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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.

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

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.

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.

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.

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.

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.

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!

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.

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.

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 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.

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 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.