Transum Maths Software

Functions

There are 366 different Starters of The Day, many to choose from. You will find in the left column below some starters on the topic of Functions. In the right column below are links to related online activities, videos and teacher resources.

A lesson starter does not have to be on the same topic as the main part of the lesson or the topic of the previous lesson. It is often very useful to revise or explore other concepts by using a starter based on a totally different area of Mathematics.

Main Page

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.

Index of Advanced Starters


Suggested

Think of a Number

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.

The short web address is:

Transum.org/go/?to=thoan

 

Curriculum for Functions:

Year 6

Pupils should be taught to express missing number problems algebraically more...

Years 7 to 9

Pupils 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 11

Pupils 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 13

Pupils 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 Baccalaureate

See 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 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."

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"My year five children look forward to their daily challenge and enjoy the problems as much as I do. A great resource - thanks a million."

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 17 June 'Starter of the Day' page by Mr Hall, Light Hall School, Solihull:

"Dear Transum,

I love you website I use it every maths lesson I have with every year group! I don't know were I would turn to with out you!"

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."

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"Really good site. Lots of good ideas for starters. Use it most of the time in KS3."

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"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!
Thanks"

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Keep it up and thank you!"

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Thanks again"

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I rate this site as a 5!"

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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.

Pupils in Primary school will use the concept of function machines to perform calculations. They will then learn to ‘work backwards’ to find the inverse function. The study of functions becomes more formal as pupils become more proficient and able to cope with more complex mathematical ideas.

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:

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Suggested

Coordinate Geometry Table

Coordinate Geometry Table

Fill in the empty cells of this table with information about lines, gradients and coordinates.

The short web address is:

Transum.org/go/?to=cgt

 

Teaching Notes:

Many Transum activities have notes for teachers suggesting teaching methods and highlighting common misconceptions. There are also solutions to puzzles, exercises and activities available on the web pages when you are signed in to your Transum subscription account. If you do not yet have an account and you are a teacher, tutor or parent you can apply for one by completing the form on the Sign Up page.

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