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 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.

Suitable for higher-attaining GCSE students who are revising Index Laws. Logarithms are not needed to solve these equations - they can all be solved by making the base the same on both sides, and then setting the powers equal to each other. Solutions are provided.

Having seen exam questions in the new GCSE that combine angles and algebra, I designed the following worksheet to challenge my top set Year 10 group. Students have to determine the value of x in each question. Later questions go beyond what I think we’re likely to see at GCSE. Answers 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.

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.

Pupils are given 36 integers (a mixture of positives and negatives) and have to put the numbers into a 6 x 6 grid so that every row and column is in ascending order. This gives them plenty of practice of ordering negative numbers by size. Solving the puzzle requires experimentation, so when I have used this in my lessons, I’ve put the sheets in plastic wallets and let pupils write on top using a whiteboard pen. There are many possible solutions; I’ve provided one. However, the smallest number (-28) must always go in the top left corner, and the largest (18) must always go in the bottom right.

Students have to find a path crossing left to right through the maze that only goes through correct answers. Diagonal moves are not allowed. Types of errors included: Forgetting to multiply the second term +/- mixed up x multiplied by x is 2x Variable changes Solution provided.

A basic worksheet that covers all the content on Exact Trigonometric Values required at GCSE level. It mostly contains basic SOH CAH TOA questions, but there are a couple of multi-step problems and a few questions that involve manipulating surds. Solutions provided.

A Bronze, Silver, Gold differentiated resource. Students are given a variety of fractions, decimals and percentages which they must place into a square grid, ensuring that every row and column is in ascending order. This hopefully makes quite a dull topic a little more interesting! There are multiple solutions to the puzzles, but I have provided one possible answer to each puzzle. However, to make the puzzles work, the smallest value must go in the top left box, and the largest value must go in the bottom right box.

The same idea as these excellent Don Steward tasks (https://donsteward.blogspot.com/2014/12/algebraic-product-puzzles.html) but extended to include factorising expressions where the common factor includes a variable. Students insert algebraic expressions into the grid so that each column and row multiplies to give the expression at the end - an example is given on the sheet to hopefully make this clearer. This is a problem solving task involving factorising! I’ve included a Powerpoint in case you want to make any changes to the task. Answers are provided on the Powerpoint.

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 simple, basic worksheet on plotting quadratics for weaker students. The variable appears in one place only, which makes filling in the table of values through substitution easier. I’ve included a co-ordinate grid and solutions to the task.

A Treasure Hunt on ratio questions of the form: Hugh and Kristian share some money in the ratio 3:4. Hugh gets £18. How much does Kristian get? Stick the questions up on the wall around the room. Students pick their own starting point, answer the question, and look for their answer on the top of a different card. This tells them which question to answer next. They end up back at the starting point if they complete all 20 questions correctly. Solution 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 an excellent resource on TES by MrMawson (https://www.tes.com/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.

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.

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.

UPDATED 16/09/22: Changed the font and added solutions. Included pdf version of the task too. A Bronze/Silver/Gold differentiated resource where pupils are given a list of fractions and a square grid. They have to put the fractions in the grid so that every row and column is in ascending order. The suggested method for doing so is to find a common denominator. There are many possible solutions to the puzzles, but I have provided one possible set of solutions as this was requested in the comments. In all solutions, the smallest fraction must always go in the top left corner, and the largest in the bottom right.

A basic worksheet on plotting straight lines of the form ax + by = c. It is differentiated into 3 sections. Bronze has equations of the form x + y = c. Silver has equations of the form ax + y = c or x + by = c. Finally, Gold contains the most general form ax + by = c. A Table of Values is given for each equation, and axes are pre-drawn. Solutions are provided.