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?

Share

Topics: Starter | Area | Mensuration | Puzzles | Ratio | Shape

• David, Kawartha Pine Ridge District School Board
•
• My main concern is that this references the shape as a right-triangle which neither is in actuality. I think this throws the students off a possible thinking path. If instead it referred to the shape less specifically, then students might more readily venture down this path.
• Transum,
•
• Good point David. The phrase 'right-angled triangles' has now been replaced with the word 'shapes' in the text above. Thanks very much for the suggestion.
• Tara, Brisbane
•
• Was trying to plan a good lesson for ratio. As a substitute teacher, putting together an engaging lesson is paramount to avert discipline issues. So thought it just perfect, in keeping with the first step of arousing the interest of the class. Thank you.
• H Rollo, Brechin High
•
• Could be used for introducing gradient.

[Transum: That is a very good idea. I too use the notion of gradient when getting students to analyse the situation.]
• Brandon, The Bronx
•
• Cheating. The top triangle, measured as one unit has an area of 32.5. If we assume each cut up piece touches the grid, then we get get triangles of area: 12 (1/2* 8*3), 8, 7 and 5 (1/2 * 5*2) = 32. It doesn't matter what the bottom triangle looks like, the top triangle is lying to us and the bottom could be anything marginally different by not quite, but almost touching the grid lines anyway you'd like. Tricky. I like it becait tests our tacit assumption that the sub-shapes all touch the grid lines, when they don't.
• Berten Stan, Oxford High
•
• Good activity,would like to see more.

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.

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:

Excellent, I would like to see more like this
Good, achieved the results I required
Satisfactory
Didn't really capture the interest of the students
Not for me! I wouldn't use this type of activity.

This starter has scored a mean of 3.3 out of 5 based on 383 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.

## Parallel or not?

As you probably guessed, even though the red lines don't look parallel they actually are.

## More Mathematical Optical illusions

Transum.org/go/?to=illusions

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.

## Hello World

You 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 not-too-distant 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. more...

 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=July26

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

Transum.org/go/?to=areatri

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

#### PowerPoint 2007:

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.

#### PowerPoint 2013:

The red and blue right-angled 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.

For Students:

For All: