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

Students are given a grid of one-step equations to solve. They’ll need 2 colouring pencils (any colours will do!) - one colour for even answers, and one colour for odd answers. I’ve included a file showing what the final image should look like! A nice activity for Friday Period 5!

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.

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.

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.

Designed for Higher GCSE Students to review their knowledge of equations of straight lines, in particular finding the equation: Between 2 points When given the gradient and a point When given a parallel line and a point Also requires an understanding of the relationship between the gradients of two lines that are perpendicular. In each line of the table, students are given some of the information about a straight line - and have to fill in the missing information!

A basic worksheet to ensure students are comfortable with the > and < symbols. Students are given 2 calculations to do, and must use the appropriate symbol to show which calculation gives the greater answer. The calculations involve integers at first, but move onto decimal calculations later. Solutions are provided.

A Tarsia activity to help students become familiar with function notation f(x), by substituting values into functions, composite functions, and inverse functions. There are 16 pieces to the puzzle - students substitute values into functions and match that piece up to its answer on another card. When completed, the 16 pieces form a square. To make things a bit more challenging, some functions do not have an answer to match with - these will go around the outside of the completed square. The 3 functions f(x), g(x) and h(x) that students need to complete the puzzle are in the PNG file - these can be projected onto the whiteboard while students work. Note that I haven’t provided students with the Inverse Functions - students must derive them on their own. Sadly, I was not able to upload the Tarsia file itself, just a pdf version, so you cannot make any edits yourself.

A task designed to make simplifying algebraic fractions a little more interesting. Students are given 24 expressions and must use them to create 12 algebraic fractions (no repeats). The aim is to create 12 algebraic fractions that can all be simplified. I’ve provided a solution to show it is possible, but there may be more than one solution! I’ve used this with a Year 12 class but it could also be suitable for able KS4.

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!).

I designed this activity for my top set Year 10 class. It involves adding, subtracting, multiplying and dividing numbers in standard form. It is designed to be done without a calculator! Initially, students are given 2 numbers in standard form, a and b, and must calculate other values such as a + b, a x b etc., but progresses onto skills such as, if you’re given b and a ÷ b, can you work out a? Good for a higher-attaining group I think! 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.

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.

I wanted a resource where students had to factorise monic quadratics that only had positive terms, so I created this task. Students factorise each of the given quadratics into double brackets. They cross off each bracket in the grid at the bottom of the page - each bracket appears multiple times, but it doesn’t matter which one they cross off. Once students have factorised every quadratic, their grids will probably all look different, but they will all have 8 letters left that weren’t crossed off that can be re-arranged to spell BUDAPEST.

I like to use the grid method for expanding double brackets, and then I use the grid method “in reverse” to factorise non-monic quadratics. To introduce this idea of working “in reverse”, I created these 2 worksheets. Students are already given the four terms inside the grid, and they have to determine what the brackets around the outside must be.

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.

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.

A task I designed to challenge some high-ability students. There are 9 questions on Multiplying Mixed Numbers, each one missing a digit. Students have to work out the missing digit in each calculation. Each of the numbers 1 - 9 will be used exactly once. 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.