If all the students in this room shook hands with each other, how many handshakes would there be altogether?

## A Mathematics Lesson Starter Of The Day

• Mr Martin Magic Maths Set, Dulwich College Beijing
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• My Y5 class found this very challenging but it really got them thinking. In the end we found the solution!
• Mr J Saye, Castle Rock High School
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• Katie S in my Year 8 Set 1 class found that if you do the multiplication for one less than how many there are in the group and half it you get the correct answer,
eg. For a class of 20 19 x 20 = 380 / 2 = 190
this is becasue the multiplication shows everyone shaking others' hands and them shaking back which would be a double hand shake which is why you half the answer.
• Mr Paul Bridges, Cantell Maths And Computing Cilloge
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• The formula for this is 0.5n^2 - 0.5n, where n is the number of people.
• Miss. Loi, 10Y3
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• We have a class of 30 here at Woodbridge High School in Essex.
Gintaras found that 30 x 29 then halved = 435
Therefore there would be 435 handshakes!!
We loved this starter....
• 7T3, Homewood School And Six Form Center
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• In our class we have 26 people and we times 26X26 and we got 325.
• Y6, Jubilee Primary School
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• We enjoyed this problem and came up with a similar method as mentioned above, but took a while to figure out the halving. One pupil also mentioned the mathematician Johann Carl Friedrich Gauss and his theory of rings (I have no idea what he was talking about, but he was right) Basically in our class we have 25 pupils present so he did 12 x 25 becahe had halved 24 (the number of one person's handshakes) then multiplied by the number in the class. He found 12 by doing 24+1, 23+2, 22+3 etc... until the two numbers touched.
• Miss Kaplan, Harrold Priory
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• Used this with my Y5 class during form time. It was great for eliciting maths discussions and getting them to really think about the problem. They needed a prompt to think about how many handshakes each person should do but we got there in the end! Same formula as everybody else.
•

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Previous Day | This starter is for 8 November | Next Day

 No. of Students No. of Handshakes 1 0 2 1 3 3 4 6 5 10 6 15 7 21 8 28 9 36 10 45 11 55 12 66 13 78 14 91 15 105 16 120 17 136 18 153 19 171 20 190 21 210 22 231 23 253 24 276 25 300 26 325 27 351 28 378 29 406 30 435 31 465 32 496

## Extension

Can you find a formula for the number of handshakes given the number of students?

If instead of handshakes, each student in the room gave every other student a present, how many presents would be given?

Christmas Present Ideas

It is often very difficult choosing Christmas presents for family and friends but so here are some seasonal, mathematics-related gifts chosen and recommended by Transum Mathematics.

## Equate board game

Here's a great board game that will give any family with school-aged kids hours of worthwhile fun. Christmas is a time for board games but this one will still be useful at any time of year. Games can be adapted to suit many levels of Mathematical ability.

For Maths tutors working with just one or small groups of pupils this game has proved to be an excellent activity for a tutorial. Deciding on the best moves can spark pertinent discussions about mathematical concepts.

Equate looks a bit like Scrabble--for aspiring mathematicians, that is. Designed by a real mathematician, it works like this: You put down tiles on a board and make points by correctly completing simple equations. Your nine tiles include both numbers and mathematical symbols; you can add on to previous plays both vertically and horizontally. more...

## How Not To Be Wrong

The maths we learn in school can seem like an abstract set of rules, laid down by the ancients and not to be questioned. In fact, Jordan Ellenberg shows us, maths touches on everything we do, and a little mathematical knowledge reveals the hidden structures that lie beneath the world's messy and chaotic surface. In How Not to be Wrong, Ellenberg explores the mathematician's method of analyzing life, from the everyday to the cosmic, showing us which numbers to defend, which ones to ignore, and when to change the equation entirely. Along the way, he explains calculus in a single page, describes Gödel's theorem using only one-syllable words, and reveals how early you actually need to get to the airport.

What more could the inquisitive adult want for Christmas? This book makes a cosy, interesting read in front of the fire on those cold winter evenings. more...

## Graphic Display Calculator

This handheld device and companion software are designed to generate opportunities for classroom exploration and to promote greater understanding of core concepts in the mathematics and science classroom. TI-Nspire technology has been developed through sound classroom research which shows that "linked multiple representation are crucial in development of conceptual understanding and it is feasible only through use of a technology such as TI-Nspire, which provides simultaneous, dynamically linked representations of graphs, equations, data, and verbal explanations, such that a change in one representation is immediately reflected in the others.

For the young people in your life it is a great investment. Bought as a Christmas present but useful for many years to come as the young person turns into an A-level candidate then works their way through university. more...

The analytics show that more and more people are accessing Transum Mathematics via an iPad as it is so portable and responsive. The iPad has so many other uses in addition to solving Transum's puzzles and challenges and it would make an excellent Christmas gift for anyone.

You have to hold iPad Air to believe it. It’s just 7.5 millimeters thin and weighs just one pound. The stunning Retina display sits inside thinner bezels, so all you see is your content. And an incredible amount of power lies inside the sleek enclosure. So you can do so much more. With so much less. more...

## Aristotle's Number Puzzle

It’s a bit of a tradition to give puzzles as Christmas Gifts to nieces and nephews. This puzzle is ideal for the keen puzzle solver who would like a challenge that will continue over the festive period (at least!).

This number puzzle involves nineteen numbers arranged into a hexagon. The goal of the puzzle is to rearrange the numbers so each of the fifteen rows add up to 38. It comes in a wooden style with an antique, aged look.

Keep the Maths in Christmaths with this reasonably priced stocking filler. more...

## The Story Of Maths [DVD]

The films in this ambitious series offer clear, accessible explanations of important mathematical ideas but are also packed with engaging anecdotes, fascinating biographical details, and pivotal episodes in the lives of the great mathematicians. Engaging, enlightening and entertaining, the series gives viewers new and often surprising insights into the central importance of mathematics, establishing this discipline to be one of humanity s greatest cultural achievements. This DVD contains all four programmes from the BBC series.

Marcus du Sautoy's wonderful programmes make a perfect Christmas gift more...

Click the images above to see all the details of these gift ideas and to buy them online.

 Teacher, do your students have access to computers?Do they have iPads or Laptops in Lessons? Whether your students each have a TabletPC, a Surface or a Mac, this activity lends itself to eLearning (Engaged Learning).

Transum.org/go/?Start=November8

Here is the URL which will take them to a related student activity.

Transum.org/go/?to=MysticRose

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