Author Archives: John Tranter

5 Resources for Maths GCSE(9-1)

Hello and welcome to the Transum Mathematics newsletter for February 2017. It is being written a little earlier than normal to make up for the fact that there was no January newsletter and that I will be travelling later in the month at the time when I would otherwise be writing this.

This month’s puzzle is about a restrained flea that jumps one foot at a time either north, south, east or west. At how many different places could he end up after 8 jumps?

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While you think about that I would like to tell you of five resources on the Transum website that have been updated recently. Although they are perfect for the UK’s GCSE exam preparation they could also be used in different ways for younger learners.

  1. Weekly Workouts. These question papers (5 more have just been added) are designed for students on the Mathematics GCSE(9-1) Foundation level courses who are hoping to achieve one of the higher grades available. Each Weekly Workout contains 7 exam-style questions. The first six can be answered online but the seventh requires the student to draw something that needs the teacher to check. Each Workout can also be printed onto one A4 page.
  2. Practice Papers. These printable papers are designed to challenge students on the Mathematics GCSE(9-1) Higher level courses. Each question is similar to a question on one of the specimen papers produced by the exam boards for the 2017 exams. Full worked solutions are available for each question for Transum subscribers.
  3. Revision Tips. This is a page of suggestions and links to resources for anyone preparing for a mathematics exam. There are links to self-marking exercises on all the basic school mathematics concepts along with puzzles, games and investigations all designed to support revision.
  4. Syllabus Checklists. This part of the Transum Mathematics website contains a growing list of objective checklists for various common mathematics exams. Students can go through each objective and classify them as easy, OK or help! They can then print the objectives they have classified as requiring help and fill in the space for notes as their understanding develops.
  5. Exam Presentation. Save this for a week before the exam. It contains the tips and tricks that students might find useful when doing their last-minute preparation. You, as a subscriber, can download the PowerPoint version of the presentation so that it can be customised to suit your situation.

In addition to the items mentioned above, many other pages on the Transum Mathematics website have been updated or changed. A Starter called Tindice provides a quick, fun (when you know the answer) Starter to a busy Maths lesson but it can also be used to initiate an investigation into the sum and product of odd and even numbers.

I often help older students with their understanding of significance testing in statistics. In particular the chi-squared test is often clouded with strange precedents and terminology. A very short presentation called Significance has been developed to simplify the concept and to get the student to analyse the data provided by the Optical Illusions survey. As a subscriber you can see the results of the significance testing in real time. The students can use their GDCs to find the connections themselves. The presentation focusses on the big picture idea and leaves you as the teacher to fill in any gaps.

The Transum website was particularly busy in the weeks leading up to Christmas. Some of the ChristMaths activities had been updated and clearly people all over the world were enjoying them. If you missed out this year why don’t you send yourself a time-delated email (to arrive on the 1st December) reminding you of the URL. An email to yourself can be flagged as ‘Delay Delivery’ in many email programmes such as Outlook.

The answer to this month’s puzzle can be found by considering the following:

Think of the flea on a coordinate grid starting at the origin. If the flea only jumps in one direction it would end up at either (0,8), (8,0), (0,-8) or (-8,0).

Now consider the possible points in the first quadrant, (x,y) where x is the number of jumps east minus the number of jumps west and y is the number of jumps north minus the number of jumps south. It is probably a good idea to sketch these points on some graph paper and you will see the pattern created by the locations. Multiply the number of points in the first quadrant by four and add the ‘return-to-origin’ possibility to find the total.

The answer is 81 different places.

That’s all for now

John

P.S. If a got 50 pence for every time I failed a maths exam I’d have about £6.30 now.

7 New Resources for the Maths Classroom

Happy Christmas and welcome to the December 2016 edition of the Transum Mathematics newsletter. We will begin with the puzzle for this month: How many positive two-digit numbers are there whose square and cube both end in the same digit? The answer is at the end of this newsletter.

While you think about that, here are the seven new resources that have appeared on the Transum website since the last newsletter.

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  1. First Impressions

I was given the idea to create this fun data collecting application by Year 13 students working on projects including the chi-squared test. It was proving difficult and time consuming for them to collect their own data in sufficient quantities in order to meaningfully apply statistical tests. First Impressions asks the pupil for their initial perceptions of optical illusions. When the activity has been completed (it takes less than two minutes) the pupil is presented with the data collected from all of the other people who have also used this app. This data can then be used by the pupil for all sorts of graphs, charts and statistical analysis. Give it a go and share your ideas.

  1. Weekly Workout

With questions similar to those on the specimen papers produced by the exam boards for the forthcoming Maths CGSE(9-1), the Weekly Workouts provide half-hour revision papers for Foundation students aspiring to achieve the higher grades. The first six questions can be answered online just like the other Transum online exercises but the seventh question on each paper requires more drawing and is best done on paper with feedback from the teacher. The number of Weekly Workouts for Foundation level pupils is growing week by week. You have probably already seen the twenty Practice Papers for Higher students haven’t you?

  1. Brainbox

This number arranging puzzle was devised by Les Page and adapted as a Transum Mathematics interactive numeracy puzzle. There are twelve levels (and a few hidden bonus levels) arranged in increasing order of difficulty and there are efficient solving strategies that you will probably soon discover for yourself. Perfect for Year 5 pupils up to pensioners.

  1. Plinko Probability

This simulation describes the motion of a ball falling through a Quincunx (Galton Board) made out of pegs. In the intro tab, a ball has an equal probability of going to the left or right of the peg. The pupil can choose to send 1, 10 or all the balls though the board (up to a maximum of hundred) and watch how the balls fall into the different containers at the bottom of the board. A nice introduction to the normal distribution.

  1. Trigonometry Advanced

A self-marking exercise on the sine rule, cosine rule and the sine formula for finding the area of a triangle. The questions are carefully arranged in increasing order of difficulty preparing pupils for the linked exam-style questions.

  1. Triangle Solver

This new, powerful resource is a large triangle to project on to your whiteboard. Drag the vertices to make the triangle roughly the shape you want then type in three measurements, a mixture of sides and angles, then within the blink of an eye the other measurements magically appear. The triangle is solved!

This Solver is not only intended to be used with standard trigonometry or Pythagoras questions but also as a resource for students learning the basic construction skills with a rulers and pair of compasses. It also works well for a class practicing drawing angles using a protractor.

The teacher could manipulate the triangle to show a base of say 13cm. Either side of this base angles of 50° and 70° are shown. The class is then challenged to make an accurate drawing of the triangle and their accuracy can be measured against the actual values the Triangle Solver produces when everyone has finished their drawings.

Similarly a triangle with only the three sides given can be projected for a class practicing ruler and compass constructions. This time it is fun to compare the measured angles of the finished triangle with the ones the Triangle Solver calculates.

  1. ChristMaths Activities

Not strictly a new resource but certainly an updated one. Don’t be tempted to stray from Mathematics when planning those festive, end-of-term lessons when there are so many Yuletide treats in this collection.

The answer to this month’s puzzle is:

  • The nine two digit numbers that end in a zero;
  • The nine two digit numbers that end in a one;
  • The nine two digit numbers that end in a five;
  • The nine two digit numbers that end in a six;

These added together give a total of 36.

Enjoy the Christmas holiday and enjoy the ChristMaths activities,

John

P.S. Calendars, their days are numbered.

November 2016 News

Welcome to yet another newsletter from Transum Mathematics. As has become traditional I will start off with the monthly puzzle.

Trains from Punspace station go either north or south. Those going north leave hourly, those going south leave hourly. If I arrive at the station at a random time the probability that the next train to leave will be going north is five times the probability that the next train to leave will be going south. How could that be?

While you are thinking about that here is some news about the latest additions to Transum Mathematics.

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Kite Maths is a very visual, practical colourful activity leading to the discovery of important geometrical theorems. A new page of interactive animations created in Geogebra has now been added. These dynamic images are great visual aids for classroom use.

Some excellent interactive activities have been created by an organisation called PhET (Physics Educational Technology) and the mathematical simulations are being added to the Transum website. Founded in 2002 by Nobel Laureate Carl Wieman, the PhET Interactive Simulations project at the University of Colorado Boulder create these appealing Maths and Science simulations. They are based on extensive education research and engage students through an intuitive, game-like environment where students learn through exploration and discovery.

During October the following PhET activities have been added: Area Builder, Grid Arithmetic, Fraction Matcher, and Function Builder. You can find them by searching for activity title using the Transum search box (in the footer of every page) or by looking them up on the relevant topic page.

The activity called Clouds was updated last month. It has now been split into five levels and the higher levels include decimals and fractions. The idea of this activity is that clouds have magically floated across some calculations obscuring one of the numbers. Pupils need to find a strategy for working out what is behind each of the clouds. Teachers will see the link with algebra, rearranging formulae or solving equations.

The Mixed Numbers exercise has also been update. Level 5 now includes a variety of questions with words and diagrams! You as the teacher can decide whether pupils should be using this exercise to practice their pen and paper techniques or use it as a calculator exercise, making sense of the calculator’s strange fraction notation.

Coming very soon (hopefully by the end of this week) are some GCSE(9-1) practice papers for pupils on a Foundation level course. Each Weekly Workout contains 7 exam-style questions. The first six can be answered online but the seventh requires the student to draw something that needs the teacher to check.

The answer to this month’s puzzle is best understood by considering what the timetable for departures might look like. If the northbound trains leave at 10 minutes past the hour and the southbound trains leave at 20 minutes past the hour then there’s only a ten minute window for you to arrive at the station for the next train to be going south. There is however a fifty minute window for arriving to find the next train is northbound. Hence the probability that the next train to leave will be going north is five times the probability that the next train to leave will be going south.

Enjoy November

John

P.S. I don’t understand how to double 2n. It sounds 4n to me.

October 2016 News

This is the Transum Newsletter for October 2016, the 10th month of the year. Have you ever noticed that the month name begins with the suffix ‘Oct-‘ suggesting eight and not ten. There is a reason for that and a quick internet search will reveal it to you.

Let’s begin with the puzzle for this month which is about three hungry children.

There was a short queue in the school canteen. Ayden was directly in front of Betsy who was directly in front of Carl.

Aden’s age is an even number but Carl’s is odd. Is a person with an even age directly in front of a person with an odd age? The answer is at the end of this newsletter.

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I am very keen to tell you about some of the new additions to the Transum website that appeared last month. The first is Maths Mind Reader. Absolutely everyone I’ve used it with have been extremely impressed with this clever web page. As a Transum subscriber you will be see the mathematics that makes it work and Secondary pupils should be able to understand and even prove the concept.

A Transum website visitor, Les Page, sent me an addictive little puzzle he has devised called Zygo. He has kindly allowed a Transum interactive version to be created which is now ready to improve the numeracy and problem solving skills of your pupils. Thanks Les.

Pupils quickly learn to recognise and name regular polygons but the new activity called Polygon People may help younger pupils to name irregular polygons too. The activity has three levels and only accepts the correct spellings.

For the older pupils (14+) the Completing the Square and Proof of Circle Theorems activities should support those entered for the higher tier of the GCSE exams (or equivalent).

At times when I have not been creating new content for the website I have had a small amount of time to look at an updated app that I have downloaded to my iPhone. Photomath has been around for a couple of years but I’ve been very impressed with the recent improvements. You point your phone camera at an equation, and it will give you the answer and show you the working. I’m still amazed it can read my handwriting!

Photomath supports arithmetic, integers, fractions, decimal numbers, roots, algebraic expressions, linear equations and inequalities, quadratic equations and inequalities, absolute equations and inequalities, systems of equations, logarithms, trigonometry, exponential and logarithmic functions, derivatives and integrals.

My only reservation against using it with pupils is some of the phrases used to explain the stages of solving an equation. “Move constant to the right side and change its sign. Move variable to the left side and change its sign” is less helpful than the notion of doing the same thing to both sides in my opinion.

The answer to this month’s puzzle is yes. We don’t know Betsy’s age but we do know it is either even or odd. Let’s consider the two possibilities.

If Betsy’s age is odd then Ayden (even) is in front of Betsy (odd) and the answer is yes.

If Betsy’s age is even then Betsy (even) is in front of Carl (odd) and the answer is yes.

So regardless of Betsy’s age, the answer is always yes.

A similar problem was devised by Hector Levesque and it was included in Alex Bellos’ Guardian blog. Unbelievably 72 per cent of the 200,000 people who answered the question got it wrong.

That’s all for this month.

John

P.S. Why do mathematicians think that Halloween and Christmas are the same?

Because 31 OCT = 25 DEC (You need to know about the octal number system to understand this month’s joke 318 = 2510)

September 2016 News

If you live in the northern hemisphere you are probably starting a new school year so happy new year to you. Wherever you live you are welcome to the Transum Mathematics newsletter for September 2016. As usual I will begin with the puzzle for this month which is called Separated Twins.

The twins have a safe. The combination of the safe is a six digit number.

Within this six digit number there are two ones separated by one other digit. There are two twos separated by two other digits and there are two threes separated by three other digits.

What is the combination?

As there was no August newsletter there are two months’ worth of new content on the Transum website to tell you about. Let’s begin with the Mathematical Optical Illusions.

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This has proved to be a useful visual aid to use while revising some basic geometrical facts with pupils. The illusion bit provides the motivation to study the diagram while you, as the teacher, can sneak in the revision questions such as ‘what is formula for the area of a circle?’, ‘What does arc mean?’ and ‘Name four different types of triangle’. I’m sure you could come up with suitably challenging questions for your pupils as you work your way through the different illusions.

Most Transum subscribers are Secondary/High School teachers but there is a significant proportion of primary teachers too.

Pie

This next item is only really relevant to Secondary teachers preparing pupils for GCSE or IGCSE exams. In the UK, next May sees the first of the new style 9 to 1 grade GCSE exams. The Transum think tank has studied the sample assessment materials produced by the exam boards and come up with similar practice questions along with fully worked solutions. These questions have been collected together into 20 practice papers which print nicely onto A4, double sided paper.

One Minute Maths is a hoot! So funny to see good mathematicians making the classic mistake. It’s a bit of fun but highlights a valuable place value, carrying issue. Give it a try (when no one is looking).

Puzzle Cube is a multi-level challenge based on the idea of a Rubik’s-style cube presented as a net. At the time of writing only one person has managed to earn a trophy for the hardest level.

Pupils in general always need more practice with basic mental arithmetic so the more different activities you have to provide that practice the better. Here’s a new two player game for your collection. It’s called Tug of War and has levels for each of the four rules. It can also be played with any of the many Pairs games on the Transum website. Scroll down the Tug of War page to see the links.

You probably already know that there are a range of times tables activities available on the Transum website but Hard Times is new. It is nothing to do with the Charles Dickens novel but is so named as it isolates the hardest times tables facts according the data collected from over ninety thousand trials as can be seen on the Statistics page.

The Calculator Workout page is a visual aid which demonstrates key skills with a common scientific calculator.

The latest pairs game is about Circle Angle Theorems. Not a substitute for practice answering questions and solving problems but a fun support activity.

I hope you enjoy the new activities on Transum.org. Don’t forget that if the website should ever go offline (let’s hope not) you can still get to your favourite activity by using one of the two mirror sites Transum.info and Transum.com. Currently you cannot log in as a subscriber on the mirror sites but if the main site looks as though it will be down for a long time that will change.

The answer to this month’s puzzle is 3 1 2 1 3 2 (or that number with the digits reversed). If you thought it was too easy you can see how this type of puzzle can be extended by looking at the Starter for September 18th.

That’s all for now. Have a worthwhile, satisfying and productive September,

John

Ps The combination locks on safes should really be called permutation locks because it does matter what order the digits are entered.

July 2016 News

Before reading the rest of this newsletter you are challenged to find five two digit numbers that are multiples of three. The ten digits used in your five numbers must all be different!

Well that’s the puzzle for this month. The answer will be at the end of this newsletter.

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More brand new activities have been added to the Transum website during the last month; the very latest of which has only just been uploaded. It is called Bidmaze and is a numeracy challenge requiring guiding a token through different mazes picking up mathematical operations on the way. Successfully completing a stage requires that the order of operations produces the given target. There are ten stages in each level and three levels. Level 1 targets the four basic operations with positive numbers. Level 2 extends level 1 to include negative numbers and level 3 includes finding squares and square roots. It is quite addictive!

Snooker Angles is a game for one or two players or teams. It involves the ability to estimate the angle (or bearing) of the direction the ball should travel to go into any one of the six pockets around the border of the snooker table.

Where’s Wallaby is an activity for pupils involving coordinates and, for those who have learned it, Pythagoras’ theorem. Choosing coordinates on a grid will reveal the distance away that a hiding wallaby is lurking. Pupils will find themselves considering the loci of all possible hiding places before making their next guess. Transum subscribers have access to the settings to change the way the clues are given and how many wallabies must be found before a trophy is awarded.

23 or Bust is a favourite game I have played with classes I have taught over the years. This new interactive version of the game is designed for two players or one player against the computer. By playing the game a number of times pupils will start to realise that there is a strategy to be revealed. An optional printable worksheet is provided to help pupils understand the strategy.

Counter couldn’t be simpler. The title says it all, it counts! This resource can be found in the Shine+Write collection and is designed for teachers to project in the classroom for a number of learning experiences.

Finally Standard Order provides a drag-and-drop list of numbers in standard form for pupils to sort. Another example of an interactive task that can’t be provided in a hard-copy textbook.

For future reference there are two ‘mirror’ sites that contain all the Transum Starters and activities. They are at www.transum.com and www.transum.info The only difference is that they don’t contain the details of your Transum subscription account so you won’t be able to log in there. If it looks like Transum.org will be offline for a long time then I will transfer the database containing your details to Transum.com so you will eventually be able to log in there too.

There are many correct solutions to this month’s puzzle but here is one: 12, 36, 45, 78 and 90.

Did you know there is a trick for quickly determining if a number is divisible by three? You can find it with similar tests for divisibility on the Divisibility Tests page.

You can find more challenges similar to this month’s puzzle, ready made to project for your Maths class, on the Hot Numbers Challenges page.

That’s all for this newsletter

John

P.S. There are three types of people in the world, those who can count and those who can’t.

 

June 2016 News

This month’s puzzle is all about numbers when written as words.  Take the smallest positive whole number containing the letter ‘a’ away from the smallest positive whole number containing all of the vowels.

Add to this total the number that has the same number of letters as its value and then add the largest number that has only one syllable.

Divide this total by the number which has all of its letters in alphabetical order.

That should keep you busy if you resist the temptation to peep at the answer at the end of this newsletter!

May was another busy month adding and improving content on the Transum Mathematics website. Here are the highlights:

The BIDMAS logo has been redesigned to show that division does not always come before multiplication as those two operations should be evaluated from left to right. The same is true for addition and subtraction. What do you think?

BIDMAS

Investigating the properties of algebraic graphs has been transformed over the last ten years with the widespread use of graphic display calculators and graph plotting software on computers and mobile devices. On Transum you can now access the wonderful Desmos on the new Graph Plotter page. The suggested investigations are in draft form at the time of writing but will be developed further during this month.

In addition to the Graph Plotter is a Graph Patterns exercise which allows pupils to earn trophies for recognising the graphs and correctly finding their equations. There are currently two levels containing linear (level 1) and quadratic (level 2) graphs.

A new Collecting Like Terms exercise has been added with links to exercises on using brackets and expanding products of two binomials.

For older students in the middle of exam revision there is a new page containing a growing list of objective checklists for various common Maths exams. The checklists are presented in an interactive format which allows students to go through each objective and classify it as easy, OK or help!

The Areas Investigation and How Many Squares (2) pages now have camera icons appear each time a shape is completed. This interface allows pupils to find shapes and then drag the ‘photos’ they have taken into some kind of order to help spot missing shapes.

Subscribers have access to the Worksheet section of the website and a printable page for teachers has just been added. It is a very simple idea but something you may find useful. When you have finished marking a lot of test papers it speeds up the task of converting a lot of test scores to percentages. It is called Test Scores To Percentages.

This idea will only save you a small amount of time compared with using a calculator or a spreadsheet but every second counts when you have a pile of marking in front of you. I personally have found it useful for speeding up the conversion and rounding of percentages for many years of test marking. You could also put tally marks next to the scores to get a quick picture of the spread of the marks.

Finally here is the answer to this month’s puzzle:

  • The smallest positive whole number containing the letter ‘a’ is 101.
  • The smallest positive whole number containing all of the vowels is 1005.
  • The number that has the same number of letters as its value is 4.
  • The largest number that has only one syllable is 12.
  • The number which has all of its letters in alphabetical order is 40.

The calculation is (1005 – 101 + 4 + 12) ÷ 40

The answer is 23.

That’s all for this month,

John

P.S. If the test question is three minus the square root of nine you can write down nothing but get full marks!

May 2016 News

Hello and welcome to the newsletter for May 2016 which begins with this month’s puzzle for your pondering pleasure!

A particular triangle is drawn such that each of its angles are square numbers. What are those angles?

Too easy? Well consider a quadrilateral having all four angles as square numbers. What would they be? The answer is at the end of this newsletter.

This month saw the OCR exam board produce more ‘Check In’ tests as free-to-download pdf files on its website. These ten-question tests are proving to be very useful with Year 9 and Year 10 pupils. Each topic in their new GCSE syllabus has been mapped to a Check In containing questions relating to the initial learning required. Questions 1-5 cover procedural calculations, Questions 6-8 assess the learner’s ability to reason and communicate mathematically and Questions 9-10 relate to problem solving tasks.

OCR also produced a delivery guide for Mensuration and it was rewarding to see that a number of the sections within the guide contained links to Transum activities.

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As usual there have been lots of updates and new content added to the Transum website this last month. The most recent addition is Digital Darts. A soon as it went live a couple of days ago it received hundreds of views and people began collecting trophies for completing the activity or winning the game. It provides a suitably challenging mental exercise for more able pupils while those who cannot cope with the mental manipulation can practise their written methods of addition and subtraction. As a subscriber you have the option to change some of the features of the game to make it easier (or harder!).

Another game that provides practice in a format more motivating than a traditional exercise is the BIDMAS Game. Players are challenged to claim squares on a grid by making given totals with the numbers that are randomly generated by four dice. This could make an engaging last ten minutes of a Maths lesson activity with the teacher challenging the whole class working as a team.

A gap in the Transum offerings has been filled with a Gradient of a Line twelve-question exercise. The questions are diagrams from which the gradient can be calculated by counting squares and then dividing rise by run. This exercise provides a small part of a larger learning experience about straight line graphs.

Another pairs game has been added. This one requires players to match digital and analogue times. This is another game that might work well if played as a teacher versus the whole class challenge at the end of the lesson.

One of the podcasts I enjoy listening to is Futility Closet. In a recent episode (number 103) some little-known mathematical history was described. In 1897, confused physician Edward J. Goodwin submitted a bill to the Indiana General Assembly declaring that he had squared the circle, a mathematical feat that was known to be impossible. The podcast episode examines the Indiana pi bill, its colourful and eccentric sponsor, and its celebrated course through a bewildered legislature. It’s definitely worth a listen!

Finally the answer to this month’s puzzle. The angles of the triangle are 16ᵒ, 64ᵒ and 100ᵒ. The angles of the quadrilateral could be 16ᵒ, 100ᵒ, 100ᵒ and 144ᵒ but if the quadrilateral was a symmetric trapezium they could be 36ᵒ, 36ᵒ, 100ᵒ and 100ᵒ. This puzzle is in fact the Starter for April 7th.

That’s all for now,

John

p.s. Try to avoid doing calculus when you are thirsty. You have heard the warning, don’t drink and derive!

April 2016 News

Easter has come early this year which means that many schools are currently still closed for the Easter holidays. That’s a pity! It means that you don’t get the opportunity to fool your pupils with the 1st April Starter. Next year maybe?… No, April 1st falls on a Saturday next year. Perhaps you could use the ‘One Out Of Ten’ joke on another day of the year.

The puzzle for this month is about three cars arriving at a three way junction at high speed. The junction has a triangular (ish) traffic island at the centre and each car has a 50% chance of turning left and a 50% chance of turning right when they arrive at the island. What is the probability of no collisions taking place?

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The answer can be found at the end of this newsletter.

March was another busy month for adding content to the website. The most significant addition is Refreshing Revision, the ultimate customisable Starter. It is called Refreshing Revision because every time you refresh the page you get different numbers and diagrams in the questions. Scroll down the page to see and select the concepts you want to be included in the Starter. It should be useable with pupils in Year 5 (with the times tables questions) all the way up to Year 11 (revising for exams).

I will continue to add more concepts to this during this month but if you have any suggestions please let me know.

The leader boards for TablesMaster and Fast Factors have been adapted so that you can filter out all but pupils from your own school. Instructions explaining how to do that are available on the Times Table Filter page. Many thanks to Matt Curtis from Edgewood School for suggesting this idea.

The Times Tables page contains links to many activities pupils can do to improve their recall of multiplication facts. A new activity was created last month called Times Square. It has nothing to do with that famous location in New York but lots to do with providing yet another way for pupils to practise their tables. The completed tables square comes complete with buttons to show some of the geometric patterns created by sets of numbers in the grid.

A number of videos found on YouTube have been added to the curated list but the one that stands out is the one about the mathematical puzzles found in an episode of the Simpsons called Mathlete’s Feat.

I was surprised recently that one of my pupils, who has strong abilities in most areas of mathematics, didn’t know the order of the months of the year. A drag and drop activity was created which he will use as part of his regular recap activities and also help him to remember the number of days in each of the Months of the Year.

Whenever I am teaching probability I would try hard to include a little bit of fun with the Snail Race. It can be adapted to a wide range of abilities and lead to some interesting questions. Last month Ben from New Zealand asked the ultimate question about snail number seven’s chance of winning the race. We have still not been able to come up with the answer but you can follow the discussion on the Snail Race Teacher’s Version page. If you are an expert in Negative Binomial Distributions we need to hear from you!

Previous newsletters can be found with podcasts (the audio versions of the newsletters) online and for the latest news of Transum updates follow @Transum on Twitter. Thanks to all you who have left comments on the Transum web pages and sent feedback about how your pupils have enjoyed using the resources.

Finally the answer to the Tri-junction puzzle. As a subscriber you can see a tree diagram which can be used for solving this puzzle on the Tree Diagrams Challenge page. The answer can be found by considering the probability of all three cars turning left or all three cars turning right. The answer is 0.53 + 0.53 = 0.25 or 25%.

Enjoy the month of April.

John

ps. Parallel lines have so much in common it’s a pity they’ll never meet.

March 2016 News

Welcome to the March 2016 Transum Mathematics newsletter.

I hope you made use of the 29th February Starter last month because it only appears every four years.

594The Tower of Hanoi Puzzle

As usual we will begin with the puzzle of the month. What is the smallest square number (greater than one) that cannot be expressed as the sum of two prime numbers? The answer is at the end of this newsletter.

There’s nothing like a good puzzle involving prime numbers. Opportunities to remind pupils of what prime numbers are and how important they are as the building blocks of the number system are perhaps too infrequent for many pupils. Transum has a number of activities which can be found by typing the word prime into the search box at the bottom of any Transum page.

‘Prime Numbers’ is one of the few school mathematics topics that occasionally appears in the news. A new prime more than 22 million digits long, five million longer than the previous largest known prime was found recently. This number, the 49th known Mersenne prime, was discovered by Dr Curtis Cooper at the University of Central Missouri. Large prime numbers are important in computer encryption and help make sure that online banking, shopping and private messaging are secure.

Don’t forget to include some of the amazing facts about prime numbers when you are teaching the basics. It will capture the imagination of some pupils and ensure the learning is long-lasting. The podcast version of this newsletter contains many more interesting prime facts.

So what has changed on the Transum website since the last newsletter? Each page gets a makeover when it reaches its third birthday but also new content is being added every month.

A Similar Shapes self-marking exercise has been added. This topic is one that typically defies intuition. When the dimensions of a solid are doubled, its volume increases by a factor of eight and facts such as that are quite hard for pupils to appreciate.

Another self-marking exercise provides practice in finding the nth term of quadratic sequences. It is not a skill every pupil will need, only those on course for higher grades, but this randomly generated quiz should prove to be a handy tool for the busy teacher.

The Human Graphs visual aid is proving to be hilarious. It has not failed to bring a smile to the faces of all those who have used it so far. It makes fun the process of recognising the shapes of the graphs of simple polynomials and really brakes the ice in any Maths lesson.

The Ludicross Puzzle challenges pupils to arrange the given numbers on the cross so that the sum of the numbers in both diagonals is the same. It is quite easy to find one solution but finding all the possible different solutions is another challenge.

Once the basics of arithmetic with negative numbers has been mastered, the Negative Magic puzzles will provide some of the practice required to consolidate the understanding. This is another randomly generated, self-marking activity that can be used many times with the same pupils.

There are many versions of the Tower of Hanoi puzzle on the internet but this one encourages pupils to find a pattern in the number sequence generated. There are a total of ten different levels but it is not expected that anyone will have the time to do the higher levels as far too many moves are required. Level 10 of this puzzle featured in an episode in the 1966 Doctor Who story called The Celestial Toymaker. The villain forces the Doctor to work on a ten-piece Tower of Hanoi puzzle (which they call The Trilogic Game) and if the Doctor manages to complete the puzzle, the Toymaker’s domain would disappear.

Finally sometimes the simplest ideas are the most useful. The Place Value Chart is certainly nothing new but the functionality it provides may help you make sense of this important yet basic topic.

Your thinking time is up! The answer to the puzzle posed at the beginning of this newsletter is 121. Did you, in the process of arriving at this answer notice that every other sum of two primes adding up to a square number included the number two? Can you think of an explanation for that?

Enjoy the month of March

John

ps. All prime numbers except 2 are odd, this makes 2 the oddest prime!