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.


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

  • CB, Kent
  • 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
  • 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
  • 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
  • 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
  • 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
  • We really enjoyed it and I thought it really got us thinking, we are really pleased to do all the staters of the day
  • Yr 8 Tops, Rego School
  • There should be quite a lot. My class managed about 30 so far.
  • Yr9 QTY, West Island School, Hong Kong
  • We enjoyed this - it kept us occupied for over 15mins.
  • Mrbeer, Essex
  • Surely with a parallelogram that crosses over the diagonals, the area is root 5 = 2.23?
  • Charles, Chelsea
  • My class found about 167 wow.
  • A And F, Dps
  • Our team got 32 different ways.
  • Jelissa, Massachusetts
  • It would be great if each quadrilateral could keep its own individual color, for a visual.

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Previous Day | This starter is for 22 March | Next Day



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.

Equate board game

Here's a great board game that will give any family with school-aged 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.

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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 Calculator

This 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. TI-Nspire 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 TI-Nspire, 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 A-level candidate then works their way through university. more...

iPad Air

The 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 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!).

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.

Online Maths Shop

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.


Student Activity



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