Missing Square Puzzle

Missing Square Puzzle

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?

A Mathematics Lesson Starter Of The Day


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

  • David, Kawartha Pine Ridge District School Board
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  • 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,
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  • 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
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  • 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
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  • 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
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  • 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
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  • Good activity,would like to see more.
  • Ben Sparks, Twitter
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Previous Day | This starter is for 26 July | Next Day

 

Chess Board Paradox

Chess Board Paradox

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?

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

Student Activity


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Answers

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Online Maths Shop

Laptops In Lessons

Teacher, do your students have access to computers such as tablets, iPads or Laptops?  This page was really designed for projection on a whiteboard but if you really want the students to have access to it here is a concise URL for a version of this page without the comments:

Transum.org/go/?Start=July26

However it would be better to assign one of the student interactive activities below.

Laptops In Lessons

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

Transum.org/go/?to=areatri

Student Activity

 




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.

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