The four coloured pieces can be put together in two different ways to make these shapes with base 13 units and height 5 units. Why is there one square missing in the second arrangement?
Tweet about this starter  Share 
Topics: Starter  Area  Mensuration  Puzzles  Ratio  Shape
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 3.4 out of 5 based on 317 votes.
Previous Day  This starter is for 26 July  Next Day
Sam Loyd presented this Chessboard Paradox at the American Chess congress in 1858. Notice the Fibonacci numbers which can be found in both of these diagrams.
As you probably guessed, even though the red lines don't look parallel they actually are.
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... 
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? 

Here a concise URL for a version of this page without the comments.
Here is the URL which will take them to a related student activity.
Students can create their own presentation of the Missing Square Puzzle to show to other classes or in an assembly. Here are some guidelines for using PowerPoint
On the Home tab, in the Drawing group, click Arrange,
point to Align, and then click Grid Settings.
Tick the Snap objects to
grid and the display grid on screen boxes. Select from the dropdown box a
spacing of 1cm.
The red and blue
rightangled triangles can be made using the "Right Triangle" tool which can
be found in the Home tab, in the Drawing group.
The green and yellow
shapes can be created by putting together a number of 1cm by 1cm squares.
Upon completion of the shape drag over the shape to select all of the
squares then select "Group" from the Format tab, Arrange group.
Turn the Snap To Grid option off an add custom animations to each of the shapes to make the first arrangement of shapes transform into the second.
The images on this page are from the Wikimedia Commons. The descriptions of the licences can be found on the following pages: Missing Square Puzzle and Sam Lloyd Image.