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This was inspired by an excellent resource on TES by MrMawson (/teaching-resource/prime-factor-decomposition-logical-puzzle-11367345). I’ve used it with higher-attaining students, but wanted to adapt it to make it a bit more accessible to lower-attaining students. In each question, students are given 2 numbers. They should draw prime factor trees for each number and look for common prime factors. The common prime factors go in the middle boxes, and the remaining prime factors go in the boxes around the outside. Solutions are provided.

A task I used with more able Year 8 students. Students are given decreasing arithmetic sequences - but most of the terms are missing. They must first determine the missing terms, and then work out the nth term. Solutions are provided.

Students are given the beginning of a sequence and must determine the next 3 terms. They also need to classify the sequence as arithmetic, geometric or quadratic. Solutions are provided.

This is similar to a resource already on TES that I really like (/teaching-resource/gcse-maths-sequences-search-worksheet-6158880) but I wanted an activity that required more substitution into nth terms rather than pattern-spotting, so this is what I came up with. Students have to find the 1st, 2nd, 5th, 10th, 50th and 100th terms of sequences using the given nth terms. They cross off all of their answers in the grid above. For ease of marking, there will be 10 numbers left over in the grid after the activity is completed. Students should add these together, and if they’ve made no mistakes, they’ll get a total of 1000. Full solutions are still provided however!

A basic fluency worksheet that makes the topic of adding fractions a bit more challenging. Rather than adding 2 given fractions, students have to determine what the missing numerator should be to give the calculation a certain answer. Solutions are provided.

A basic worksheet to help my Year 9s understand that just because 12 parts of a shape are shaded, that doesn’t necessarily mean 12% of the shape is shaded! I got my class to first of all determine the fraction shaded, and then change the denominator to 100 to determine the percentage shaded. It comes in 2 parts - in the first part, the denominators of the fractions multiply easily up to 100. In the second part, they don’t, e.g. 24/40, so they need to be simplified first. Solutions are provided.

A puzzle to make the topic of dividing in ratio a little bit more interesting, inspired by a similar Don Steward task: https://donsteward.blogspot.com/2014/11/mobile-moments.html The numbers along the top of the bars tell student what ratio to divide the top number in. For example, on question 4, you should split 42 into the ratio 3:4 and put the answers in the bubbles. They should then split their answer of 24 in the ratio 1:2. Solutions are provided.

This was inspired by a task from Don Steward: https://donsteward.blogspot.com/2014/12/algebraic-product-puzzles.html I wanted some similar puzzles on Quadratics that were more accessible to weaker students, without any negative terms, so that’s what I created! Students have to fill in each blank cell with a bracket so that every row and column multiplies to make the quadratic expression at the end. Of course this could be done by random trial and error, but it makes much more sense to factorise the Quadratics! An example is given on the sheet to help students understand how the puzzles work. Answers are provided.

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.