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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.

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 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.

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.

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.

A set of questions I designed for my foundation group on determining coefficients in order to produce identities. Answers are provided.

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

A presentation I designed to help me deliver the “Number Families” task from nrich (https://nrich.maths.org/13123). Rather than jumping straight in to set notation, it starts off getting pupils to list what they know about certain numbers. Then they imagine that numbers that share a certain property can be placed in the same “bucket”. This idea of a “bucket” is then used to introduce set notation.

An activity that I designed to make ordering fractions a bit more challenging for the more able in my group. Pupils are given 4 algebraic fractions, and must order them by size for particular values of the unknown. Solutions are provided.

Some questions on Bearings & right-angled Trigonometry that I designed for my Year 11 students. The worksheet is scaffolded - each question comes in a pair. In the first question, I have drawn the complete diagram for students. In the second question, the diagram has been drawn but not labelled - students must do this for themselves. 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.

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.

An activity that gets pupils to practise division problems where the answer is a decimal, a skill which is motivated by a need to find approximations to the irrational number pi. There are 3 different levels of questions for pupils to attempt. Some of the questions really are quite challenging!