# Maths Advent Calendar

Glad tidings and welcome to the Transum Subscribers’ Newsletter for December 2018. I am writing it a few days early due to the fact that I’ll be enjoying a weekend break in the sun when I would have normally written this on the first of the month. Lucky me!

Let’s begin with a festive theme. Here is the puzzle of the month:

St Nicolas’ Yuletide Choir is rehearsing daily for the local school’s Christmas assembly. Each member of the choir has blonde hair or blue eyes; One quarter of the members with blonde hair do not have blue eyes and one third of the members with blue eyes have blonde hair.

What percentage of the choir members do not have blue eyes? The answer is at the end of this newsletter.

As soon as November is over it is quite acceptable to have a festive theme to your Maths lessons. To support this you can, starting on the 1st December, open a door of the Maths Advent Calendar and for each of the days leading up to the 25th enjoy a seasonal activity (from the Christmaths collection), laugh at a cracker joke and solve a mathematical word puzzle. Transum subscribers are able to open doors before the corresponding dates by using the unlock button which can be found lower down the Advent Calendar page when you are signed in.

This last month I have been working enthusiastically improving and adding to the resources at Transum.org. I have just finished Parallel Vectors, yet another activity in the Vectors collection. It is a quick, drag and drop, challenge to match vector expressions with others that represent parallel vectors.

I then copied that activity format to produce Parallel Graphs requiring the rearrangement of equations into the y=mx+c format to find their gradients.

A new vector activity that will appeal to a wider range of pupils is called Vector Maze. Already many have earned Transum Trophies for completing it and the optional challenge is to find the shortest route from start to finish. Chick on the instructions tab to see the latest world record.

Convoluted is the name I plucked out of the air for another brand new activity providing practice recognising multiples. There are three levels with the first including multiples of 2 to 5 while the last level includes multiples up to 12. Pupils can time themselves completing a level and work to improve their personal bests.

Don’t forget there’s also an audio version of this newsletter in the form of a podcast. This month the podcast also includes an advert I heard on Heart Radio for Maths teachers which I quite liked.

Thousands of Transum Trophies are earned by pupils each week from locations across the globe. You may be surprised to hear that the top trophy earner (going by the name of Algebromaths) currently has 797 trophies in his or her trophy cabinet. Amazing!

The answer to this month’s puzzle is 10%. Sketch a Venn diagram with two overlapping circles representing blond and blue. Write x in the region representing the fraction of members with blond hair but not blue eyes. Now use the clues in the question to write the fractions of the members in the other two regions in terms of x. Now form an equation showing the three expressions you have written sum to one. Solve the equation to find x, the percentage of the choir members that do not have blue eyes.

Merry Christmas,

John

1. Deck the halls with boughs of holly, Fa (La)9

# Christmaths Activities

As December has begun I hope you don’t consider it too early for me to wish you a Merry Christmas. As usual this newsletter will begin with a puzzle of the month. A slightly more difficult puzzle this month that could keep you thinking right through the holiday.

Young Noel Stocking checked his bank account to see how much money he had to buy Christmas presents. When he recorded the balance he wrote down the number of pence for pounds and the number of pounds for pence. A transposition error. “Wahoo” he exclaimed “I’m rich!”

While in this good mood Noel promised 50p to his younger sister Merry. He adjusted his record accordingly which now turns out to be exactly double the amount in the bank.

How much does Noel have in the bank?

Many of the activities on the website have been updated during November and, in preparation for the festive season, the Christmaths collection has been brightly polished. Here are my favourites:

Christmas Ornaments: A puzzle which can be solved online or by using the printable boards so the task can be done in a very practical way with real Christmas ornaments. Problem solving, trial and improvement and logic all wrapped up in one for Christmas.

Christmas Eve Snow: This is a letters-replace-digits puzzle which comes with clues and, if you scroll down to the bottom of the page, a step-by-step guide for solving this kind of puzzle.

Christmas Tables: This is the special Starter for Christmas Day. When I first saw the Betty Edwards drawing I was amazed that the sense of perspective is so powerful. You will need Flash to view the animation.

Cracker Joke: This is a basic numeracy activity where answers to simple calculations are converted to letters to spell out a maths joke. Each time the page loads the calculations change. You can change the joke too.

The Power of Christmas: This Starter works well with Year 11 and Year 12 pupils as it tests their understanding of indices. Finding one solution is fine but the real challenge is to find all four solutions.

The Twelve Days of Christmas: This is a well-worn and time-honoured problem that’s certainly doesn’t deteriorate with age. I particularly like the solution as sung by Natalie Cole.

Christmas Tree Trim: This is just one of the activities on the Transum website that allows pupils to demonstrate their systematic listing skills. There are eight levels of difficulty and a trophy available for each level.

The links to all of these activities (and more) can be found on the Christmaths page. The last week of term is a great time to do some out-of-the-ordinary mathematics with your pupils and there are plenty of ideas on that page. In my experience some of the end-of-term, fun maths has turned out to be the most memorable and enjoyable learning my pupils did all year!

Have your pupils encountered the binary system? There is a visual aid you can use called Binary Lights to demonstrate how binary works. The reason I mention this is that recently I heard a nice idea about counting on your fingers. It’s common knowledge that you can count to ten with the help of fingers and thumbs but if you use binary you can count up to over 1000! Scroll down the Binary Lights page to see a video demonstration.

The answer to this month’s puzzle is £16.33. I found this answer with the aid of a spreadsheet. Please let me know if you have another way of finding this answer.

That’s all for this month

Enjoy the holiday

John

Q. How is an artificial Christmas tree like the square root of minus nine?

A: Neither has real roots!

# 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.

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.