If all the students in this room shook hands with each other, how many handshakes would there be altogether?
Topics: Starter  Investigations  Number  Problem Solving
Solving the classical #handshakes problem in a #maths lesson with a difference. #GirlsInSTEM pic.twitter.com/cWQKcSf4AC
— MSY_STEAM (@MSY_STEAM) October 10, 2017
How did you use this starter? Can you suggest
how teachers could present or develop this resource? Do you have any comments? It is always useful to receive
feedback and helps make this free resource even more useful for Maths teachers anywhere in the world.
Click here to enter your comments.
If you don't have the time to provide feedback we'd really appreciate it if you could give this page a score! We are constantly improving and adding to these starters so it would be really helpful to know which ones are most useful. Simply click on a button below:
This starter has scored a mean of 3.2 out of 5 based on 631 votes.
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 
Can you find a formula for the number of handshakes given the number of students?
Edward and Lucy invite four couples to dinner. Each person shakes hands only with the people that he or she has not met before. Edward then asks his wife and eight guests how many hands they shook, and he receives nine different answers. How many people did Lucy shake hands with?
Bellos, Alex. Can You Solve My Problems?: a Casebook of Ingenious, Perplexing and Totally Satisfying Puzzles. Guardian Books, 2017.
Your access to the majority of the Transum resources continues to be free but you can help support the continued growth of the website by doing your Amazon shopping using the links on this page. Below is an Amazon search box and some items chosen and recommended by Transum Mathematics to get you started.
Have you read Craig's book yet?Craig Barton must surely be the voice of Mathematics teachers in the UK. His wonderful podcasts interviewing the industry experts have culminated in this wonderful book. As Craig says: "I genuinely believe I have never taught mathematics better, and my students have never learned more. I just wish I had known all of this twelve years ago..." more... "How I wish I'd taught Maths" is an extraordinary and important book. Part guide to research, part memoir, part survival handbook, it’s a wonderfully accessible guide to the latest research on teaching mathematics, presented in a disarmingly honest and readable way. I know of no other book that presents as much usable research evidence on the dos and don’ts of mathematics teaching in such a clear and practical way. No matter how long you have been doing it, if you teach mathematics—from primary school to university—this book is for you." Dylan Wiliam, Emeritus Professor of Educational Assessment, UCL. 
Casio Classwiz CalculatorThere is currently a lot of talk about this new calculator being the best in its price range for use in the Maths classroom. The new ClassWiz features a highresolution display making it easier to view numerical formulas and symbols but it isn't a graphical calculator as such (it has the capacity to draw graphs on your smart phone or tablet, via a scannable QR code and an app). As well as basic spreadsheet mode and an equation solving feature you also get the ability to solve quadratic, cubic or quartic polynomial inequalities and the answer is given just as it should be written down, using the correct inequality symbols! This calculator has a highperformance processor and twice the memory of previous models ensuring speedy operation and superior computational power.more... 
Hello WorldYou are buying a (driverless) car. One vehicle is programmed to save as many lives as possible in a collision. Another promises to prioritize the lives of its passengers. Which do you choose? Welcome to the age of the algorithm, the story of a nottoodistant future where machines rule supreme, making important decisions – in healthcare, transport, finance, security, what we watch, where we go even who we send to prison. So how much should we rely on them? What kind of future do we want? Hannah Fry takes us on a tour of the good, the bad and the downright ugly of the algorithms that surround us. In Hello World she lifts the lid on their inner workings, demonstrates their power, exposes their limitations, and examines whether they really are an improvement on the humans they are replacing. This calculator has a highperformance processor and twice the memory of previous models ensuring speedy operation and superior computational power.more... 
Teacher, do your students have
access to computers? 

Here a concise URL for a version of this page without the comments.
Transum.org/go/?Start=November8
Here is the URL which will take them to a related student activity.