Earliest recommended Year group: Year 10. Pupils are given the nth term of a sequence and are asked to find specific (non consecutive) terms in the sequence. It is the Fibonacci sequence. The task involves surds and indices. Then they are asked to prove that the ratio of consecutive terms tends to the golden ratio. This is from the “Something in Common” collection of resources by John Burke. They allow consolidation of key skills, prevent students from copying each other (as all the questions are different), make marking and assessing easy for the teacher (as all the answers are the same!), and provide a lovely extra challenge for students as they try to figure out exactly what is going on! To access the full collection, and read John’s background notes, please visit: http://www.mrbartonmaths.com/common.htm

Earliest recommended Year group: Year 12. Given certain facts about a parabola the pupils have to determine its equation. Then they need to integrate the function to work out ratios of areas. There is a neat solution that makes it very easy to do - which you can show them at the end. A further extension is to challenge them to do it without integration. This is from the “Something in Common” collection of resources by John Burke. They allow consolidation of key skills, prevent students from copying each other (as all the questions are different), make marking and assessing easy for the teacher (as all the answers are the same!), and provide a lovely extra challenge for students as they try to figure out exactly what is going on! To access the full collection, and read John’s background notes, please visit: http://www.mrbartonmaths.com/common.htm

Earliest recommended Year group: Year 13. Given the 3D coordinates of four points what is the volume of the tetrahedron that is formed by joining them with line segments? This brings together just about everything they need to know about vectors and so is a good revision task. Using the triple product to solve it takes some of the fun out (hence suitable up to C4). Of course, the volumes are all the same.... but why? This is from the “Something in Common” collection of resources by John Burke. They allow consolidation of key skills, prevent students from copying each other (as all the questions are different), make marking and assessing easy for the teacher (as all the answers are the same!), and provide a lovely extra challenge for students as they try to figure out exactly what is going on! To access the full collection, and read John’s background notes, please visit: http://www.mrbartonmaths.com/common.htm

Earliest recommended Year group: Year 7. Get pupils to draw a quadrilateral that they think will not tessellate. Then reproduce it using the Geogebra file and show that it does. Then show a picture proof. This is from the “Something in Common” collection of resources by John Burke. They allow consolidation of key skills, prevent students from copying each other (as all the questions are different), make marking and assessing easy for the teacher (as all the answers are the same!), and provide a lovely extra challenge for students as they try to figure out exactly what is going on! To access the full collection, and read John’s background notes, please visit: http://www.mrbartonmaths.com/common.htm

Earliest recommended Year group: Year 11. Work out the area of a triangle with an inscribed circle. Answers are all different but easily calculated from the given parameters. This is from the “Something in Common” collection of resources by John Burke. They allow consolidation of key skills, prevent students from copying each other (as all the questions are different), make marking and assessing easy for the teacher (as all the answers are the same!), and provide a lovely extra challenge for students as they try to figure out exactly what is going on! To access the full collection, and read John’s background notes, please visit: http://www.mrbartonmaths.com/common.htm

Earliest recommended Year group: Year 12. Based on the nRich activitiy. An algebra task thinly disguised as a probability question. Answers are different but are consecutive triangular numbers. This is from the “Something in Common” collection of resources by John Burke. They allow consolidation of key skills, prevent students from copying each other (as all the questions are different), make marking and assessing easy for the teacher (as all the answers are the same!), and provide a lovely extra challenge for students as they try to figure out exactly what is going on! To access the full collection, and read John’s background notes, please visit: http://www.mrbartonmaths.com/common.htm

Earliest recommended Year group: Year 13. You have to run from tree A to tree B whilst touching a fence. Where should you touch the fence to minimise the distance you have to run? This is from the “Something in Common” collection of resources by John Burke. They allow consolidation of key skills, prevent students from copying each other (as all the questions are different), make marking and assessing easy for the teacher (as all the answers are the same!), and provide a lovely extra challenge for students as they try to figure out exactly what is going on! To access the full collection, and read John’s background notes, please visit: http://www.mrbartonmaths.com/common.htm

Earliest recommended Year group: Year 10. Pupils are presented with a number of simultaneous equations to solve. How quickly will they spot that they only need to select one pair? How many will select the easiest pair rather than just the first two in the list?....... This is from the “Something in Common” collection of resources by John Burke. They allow consolidation of key skills, prevent students from copying each other (as all the questions are different), make marking and assessing easy for the teacher (as all the answers are the same!), and provide a lovely extra challenge for students as they try to figure out exactly what is going on! To access the full collection, and read John’s background notes, please visit: http://www.mrbartonmaths.com/common.htm

Earliest recommended Year group: Year 12. Pupils need to work out the equation of a cubic and draw a tangent at a specific place. All tangents should go through the first root. This is from the “Something in Common” collection of resources by John Burke. They allow consolidation of key skills, prevent students from copying each other (as all the questions are different), make marking and assessing easy for the teacher (as all the answers are the same!), and provide a lovely extra challenge for students as they try to figure out exactly what is going on! To access the full collection, and read John’s background notes, please visit: http://www.mrbartonmaths.com/common.htm

A video from the Autograph team. The Central Limit Theorem tells us that regardless of the parent distribution, the distribution of the sample means will have a Normal distribution. Clicking on the web-link below takes you to all the videos in this series.

A video from the Autograph team. In this investigation into a strange property of cubics, students would normally first be introduced to a special case, for example y = (x -2)(x + 3)(x + 4), and then asked to look at this more general case. Clicking on the web-link below takes you to all the videos in this series.

An Autograph Player activity where students must figure out how 6 vectors have been created. You can use this activity on the interactive whiteboard, or for your students to investigate on their own. Autograph does not need to be installed to use this activity (so your students can even use it at home), but you will need to install the free Autograph Player add-on (instructions given after clicking the link). For a full list of Autograph Activities, please click on the other web-link.

Earliest recommended Year group: Year 12. Skew lines in 3d space in vector form. How close do they get? This is from the “Something in Common” collection of resources by John Burke. They allow consolidation of key skills, prevent students from copying each other (as all the questions are different), make marking and assessing easy for the teacher (as all the answers are the same!), and provide a lovely extra challenge for students as they try to figure out exactly what is going on! To access the full collection, and read John’s background notes, please visit: http://www.mrbartonmaths.com/common.htm

Earliest recommended Year group: Year 12. Projectiles. You want to shoot a monkey hanging in a tree. But he's a cheeky monkey and at the exact moment you fire, he lets go and falls to the ground. Knowing this, where should you aim to be sure of hitting your target? This is from the “Something in Common” collection of resources by John Burke. They allow consolidation of key skills, prevent students from copying each other (as all the questions are different), make marking and assessing easy for the teacher (as all the answers are the same!), and provide a lovely extra challenge for students as they try to figure out exactly what is going on! To access the full collection, and read John’s background notes, please visit: http://www.mrbartonmaths.com/common.htm

The 2nd in Mr Barton’s Gapminder World Video series. Here we look at how the world has developed over the last two hundred years by focusing on the relationship between a country’s life expectancy and the average income of the country’s inhabitants. For the analysis we look specifically on three countries: China, Rwanda and the UK. Below the video you will find an option to download it and play it on a larger screen, or by clicking on the web-link you can see all the videos in this series

I know, I know, guilty as charged! This week’s Web Whizz video features my website. However, hopefully you will forgive me when you see the brand new and completely free Autograph Player activities that are now available. Unlike Autograph files, these activities do not need the software installed, which means you can use them completely freely to demonstrate topics in class, or set them as homework assignments for your students. Here we look at activities about transformations, angles, circle theorem, battleships and scatter diagrams.

Worksheet for the well known flowerbed investigation.

The 66th in Mr Barton's Autograph Video tutorial series. The second of the Autograph Puzzle Trilogy! Here we look at another a lovely pencil and paper puzzle inspired by Don Steward’s amazing Median Maths Blog. Students are given four co-ordinates and asked to consider the shape that would be formed by joining up the midpoints of pairs of these co-ordinates. What type of quadrilateral is it? How do they know? We can then turn to Autograph to construct the puzzle and investigate it even further. Click on the link to see all my Autograph videos

MEI has kindly shared the following resources to support the use of ICT in A/AS Level maths. These are practical activities that look at how we can use Autograph to enhance the study of differentiation and integration (calculus), predominantly at AS level. These are ideal for use in a computer room or for students to investigate at home. The pdf file contains full instructions and challenges, and the attached Autograph and Excel files can be used to demonstrate and consolidate understanding back in the classroom. Please click on the web-link to find out more about the work of MEI.

The master grid to accompany the above activity.