Functions Starters:Get A Wiggle On: A mixture of calculations to get your brain working at the start of a mathematics lesson. Lemon Law: Change the numbers on the apples so that the number on the lemon is the given total. Pyramid Puzzle: Arrange numbers at the bottom of the pyramid which will give the largest total at the top. Think Back: A problem which can be answered by forming an algebraic equation then solving it. THOAN: THOAN stands for 'Think of a number' and there are four randomly generated THOAN puzzles to solve.
Small images of these Starters :: Index of Starters Functions Advanced Starters:Catering for a Function: Find f(x) given f(x-1). GDC Challenge: Produce the given graph on a graphic display calculator Permutable Functions: Find pairs of functions that are commutative under composition. SuggestedThink of a Number Ten students think of a number then perform various operations on that number. You have to find what the original numbers were.
Curriculum for Functions:Year 6Pupils should be taught to express missing number problems algebraically more... Years 7 to 9Pupils should be taught to relate the language of ratios and the associated calculations to the arithmetic of fractions and to linear functions more... Pupils should be taught to recognise, sketch and produce graphs of linear and quadratic functions of one variable with appropriate scaling, using equations in x and y and the Cartesian plane more... Pupils should be taught to find approximate solutions to contextual problems from given graphs of a variety of functions, including piece-wise linear, exponential and reciprocal graphs more... Years 10 and 11Pupils should be taught to where appropriate, interpret simple expressions as functions with inputs and outputs; {interpret the reverse process as the ‘inverse function’; interpret the succession of 2 functions as a ‘composite function’} more... Pupils should be taught to recognise, sketch and interpret graphs of linear functions, quadratic functions, simple cubic functions, the reciprocal function y = with x not equal to 0, {the exponential function y = kx for positive values of k, and the trigonometric functions (with arguments in degrees) y = sin x, y = cos x and y = tan x for angles of any size} more... Pupils should be taught to sketch translations and reflections of the graph of a given function more... Pupils should be taught to plot and interpret graphs (including reciprocal graphs {and exponential graphs}) and graphs of non-standard functions in real contexts, to find approximate solutions to problems such as simple kinematic problems involving distance, speed and acceleration more... Years 12 and 13Pupils should be taught to work with quadratic functions and their graphs. The discriminant of a quadratic function, including the conditions for real and repeated roots. Completing the square. Solution of quadratic equations including solving quadratic equations in a function of the unknown. more... Pupils should be taught to understand and use graphs of functions; sketch curves defined by simple equations including polynomials. The modulus of a linear function. Reciprocal graphs including their vertical and horizontal asymptotes. Interpret algebraic solution of equations graphically; use intersection points of graphs to solve equations. Understand and use proportional relationships and their graphs more... Pupils should be taught to understand and use composite functions; inverse functions and their graphs more... Pupils should be taught to understand the effect of simple transformations on the graph of y = f(x), including sketching associated graphs: y = af(x), y = f(x) + a, y = f(x + a), y = f(ax) and combinations of these transformations more... International BaccalaureateSee the Functions sub-topics, syllabus statements, exam-style questions and learning resources for the IB AA course here. Exam-Style Questions:There are almost a thousand exam-style questions unique to the Transum website. Feedback:Comment recorded on the 3 October 'Starter of the Day' page by S Mirza, Park High School, Colne: "Very good starters, help pupils settle very well in maths classroom." Comment recorded on the 9 May 'Starter of the Day' page by Liz, Kuwait: "I would like to thank you for the excellent resources which I used every day. My students would often turn up early to tackle the starter of the day as there were stamps for the first 5 finishers. We also had a lot of fun with the fun maths. All in all your resources provoked discussion and the students had a lot of fun." Comment recorded on the 8 May 'Starter of the Day' page by Mr Smith, West Sussex, UK: "I am an NQT and have only just discovered this website. I nearly wet my pants with joy. Comment recorded on the 19 October 'Starter of the Day' page by E Pollard, Huddersfield: "I used this with my bottom set in year 9. To engage them I used their name and favorite football team (or pop group) instead of the school name. For homework, I asked each student to find a definition for the key words they had been given (once they had fun trying to guess the answer) and they presented their findings to the rest of the class the following day. They felt really special because the key words came from their own personal information." Comment recorded on the 19 June 'Starter of the Day' page by Nikki Jordan, Braunton School, Devon: "Excellent. Thank you very much for a fabulous set of starters. I use the 'weekenders' if the daily ones are not quite what I want. Brilliant and much appreciated." Comment recorded on the 21 October 'Starter of the Day' page by Mr Trainor And His P7 Class(All Girls), Mercy Primary School, Belfast: "My Primary 7 class in Mercy Primary school, Belfast, look forward to your mental maths starters every morning. The variety of material is interesting and exciting and always engages the teacher and pupils. Keep them coming please." Comment recorded on the s /Indice 'Starter of the Day' page by Busolla, Australia: "Thank you very much for providing these resources for free for teachers and students. It has been engaging for the students - all trying to reach their highest level and competing with their peers while also learning. Thank you very much!" Comment recorded on the 28 September 'Starter of the Day' page by Malcolm P, Dorset: "A set of real life savers!! Comment recorded on the 10 April 'Starter of the Day' page by Mike Sendrove, Salt Grammar School, UK.: "A really useful set of resources - thanks. Is the collection available on CD? Are solutions available?" Comment recorded on the 9 October 'Starter of the Day' page by Mr Jones, Wales: "I think that having a starter of the day helps improve maths in general. My pupils say they love them!!!" Comment recorded on the 5 April 'Starter of the Day' page by Mr Stoner, St George's College of Technology: "This resource has made a great deal of difference to the standard of starters for all of our lessons. Thank you for being so creative and imaginative." Comment recorded on the 14 September 'Starter of the Day' page by Trish Bailey, Kingstone School: "This is a great memory aid which could be used for formulae or key facts etc - in any subject area. The PICTURE is such an aid to remembering where each number or group of numbers is - my pupils love it! Comment recorded on the s /Coordinate 'Starter of the Day' page by Greg, Wales: "Excellent resource, I use it all of the time! The only problem is that there is too much good stuff here!!" Comment recorded on the 18 September 'Starter of the Day' page by Mrs. Peacock, Downe House School and Kennet School: "My year 8's absolutely loved the "Separated Twins" starter. I set it as an optional piece of work for my year 11's over a weekend and one girl came up with 3 independant solutions." Comment recorded on the 6 May 'Starter of the Day' page by Natalie, London: "I am thankful for providing such wonderful starters. They are of immence help and the students enjoy them very much. These starters have saved my time and have made my lessons enjoyable." Comment recorded on the i asp?ID_Top 'Starter of the Day' page by Ros, Belize: "A really awesome website! Teachers and students are learning in such a fun way! Keep it up..." Comment recorded on the 3 October 'Starter of the Day' page by Mrs Johnstone, 7Je: "I think this is a brilliant website as all the students enjoy doing the puzzles and it is a brilliant way to start a lesson." Comment recorded on the 24 May 'Starter of the Day' page by Ruth Seward, Hagley Park Sports College: "Find the starters wonderful; students enjoy them and often want to use the idea generated by the starter in other parts of the lesson. Keep up the good work" Comment recorded on the 1 May 'Starter of the Day' page by Phil Anthony, Head of Maths, Stourport High School: "What a brilliant website. We have just started to use the 'starter-of-the-day' in our yr9 lessons to try them out before we change from a high school to a secondary school in September. This is one of the best resources on-line we have found. The kids and staff love it. Well done an thank you very much for making my maths lessons more interesting and fun." Comment recorded on the 11 January 'Starter of the Day' page by S Johnson, The King John School: "We recently had an afternoon on accelerated learning.This linked really well and prompted a discussion about learning styles and short term memory." Comment recorded on the 3 October 'Starter of the Day' page by Fiona Bray, Cams Hill School: "This is an excellent website. We all often use the starters as the pupils come in the door and get settled as we take the register." Comment recorded on the 2 May 'Starter of the Day' page by Angela Lowry, : "I think these are great! So useful and handy, the children love them. Comment recorded on the 1 August 'Starter of the Day' page by Peter Wright, St Joseph's College: "Love using the Starter of the Day activities to get the students into Maths mode at the beginning of a lesson. Lots of interesting discussions and questions have arisen out of the activities. Comment recorded on the 12 July 'Starter of the Day' page by Miss J Key, Farlingaye High School, Suffolk: "Thanks very much for this one. We developed it into a whole lesson and I borrowed some hats from the drama department to add to the fun!" Comment recorded on the 25 June 'Starter of the Day' page by Inger.kisby@herts and essex.herts.sch.uk, : "We all love your starters. It is so good to have such a collection. We use them for all age groups and abilities. Have particularly enjoyed KIM's game, as we have not used that for Mathematics before. Keep up the good work and thank you very much Comment recorded on the 2 April 'Starter of the Day' page by Mrs Wilshaw, Dunsten Collage,Essex: "This website was brilliant. My class and I really enjoy doing the activites." Comment recorded on the 7 December 'Starter of the Day' page by Cathryn Aldridge, Pells Primary: "I use Starter of the Day as a registration and warm-up activity for my Year 6 class. The range of questioning provided is excellent as are some of the images. Comment recorded on the 28 May 'Starter of the Day' page by L Smith, Colwyn Bay: "An absolutely brilliant resource. Only recently been discovered but is used daily with all my classes. It is particularly useful when things can be saved for further use. Thank you!" Comment recorded on the 9 April 'Starter of the Day' page by Jan, South Canterbury: "Thank you for sharing such a great resource. I was about to try and get together a bank of starters but time is always required elsewhere, so thank you." Comment recorded on the 19 November 'Starter of the Day' page by Lesley Sewell, Ysgol Aberconwy, Wales: "A Maths colleague introduced me to your web site and I love to use it. The questions are so varied I can use them with all of my classes, I even let year 13 have a go at some of them. I like being able to access Starters for the whole month so I can use favourites with classes I see at different times of the week. Thanks." |
Notes:A relationship between two sets can be called a mapping. Elements of the first set (domain) are mapped to elements of the second set (range). A function is a special type of mapping for which one value in the domain maps to one, and only one value in the range. Functions Teacher Resources:Graphing Quadratics: Describe how changing the coefficients of a quadratic function changes the graph of the function Transformations of Functions: A visual aid showing how various transformations affect the graph of a function. Functions Activities:Think of a Number: Ten students think of a number then perform various operations on that number. You have to find what the original numbers were. Function Builder: An interactive function machine for patterns, numbers and equations. Graph Equation Pairs: Match the equation with its graph. Includes quadratics, cubics, reciprocals, exponential and the sine function. Name that Graph: Choose from the given functions the one that best describes the shape of the graph. Functions: An online exercise on function notation, inverse functions and composite functions. Domain, Range and Asymptotes: Match the functions with their features. A drag and drop activity. Coordinate Geometry Table: Fill in the empty cells of this table with information about lines, gradients and coordinates. Alternatively, for the more advanced student, there is an ever-growing collection of Exam-Style Questions with worked solutions on the topic of Functions. Functions Investigations:Function Builder: An interactive function machine for patterns, numbers and equations. Functions Videos:What Are Functions?: A basic introduction to the concept of functions. Domain and Range: Domain and range of a function given a formula from Khan Academy. Functions External Links:Links to other websites containing resources for Functions are provided for those logged into 'Transum Mathematics'. Subscribing also opens up the opportunity for you to add your own links to this panel. You can sign up using one of the buttons below: SearchThe activity you are looking for may have been classified in a different way from the way you were expecting. You can search the whole of Transum Maths by using the box below.
OtherIs there anything you would have a regular use for that we don't feature here? Please let us know. SuggestedCoordinate Geometry Table Fill in the empty cells of this table with information about lines, gradients and coordinates.
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