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.
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.
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, then there are some basic fluency questions.
To make things a bit 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 31/03/18: Changed the fractions in each puzzle so that they’re not pixelated and difficult to read when printed.
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.
No solutions are provided as there are many possible solutions. However, the smallest fraction must always go in the top left corner, and the largest in the bottom right.
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.
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 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.
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.
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 blue questions at the top only have positive terms in the quadratic, while the yellow 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 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 so I haven’t provided answers. However, to make it work, the smallest value must go in the top left box, and the largest value must go in the bottom right box.
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. There are no pre-drawn axes included, sorry, you’ll have to download them elsewhere.
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!
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 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. I personally have used this with a mixed ability Y7 class.
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.
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.
I used this when teaching Year 7 how to expand double brackets. They had to put expressions into the grids, so that each row and column multiplies to give the quadratic expression at the end. This helped them discover how to factorise quadratics!
Answers are provided.
Inspired by a similar, but more difficult, task from Don Steward: https://donsteward.blogspot.com/2014/12/algebraic-product-puzzles.html
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.