This activity is inspired by something I saw on the Mathspad website, but I wanted a simpler version to use in a first lesson with Year 7 on expanding double brackets. There are therefore no negatives in this activity, and the leading coefficient in the quadratics you obtain is always 1. The students are given a table of algebraic expressions and 15 quadratics they are trying to create. They pick 2 expressions from the table, multiply them together and see if they’ve created one of the quadratics. If not, they try again! Each expression can only be used once, although most expressions appear multiple times in the table. I’ve used this with a mixed ability Year 7 group, and it worked well. Weaker students can pick expressions at random and see what they get, whereas stronger students may start with the quadratic and ask themselves how they can create it - essentially factorising quadratics! Solutions are provided.

I wanted something a little more challenging on the topic of Trapezia that still gave my students plenty of practice calculating areas, so I designed these questions. In each question, students are given a pair of trapezia and are told how their areas are linked (one is a multiple of the other). Students have to determine the area of one trapezium, use that to determine the area of the other one, and then finally use that to determine a missing value. Sheets I and II are very similar, but sheet III is a bit more challenging. Solutions are provided.

A set of questions I put together for my Year 11 Foundation group. I designed them to be similar to Question 9 on AQA Practice Practice Set 4 Paper 3 for the new 9-1 GCSE. Solutions are provided.

A task I designed to make my lesson on the area of a parallelogram a little more interesting! Students are given a variety of parallelograms where the side lengths are algebraic expressions. Students are given 9 possible values for x and have to substitute these values into the parallelograms, and then calculate their areas. Their aim is to create parallelograms with given areas. Solutions are provided.

6 questions I designed to stretch the most able in my Year 11 foundation group. I have provided an editable Powerpoint version of the worksheet, and a pdf which has 2 copies per A4 sheet. Answers are also provided.

I really liked Don Steward’s task on equable parallelograms (https://donsteward.blogspot.co.uk/2017/11/equable-parallelograms.html) but wanted some questions that were a little bit easier for my Year 10 group, so I designed these. In each of paralleograms on the sheet, the area is equal to the perimeter. Students should use this fact to set up an equation, which they can solve to find the value of the unknown. Solutions are provided.

Students must use their knowledge of similar shapes and linear equations in order to determine the value of an unknown. Solutions are provided.

4 questions that I created to challenge my more able Year 8 students when we covered solving equations with brackets. Requires knowledge of: how to find the area of a rectangle and triangle, how to divide a quantity in a ratio, and how to calculate the mean and range of a set of numbers. Answers are provided (and they’re fractions to make things a bit trickier!).

A simple worksheet - nothing fancy. Students are given 30 linear equations in a grid (all of the form ax + b = c), some of which have integer answers, and some of which have fractional answers. They have to solve the equations and colour in the boxes according to what type of solution the equation has. Like I said, this worksheet is nothing fancy so it doesn’t make a picture when they’ve finished colouring! I’ve provided answers as well.

Students must use their knowledge of triangles and quadrilaterals to form and solve simultaneous equations. Answers are provided.

These are sets of starter questions that I have used with my Year 11 (Foundation) and Year 10 (borderline Higher/Foundation) classes this year. Each set of starters contains between 5 and 10 lessons worth of starters that test the same topics each lesson. Solutions are provided to all questions. The cover image shows the format of all starters. Topics tested are: Year 11 Set 1: Expanding brackets, collecting like terms, solving equations, prime factorisation, nth term of arithmetic sequences, percentages of amounts, substitution & sharing in a ratio. Year 11 Set 2: Averages, rounding, division, FDP, multiplying and dividing fractions, sharing in a ratio, factorising quadratics, expanding double brackets, mixed numbers and improper fractions, fractions of amounts, simplifying fractions. Year 11 Set 3: Multiplying fractions by integers, column addition, exterior angles of polygons, ordering negatives, fractions of amounts, solving equations, ratio and probability. Year 11 Set 4: Simplifying expressions, expressing one quantity as a fraction of another, standard form, multiplying mixed numbers, recognising arithmetic and geometric sequences, recognising parallel lines, percentage increase. Year 11 Set 5: Finding and using the nth term of an arithmetic sequence, converting mixed numbers to improper fractions, expanding double brackets, solving quadratics, multiplying and dividing decimals, probability. Year 11 Set 6: Solving equations (xs on both sides), number facts, calculating with negatives, ratio problems, simultaneous equations. Year 10 Set 1: Substitution, expanding double brackets, solving equations, significant figures, simplifying expressions, estimating square roots, index laws. Year 10 Set 2: Angles in parallel lines, angles in polygons, averages, index laws, recurring decimals, solving equations. Year 10 Set 3: Volume of cuboids, geometric notation, simplifying expressions, calculating with negatives, percentage increase and decrease, algebraic fractions, ordering fractions, solving equations. Year 10 Set 4: Re-arranging formulae, standard form, sharing in a ratio, factorising quadratics, expanding single brackets, substitution, estimation, multiplying and dividing decimals, index laws, expanding double brackets.

I wanted something a bit more challenging for my more able Year 7s on the topic of ‘converting between Mixed Numbers and Improper Fractions’, so I put together this activity. Students are given a sequence of Mixed Numbers and Improper Fractions, and must tell me what (simplified) fraction must be added or subtracted at each step to reach the next number in the sequence. Solutions are provided.

Students have to determine the roots, y-intercept and turning point of each of the given quadratic graphs using an algebraic method. The graphs are not drawn accurately, although I’ve tried my best to get them in roughly the correct position. Solutions are provided.

A Bronze/Silver/Gold differentiated resource where pupils are given a list of decimals and a square grid. Pupils have to put the decimals into the grid so that each row and column is in ascending order. In Bronze, the integer part of each decimal is the same. In Silver, the integer parts are different. In Gold, negatives are introduced. The grids get progressively larger as you move from Bronze to Gold as well. Each puzzle has multiple solutions, but I’ve provided one possible solution to each. Update 16/9/22: Changed the design of the tasks, but the content is the same.

This was designed for my Year 11 Foundation class. It is a second lesson after students have already had an introduction to solving quadratic equations by factorising, All quadratics in this lesson can be solved by factorising - they just must be re-arranged to give a quadratic equal to 0. There are 3 examples to go through - one which is a recap of previous work, and 2 quadratics that need to be re-arranged. There are 20 fluency questions for students to work through. The bronze questions at the top only have positive terms in the quadratic, while the gold questions underneath introduce some negatives. There are 2 problem solving questions at the end as an extension, or to finish off the lesson. These are both based on past exam questions.

28/09/22: New and improved Powerpoint uploaded! The lesson starts with a quick recap of square and cube roots which all have integer values. Students are then asked what the square root of 32 is. It’s not an integer, but we can find an approximate value by determining which 2 integers its value lies. Some examples of how to do this are given (which are fully animated), then there are some basic fluency questions which can be done on mini-whiteboards so you can assess student understanding. There is a slide of questions for students to work on independently in their books. To make things a little more interesting/challenging, there is also some work on solving basic quadratics provided. Rather than leaving the answers as a surd, I get pupils to give me approximate answers, so that they get some more practice estimating square roots! Answers to all questions are given, and no printing is required.

A set of questions I designed for my foundation group on determining coefficients in order to produce identities. Answers are provided.

A quick (less than 30 mins) investigation that I did with my Year 7s on Semiprimes.

A presentation I designed to help me deliver the “Number Families” task from nrich (https://nrich.maths.org/13123). Rather than jumping straight in to set notation, it starts off getting pupils to list what they know about certain numbers. Then they imagine that numbers that share a certain property can be placed in the same “bucket”. This idea of a “bucket” is then used to introduce set notation.

An activity that I designed to make ordering fractions a bit more challenging for the more able in my group. Pupils are given 4 algebraic fractions, and must order them by size for particular values of the unknown. Solutions are provided.