoint for a couple of lessons if pupils need to be taken through the content more gradually. In the Powerpoint, pupils are introduced to the meaning of key words such as co-efficient, linear and equation, shown how to solve equations using the balance method and also how to construct and solve a linear equation when given information. There are plenty of worked examples and questions for pupils to attempt.

A worksheet which includes 10 questions each on percentage increase and decrease. This resource is mainly suitable for KS3 students, although it may also benefit GCSE Foundation students. As well as increasing or decreasing a number by a certain percentage, worded questions involving VAT are also included. This resource has multiple applications: it could be useful as a check of the prior knowledge of students or to check their understanding of what has been taught as a summative test or included as the main activity within a lesson.