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!
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.
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.
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.
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 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. 18/40, so they need to be simplified first.
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 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.
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 proper fraction must be added or subtracted at each step to reach the next number in the sequence. Solutions are provided.
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.
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 a starting point, answer the question, and look for their answer at the top of the next card. They should end up back at their starting point if they get all the questions correct. Solution provided.
This is similar to a resource already on TES that I really like (https://www.tes.com/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!
Students have to find a path crossing left to right through the maze that only goes through correct answers. Diagonal moves are not allowed. 2 copies of the maze are provided per A4 sheet.
Types of errors included:
Forgetting to multiply the second term
+/- mixed up
x multiplied by x is 2x
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.
The same idea as these excellent Don Steward tasks (https://donsteward.blogspot.com/2014/12/algebraic-product-puzzles.html) except extended to include factorising expressions where the common factor includes a variable. (2 copies per A4 sheet).
Students insert algebraic expressions into the grid so that each column and row multiplies to give the expression at the end. A problem solving task involving factorising!
Answers are provided.
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!).
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.