Quad Areas

A Mathematics Lesson Starter Of The Day

Calculate the areas of all the possible quadrilaterals that can be constructed by joining together dots on this grid:

Teacher: Click on the dots above to show joining lines. Assume that the vertical and horizontal distances between adjacent dots is one unit.

A printable sheet for student use is available here.

A Flash version of the grid is here.


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Topics: Starter | Area | Geometry | Investigations | Mensuration | Shape

  • CB, Kent
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  • I can find 10 different quadrilaterals (if you're allowed to count Big Square and Small Square). Areas - two 1s, two 1.5s, four 2s, one 3, one 4. Can't find the 2.5 at all. Am I missing something really obvious?
  • 8K3, Kettlethorpe High School
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  • We found 11 which included the area of 2.5. (top left to top right to middle right to bottom middle to top left).
  • Snev, Holy Trinity, Crawley
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  • There are 14 different quadrilaterals and their total area is 31.5 cm2 assuming the dots are 1 cm apart. (2x1)(4x1.5)(5x2)(1x2.5)(1x3)(1x4). The 2.5 cm2 quadrilateral joins dots 1,2,6 and 7.
  • Louise And Laura., Carnoustie High School
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  • The problem was very challenging and we all enjoyed it. It was more challenging than Friday's.
  • Claire, Sam And Mr A, Alcester High School
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  • We found 16 quadrilaterals, (5x1)(5x2)(3x1.5)(1x2.5)(1x3)(1x4)
    Only took us 3 minutes too (-ish!).
  • Nairn Spink, 2AY2, High School Of Dundee
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  • We really enjoyed it and I thought it really got us thinking, we are really pleased to do all the staters of the day
    thanks
    :).
  • Yr 8 Tops, Rego School
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  • There should be quite a lot. My class managed about 30 so far.
  • Yr9 QTY, West Island School, Hong Kong
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  • We enjoyed this - it kept us occupied for over 15mins.
  • Mrbeer, Essex
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  • Surely with a parallelogram that crosses over the diagonals, the area is root 5 = 2.23?
  • Charles, Chelsea
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  • My class found about 167 wow.
  • A And F, Dps
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  • Our team got 32 different ways.
  • Jelissa, Massachusetts
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  • It would be great if each quadrilateral could keep its own individual color, for a visual.

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Answers

One possible solution
1 square unit
One possible solution
1.5 square units
One possible solution
2 square units
One possible solution
2.5 square units
One possible solution
3 square units
One possible solution
4 square units

Christmas Present Ideas

It is often very difficult choosing Christmas presents for family and friends but so here are some seasonal, mathematics-related gifts chosen and recommended by Transum Mathematics.

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Graphic Display Calculator

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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 A-level candidate then works their way through university. more...

iPad Air

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Aristotle's Number Puzzle

It’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!).

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Click the images above to see all the details of these gift ideas and to buy them online.


Laptops In Lessons

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).

Laptops In Lessons

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

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Student Activity

 


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