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 Graphs. 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

Graphs Starters:

Choc Bar Chart: Interpret data given in the form of a bar chart then create a new bar chart showing the given statistics.

Graph Picture: Plot the given coordinates then join them up to form a picture.

Pie Chart: An exercise in estimating what the sectors of a pie chart represent.

GDC Challenge: Produce the given graph on a graphic display calculator

Maximum Product: Two numbers add up to 10. What's the largest possible product they could have?

Parallel Graphs: Determine from their equations which of the straight line graphs are parallel and perpendicular.

Venn Graphs: Type the equation of a graph into each section of the Venn diagram.

Function Builder

An interactive function machine for patterns, numbers and equations.

Transum.org/go/?to=functionbuilder

Curriculum for Graphs:

Years 7 to 9

Pupils should be taught to model situations or procedures by translating them into algebraic expressions or formulae and by using graphs 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 interpret mathematical relationships both algebraically and graphically more...

Pupils should be taught to reduce a given linear equation in two variables to the standard form y = mx + c; calculate and interpret gradients and intercepts of graphs of such linear equations numerically, graphically and algebraically more...

Pupils should be taught to use linear and quadratic graphs to estimate values of y for given values of x and vice versa and to find approximate solutions of simultaneous linear equations 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 interpret and construct tables and line graphs for time series data more...

Pupils should be taught to use the form y = mx + c to identify parallel {and perpendicular} lines; find the equation of the line through 2 given points, or through 1 point with a given gradient more...

Pupils should be taught to interpret the gradient of a straight line graph as a rate of change; recognise and interpret graphs that illustrate direct and inverse proportion more...

Pupils should be taught to identify and interpret roots, intercepts and turning points of quadratic functions graphically; deduce roots algebraically {and turning points by completing the square} more...

Pupils should be taught to {interpret the gradient at a point on a curve as the instantaneous rate of change; apply the concepts of instantaneous and average rate of change (gradients of tangents and chords) in numerical, algebraic and graphical contexts} 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...

Pupils should be taught to {calculate or estimate gradients of graphs and areas under graphs (including quadratic and other non-linear graphs), and interpret results in cases such as distance-time graphs, velocity-time graphs and graphs in financial contexts} more...

Pupils should be taught to {recognise and use the equation of a circle with centre at the origin; find the equation of a tangent to a circle at a given point} more...

Pupils should be taught to solve quadratic equations {including those that require rearrangement} algebraically by factorising, {by completing the square and by using the quadratic formula}; find approximate solutions using a graph more...

Pupils should be taught to solve 2 simultaneous equations in 2 variables (linear/linear {or linear/quadratic}) algebraically; find approximate solutions using a graph more...

Years 12 and 13

Pupils should be taught to understand and use the equation of a straight line, including the forms y – y1 = m(x – x1) and ax + by + c = 0; Gradient conditions for two straight lines to be parallel or perpendicular. Be able to use straight line models in a variety of contexts more...

Pupils should be taught to locate roots of f (x) = 0 by considering changes of sign of f(x) in an interval of x on which f(x) is sufficiently well behaved. Understand how change of sign methods can fail more...

Pupils should be taught to understand and apply the language of statistical hypothesis testing, developed through a binomial model: null hypothesis, alternative hypothesis, significance level, test statistic, 1-tail test, 2-tail test, critical value, critical region, acceptance region, p-value; extend to correlation coefficients as measures of how close data points lie to a straight line. and be able to interpret a given correlation coefficient using a given p-value or critical value (calculation of correlation coefficients is excluded) more...

Pupils should be taught to understand and use the coordinate geometry of the circle including using the equation of a circle in the form (x – a)2 + (y – b)2 = r2 Completing the square to find the centre and radius of a circle; use of the following properties: the angle in a semicircle is a right angle, the perpendicular from the centre to a chord bisects the chord, the radius of a circle at a given point on its circumference is perpendicular to the tangent to the circle at that point more...

Pupils should be taught to interpret scatter diagrams and regression lines for bivariate data, including recognition of scatter diagrams which include distinct sections of the population (calculations involving regression lines are excluded). Understand informal interpretation of correlation. Understand that correlation does not imply causation more...

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 the parametric equations of curves and conversion between Cartesian and parametric forms more...

Pupils should be taught to use parametric equations in modelling in a variety of contexts 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 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...

Pupils should be taught to use of functions in modelling, including consideration of limitations and refinements of the models 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 26 March 'Starter of the Day' page by Julie Reakes, The English College, Dubai:

"It's great to have a starter that's timed and focuses the attention of everyone fully. I told them in advance I would do 10 then record their percentages."

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.
Thanks for such a great resource!"

Comment recorded on the 10 September 'Starter of the Day' page by Carol, Sheffield PArk Academy:

"3 NQTs in the department, I'm new subject leader in this new academy - Starters R Great!! Lovely resource for stimulating learning and getting eveyone off to a good start. Thank you!!"

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.
I rate this site as a 5!"

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 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 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 23 September 'Starter of the Day' page by Judy, Chatsmore CHS:

"This triangle starter is excellent. I have used it with all of my ks3 and ks4 classes and they are all totally focused when counting the triangles."

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 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.
Could we have some on angles too please?"

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.
To the creator of this website and all of those teachers who have contributed to it, I would like to say a big THANK YOU!!! :)."

Comment recorded on the 16 March 'Starter of the Day' page by Mrs A Milton, Ysgol Ardudwy:

"I have used your starters for 3 years now and would not have a lesson without one! Fantastic way to engage the pupils at the start of a lesson."

Comment recorded on the 17 November 'Starter of the Day' page by Amy Thay, Coventry:

"Thank you so much for your wonderful site. I have so much material to use in class and inspire me to try something a little different more often. I am going to show my maths department your website and encourage them to use it too. How lovely that you have compiled such a great resource to help teachers and pupils.
Thanks again"

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 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 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 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 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 14 October 'Starter of the Day' page by Inger Kisby, Herts and Essex High School:

"Just a quick note to say that we use a lot of your starters. It is lovely to have so many different ideas to start a lesson with. Thank you very much and keep up the good work."

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 February 'Starter of the Day' page by Terry Shaw, Beaulieu Convent School:

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

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 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 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 28 September 'Starter of the Day' page by Malcolm P, Dorset:

"A set of real life savers!!
Keep it up and thank you!"

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 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 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 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:

This topic includes algebraic and statistical graphs including bar charts, line graphs, scatter graphs and pie charts.

A graph is a diagram which represents a relationship between two or more sets of numbers or categories. The data items are shown as points positioned relative to axes indicating their values. Pupils are typically first introduced to simple bar charts and learn to interpret their meaning and to draw their own. More sophisticated statistical graphs are introduced as the pupil's mathematical understanding develops.

Pupils also learn about coordinates as a pre-requisite for understanding algebraic graphs. They then progress to straight line graphs before learning to work with curves, gradients, intercepts, regions and, for older pupils, calculus.

Graphs Teacher Resources:

A Show Of Hands: Produce a number of graphs and charts from a quick show of hands.

Pie Chart Creator: A quick and convenient tool for rapidly creating simple pie charts.

Graph Paper: Flexible graph paper which can be printed or projected onto a white board as an effective visual aid.

Cartoon Scatter Graph: Place the cartoon characters on the scatter graph according to their height and age.

Correlation: Arrange the given statements in groups to show the type of correlation they have.

Human Scatter Graphs: Pupils move to positions in the room according to their data relative to the walls as axes.

Helicopter View: An animated introduction to distance-time graphs. Arial photographs of vehicles moving along a road placed side to side form a graph.

Hurdles Race: An animated distance time graph to be viewed while a student interprets the graph and comments on the race that produced the graph.

Comparing Graphs: Would you recognise a misleading graph if you saw one? Try this comparative judgement exercise to rate statistical graphs.

Straight Line Graphs: 10 straight line graph challenges for use with computer graph plotting software or a graphical display calculator.

Graph Plotter: An online tool to draw, display and investigate graphs of many different kinds.

Human Graphs: Students should be encouraged to stand up and make the shapes of the graphs with their arms.

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.

Graphs Activities:

Function Builder: An interactive function machine for patterns, numbers and equations.

Bar Charts: Practise constructing and interpreting bar charts for everyday situations.

Pie Charts: Develop the skills to construct and interpret pie charts in this self-marking set of exercises.

Gradient of a Line: Practise the skill of finding the gradients of straight lines by counting squares and dividing rise by run.

Plotting Graphs: Complete a table of values then plot the corresponding points to create a graph.

Histograms: Practise drawing and reading information from histograms displaying grouped data

Deconstructing Graphs: Fill in the tables of values from the information that can be read from the given graphs.

Straight Line Graph Equation: An online exercise about the equation y=mx+c and the features of a straight line graph.

Cartoon Scatter Graph: Place the cartoon characters on the scatter graph according to their height and age.

Graphs of Vertical and Horizontal Lines: Questions about the equations of straight line graphs that are parallel to the axes.

Estimating Correlation: Practise the skill of estimating the correlation of data on a scatter graph in this self marking exercise.

Correlation: Arrange the given statements in groups to show the type of correlation they have.

Don's Graph Snaps: Complete the tables and find the equations of the graphs that can be seen in the snaps.

Fill Graph Pairs: If the container is gradually filled with a steady flow of water which height-time graph would be produced?

Reading Graphs and Charts: Answer real-life problems from different types of graphs and charts including piece-wise linear graphs.

Completing the Square: Practise this technique for solving quadratic equations and analysing graphs.

Graph Equation Pairs: Match the equation with its graph. Includes quadratics, cubics, reciprocals, exponential and the sine function.

Linear Programming: A selection of linear programming questions with an interactive graph plotting tool.

Travel Graphs: Test your understanding of distance-time and speed-time graphs with this self-marking exercise.

Graph Patterns: Find the equations which will produce the given patterns of graphs.

Comparing Graphs: Would you recognise a misleading graph if you saw one? Try this comparative judgement exercise to rate statistical graphs.

Graph Match: Match the equations with the images of the corresponding graphs. A drag-and-drop activity.

Graph Plotter: An online tool to draw, display and investigate graphs of many different kinds.

Using Graphs: Use the graphs provided and create your own to solve both simultaneous and quadratic equations.

Plotting Scatter Graphs: Plot scatter graphs from data representing a number of different everyday situations.

Parallel Graphs: Collect together in groups the equations of the graphs that are parallel to each other.

Perpendicular Pairs: Find the pairs of equations that will produce perpendicular graphs.

Yes No Questions: A game to determine the mathematical item by asking questions that can only be answered yes or no.

Equation of a Line Through Points: Match the equations of the straight line graphs to the clues about gradients and points.

Circle Equations: Recognise and use the equation of a circle with centre at the origin and the equation of a tangent to a circle.

Differentiation: Practise the technique of differentiating polynomials with this self marking exercise.

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

Integration: Exercises on indefinite and definite integration of basic algebraic and trigonometric functions.

Graphs Investigations:

Function Builder: An interactive function machine for patterns, numbers and equations.

Graph Plotter: An online tool to draw, display and investigate graphs of many different kinds.

Search for Infinity: Manipulate the Lissajou curve to produce a perfectly symmetrical (vertically and horizontally) infinity symbol.

Graphs Videos:

Transum's Graphs Video

Straight Line Graphs Video: After drawing a straight line graph learn about its equation in the form y = mx + c.

Scatter Graphs: Maths teachers from England construct a scatter graph from their heights and shoe sizes.

Travel Graphs Video: Learn about distance-time graphs, speed-time graphs and how to interpret them.

Human Graph Shapes Video: Chapel Hill-Chauncy Hall teacher Kelly Overbye demonstrates how she uses Multiple Intelligences, to teach her students about the slope of graphs. [Similar to Transum's Human Graphs]

Equation of Line through Points Video: A short video showing how to find the equation of a line that passes through given points.

Log Tables: Logarithms and log tables - what Transum used before calculators! A Numberphile video.

Graphs Worksheets/Printables:

Graph Picture Axes: Four sets of axes and coordinates from which reflecting pictures can be drawn.

Line Graph Challenge: A challenge to produce the straight line patterns using a GDC or graph plotting software.

Links to other websites containing resources for Graphs 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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Integration

Exercises on indefinite and definite integration of basic algebraic and trigonometric functions.

Transum.org/go/?to=integration

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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