51����

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.

My attempt at making practice of multiplying and dividing negative numbers a little more interesting! Students are given completed multiplication grids - but the numbers around the outside (which can be negative or positive) are missing. Students have to work out where the numbers should go to give the completed grid. Solutions are provided.

A couple of activities on Frequency Trees (aimed at KS3). The worksheets are provided in pdf and Word, in case you want to make any edits. Solutions are provided. In “complete using the clues”, students are given 3 blank frequency trees, and 4 clues to go with each. They must use the clues to fill in each frequency tree. This requires some basic knowledge of fractions of amounts and ratio. In “true or false”, students are given a partially completed frequency tree and must fill in the remainder - this requires some basic number facts. Using their completed frequency tree, they must then decide which of the 13 statements at the bottom of the page are true. This will require some knowledge of fractions of amounts, percentages of amounts, and ratio.

Students solve quadratic equations by completing the square, giving their answers in both surd form and as decimals. The answers are all jumbled up, and students must match the answers to the correct quadratic equation. There are a couple of quadratics where the coefficient of x is odd, and some knowledge of simplifying surds will be required. Solutions are provided.

A way to make solving equations a bit more interesting! Students have to pick 2 of the algebraic expressions and set them equal to each other. They then solve the equation they’ve created, and hope the answer is one of the targets on the right hand side of the page. If not, they create another equation! When I use this in my lessons, I say the first person to create an equation with a target answer gets to “claim” that answer and gets their name on the board. I find the students are really motivated by this, and do a lot more practice than they usually would! Possible solutions are provided.

A Treasure Hunt on converting decimals to fractions ( which should be in simplest form). Print out the questions and place around the room. Students decide which card they want to start on. Students answer the question by converting the decimal to a fraction, and look for their answer at the top of a different card - this tells them which question to answer next. They then repeat the process, and if they’re correct, they should end up back at their starting point after 20 questions. Solution is provided.

A Treasure Hunt on converting fractions to decimals and vice versa. Print off the questions and place them around the classroom. Students pick a starting point, answer the question and look for their answer at the top of a different card - this tells them which question to answer next. If they’re correct, they should end up back at their starting point after completing 20 questions. The number in the top right of each card is the question number. The solution is 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.

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.

A Treasure Hunt based on finding the input value in a function machine when given the output. Print out the cards and stick them around the classroom. Students pick their own starting point, answer the question, and look for their answer at the top of a different card. This tells them which question to do next, and then they repeat the process. They should end up back at their starting point if they get all the questions correct. Solution provided.

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 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 treasure hunt based on ratio questions like: Hugh and Kristian share some money in the ratio 9:7. Hugh gets £10 more than Kristian. How much does each person get? Students pick their own starting point, answer the question, and look for their answer at the top of another card. This tells them which question to answer next, and then they repeat the process. They should end up back at their starting point if they get all 20 questions correct. Solution 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.

Inspired by “The Simple Life” - a task from Colin Foster: https://nrich.maths.org/13207 I wanted a simpler version to suit my weaker group. Students are given a variety of algebraic expressions in the form a(bx + c) and must pick 2 to add up. They are given 8 answers to aim for. Possible solutions are provided - there may be other solutions, I’m not really sure!

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.

Used with an able Year 10 group as a way to revise factorising into single brackets. Students are given a partially completed multiplication grid with algebra, and must deduce what expressions go in the remaining boxes. As a starting point, look at the 3rd column: by factorising 6x + 8 and 15x + 20, we deduce that (3x + 4) must go at the top of this column. Solutions are provided.

An activity that gets students to practise finding fractions of amounts, which also introduces an element of problem solving. Students create their own questions. They pick a numerator, pick a denominator, and work out that fraction of the large number at the top of the screen. They’re aiming to create calculations with the given answers on the screen. Some students might pick their fractions completely at random, whereas others may approach things a bit more logically… There are 6 different activities, with varying degrees of difficulty. Some answers can be made via more than one calculation, but I’ve made a suggestion on how to complete each problem.

8 Time Series graphs and questions to accompany them. As well as questions on basic graph reading skills, I’ve also included questions that test other skills, for example averages, percentage increase, and writing one amount as a fraction of another. Solutions to all questions are provided. It’s possible to get all questions on one doubled-sided piece of A4 if you print 2 pages per sheet. Apart from the football-related graphs, all data is completely fictional! I’ve also uploaded the word documents so you can make any changes, if desired.

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.