Two players play a game with every bus number they see.
14
14
Player 1 doubles the bus number. Player 2 adds up its factors.
Whoever gets the largest total wins. Play the game with a friend.
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Topics: Starter  Arithmetic  Factors  Mental Methods  Mixed  Number
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Previous Day  This starter is for 28 April  Next Day
Bus Number 
Double  Factors  Sum of Factors  Winner 
1  2  1  1  Player 1 
2  4  1 2  3  Player 1 
3  6  1 3  4  Player 1 
4  8  1 2 4  7  Player 1 
5  10  1 5  6  Player 1 
6  12  1 2 3 6  12  Draw 
7  14  1 7  8  Player 1 
8  16  1 2 4 8  15  Player 1 
9  18  1 3 9  13  Player 1 
10  20  1 2 5 10  18  Player 1 
11  22  1 11  12  Player 1 
12  24  1 2 3 4 6 12  28  Player 2 
13  26  1 13  14  Player 1 
14  28  1 2 7 14  24  Player 1 
15  30  1 3 5 15  24  Player 1 
16  32  1 2 4 8 16  31  Player 1 
17  34  1 17  18  Player 1 
18  36  1 2 3 6 9 18  39  Player 2 
19  38  1 19  20  Player 1 
20  40  1 2 4 5 10 20  42  Player 2 
21  42  1 3 7 21  32  Player 1 
22  44  1 2 11 22  36  Player 1 
23  46  1 23  24  Player 1 
24  48  1 2 3 4 6 8 12 24  60  Player 2 
25  50  1 5 25  31  Player 1 
It is better to be Player 1! It is much easier to double a number than work out the factors and add them up and as you can see Player 1 is more likely to win.
Player 2 will only win when the bus number is an "abundant number". What is the next abundant number after 24?
Imagine you are the driver of a bus that begins its route with twelve passengers.
At the first stop one person gets off the bus and five people get on.
At the second stop two people get off the bus and seven people get on.
At the third stop nine people get off the bus and six people get on.
What is the name of the bus driver?
Christmas Present Ideas
It is often very difficult choosing Christmas presents for family and friends but so here are some seasonal, mathematicsrelated gifts chosen and recommended by Transum Mathematics.
Equate board gameHere's a great board game that will give any family with schoolaged 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 Scrabblefor 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 WrongThe 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 onesyllable 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 CalculatorThis 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. TINspire 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 TINspire, 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 Alevel candidate then works their way through university. more... 
iPad AirThe 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... Before giving an iPad as a Christmas gift you could add a link to iPad Maths to the home screen. 
Aristotle's Number PuzzleIt’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... 
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? 

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