# 7 new additions to Transum Mathematics

Here is the Transum Mathematics Newsletter for May 2017. As last month’s puzzle was quite difficult (particularly if you did not have access to pen and paper), this month’s is a little easier. It’s the sort of puzzle that you could throw out to your pupils at the end of the lesson and is inspired by the forthcoming exam season.

Mac has taken seven maths exams this year. His average mark is 78%. What mark must he get on the eighth exam to raise his average to 80%?

While you think about that I’ll alert you to some of the new content added to the Transum website this last month.

The Manifest Game

Manifest: This is a new game that I have played with some pupils and the excitement it generated was immense. I thoroughly recommend it if you would like to end your lesson with a little bit of strategical thinking thinly disguised as fun. The rules of the game couldn’t be simpler.

Players take turns arranging their cards to make a single digit number, a two digit number, a three digit number and a four digit number. They should do this while the other player is not looking. The player with the largest single digit number wins one point, the largest two digit number wins two points, the largest three digit number wins three points and the largest four digit number wins four points.

The Transum interactive version of the game is designed to build suspense and anticipation at the ‘compare numbers’ stage. Give it a go, you will love it.

Screen Test: A selection of short (one to two minutes) factual videos have been chosen for this test of memory. When the video has finished playing you can reveal the mathematical questions about the video. The first questions test recall while the latter questions require application of the facts. A little bit of variety in a Maths lesson can be provided by this five-minute activity.

Bearings: A five-level, self-marking quiz on three-figure bearings. Level 2 is a measuring exercise with an online protractor provided. If you are planning on using this activity with your pupils be sure to develop bearing estimation skills first by using the Plane Bearings visual aid.

Box Plots: Level 3 of this online exercise is a major new manipulative feature. Pupils can drag the handles on the box-and-whisker diagrams to create the correctly-aligned box plot.

Averages: Not strictly a new activity (3528 people have already earned a Transum Trophy for completing it) but this online exercise has been updated and some of the levels changed.

For most of the online exercises the Check button can now be double clicked to make it float at the bottom of your screen. This makes it much easier to check answers as you are working through an exercise rather than just at the end. Transum excises are designed for frequent checking and the pupil is encouraged to change wrong answers and click the Check button again.

Many schools have direct links to Transum activities in their schemes of work and at least one of the major exam boards links to Transum activities in their publications. There is now a short URL for each activity (scroll down the page to find it) making it easier for teachers to include the link in their scheme of work or learning management system. The short link is also ideal to show or send to pupils.

It is not too long now until some of your students sit the brand new GCSE(9-1) examinations. Many people have talked about how the new numbered grading system will be understood by those outside education who have been used to the lettered grades. When I took my O Level Maths exam in 1974 it was also a set on numbered grades but going in the opposite direction; the top grade was a one!

An amusing reflection on the new 9-1 grades was included in the News Quiz on BBC Radio 2 last week. The excerpt has been included in the podcast version of this newsletter.

Talking of Maths exams, I would like to invite you to send your pupils a pre-exam present. Send them the URL of the Transum Exam Revision page. The page contains tips and links to useful revision resources such as my Exam Tips Presentation (a poem) and the Exam-Style questions.

But if they have done too many past papers already how about inviting them to take the Tran Tunnels adventure which is full of GCSE style activities and accompanied by music (The Goldberg Variations).

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

In order for his average mark on eight exams to be 80% the total of the percentages on all eight exams must be 8 x 80% = 640%

His total percentage on the first seven exams is 7 x 78% = 546.

Therefore the mark he must earn on the eighth exam is 640 – 546 = 94%

That’s all for this month.

John

P.S. Theorem: a cat has nine tails.

Proof: No cat has eight tails. A cat has one tail more than no cat. Therefore, a cat has nine tails.

# 7 great Maths games to play instead of doing traditional exercises.

Before getting into the main theme of this newsletter let’s begin with this month’s puzzle.

A 10cm long cylindrical hole is drilled straight through the centre of a solid sphere. What is the volume of the remaining part of the sphere? The answer is at the end of this newsletter.

A good mathematics exercise is structured to lead the learner through from simple, confidence-building questions to harder questions that deepen understanding. In addition to this an exercise should provide the repetitive practice needed to fuse the method into long term memory.

To prevent this repetitive practice becoming boring the exercise could be presented in the form of a game so that the same objectives are achieved in a more fun-filled, exiting manner. Here are seven Transum games that work well with learners of a wide range of ages.

• Pairs Games for remembering connections whether it be parts of a circle and their names or common fractions and their decimal equivalents.
• Digital Darts is an online game for one or two players requiring skill, strategy and lots of mental arithmetic.
• Rounding Snap is a fast and furious game. If the last card put down equals the previous card to the nearest whole number then all players race to shout SNAP!
• Connect 4 Factors a game for one or two players. The winner is the first to line up four numbers with a common factor.
• Choose Your Average is a game for two players. You should know how to find the mean, median and range of a set of numbers before starting this game.
• Two Dice Bingo is a whole class game. Use it to provide a purpose for drawing up a possibility space.
• Hi-Low Predictions A version of the Play Your Cards Right TV show. Calculate the probabilities of cards being higher or lower.

And two brand new games this month both provide practice related to number sequences:

Watsadoo requires quick thinking. Players need to quickly identify the falling numbers as odd, even, square, cube, triangular or prime. At the time of writing no one has successfully complete a level greater than two.

The Square Pairs Game is for two players who take turns to select two numbers that add up to a square number. Please try this game and let us know any strategies you invent!

Another new activity is called Mix and Math. Determine the nature of adding, subtracting and multiplying numbers with specific properties.

Upper and Lower Bounds is a traditional exercise with five levels of difficulty. Learners have to determine the upper and lower bounds when rounding or truncating quantities used in calculations.

Finally an new set of Circle Game cards has been added so you can play this whole class game with simple equations.

Now for the answer to the puzzle presented at the beginning of this newsletter.

One approach is to let the sphere have a radius, say R, and then do some calculations using the formulas for the volumes of a sphere, cylinder and a spherical cap. A much quicker method however requires a little creative thinking. As the puzzle has been presented in this newsletter you can assume that there is a solution. As the size of the sphere is not given it is reasonable to assume the solution is independent of any sphere dimensions. In that case you can consider the limiting case, one in which the radius of the sphere is 5cm and the radius of the spherical hole is zero. The remaining volume would then be the total volume of the sphere which equals 524 cubic centimetres to three significant figures.

Don’t forget to look at all of the GCSE(9-1) questions on the Transum website now that we are in countdown mode.

That’s all for this month,

John

P.S. There are 10 kinds of people in this world. Those that understand binary and those that don’t.