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.

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.

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?

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.

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.

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.

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.

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.