Area Two

Starter of The Day Transum Mathematics Topics

Carol, Sheffield PArk Academy
3 NQTs in the department, I'm new subject leader in this new academy - Starters R Great!! Lovely resource for stimulating learning and getting eveyone off to a good start. Thank you!!
Mark, New Zealand
I used this for a struggling class of 13 year olds and it worked really well. From simple triangles of area 2 we used it to show that obtuse triangles can be made too: the grid makes working out areas so easy.

Next time I will give them a sheet to record their findings though.
Matt, Seb and David, Chatham Grammar School for Boys
We reckon there are at least 25!
Miss Reakes, West Island School, HK
This is a great starter for a mixed ability class due to it's open ended posibilities. The brighter ones using fractions other than a half didn't want to stop! I gave dotted paper to the weaker ones to start them off immediately.
C J Southward, Limehouse School Cumbria
My year 9s scored way over 45 including trapeziums and long triangles.
William Hulme Grammar Academy, Year 8 Set 1
We got 18 different shapes but when you rotate and manipulate these base shapes we had over 50. But we only 10 minutes on it as a starter.
M Mc Crea, Holy Cross College
My students took a while to grasp the complete concept but then some of the Girls especially warmed to the task and after a gentle nudge, found over 140, with rotations and all the different shapes already mentioned by the other teachers here.
Mr Bentley, Braeview Primary, Happy Valley, Australia
We found 26 different shapes that totalled over 300. We stuck to regular shapes to make it easier. Five of my mathematicians stuck with this for nearly an hour.
Mike, New Jersey, USA
I suspect that there are thousands (not counting reflections/rotations)
for example (0,0)(2,1)(1,2)(3,1)(5,2)(4,1)(0,0), and all those points can be slid individually horizontally, making tons of permutations.
Ilona Vashchyshyn,
The challenge: Write your name so that it covers an area of exactly 100 cm squared.

Love the different strategies students used. E.g. Leia, who chose to make each letter 25 cm^2.
Nathan, Dulwich College Beijing
There are at LEAST 69 different shapes that have the area of 2 square units, using your graph. If there is unlimited graph space, the answer would be infinity!

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.
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Answers

The total number of shapes with an area of 2 square units can you make by joining dots on the grid with straight lines will vary according to the answers to the following questions:

Are reflections of a shape different from the original?
Are rotations of a shape different from the original?
Are congruent shapes drawn at different positions on the grid different from the original?

You as teacher may choose to answer these questions at the beginning of the activity or let the class agree on the answers as the questions naturally arise from their work.

Having said that here are some shapes that should be included in the solution.

Rectangle :: 2 by 1
Triangle :: base 1 height 4 (a number of different angles of leaning)
Triangle :: base 2 height 2 (a number of different angles of leaning)
Parallelogram :: base 2 height 1 (a number of different angles of leaning)
Parallelogram :: base 1 height 2 (a number of different angles of leaning)
Trapezium :: base 3 top 1 height 1 (a number of different angles of leaning)

If pupils have realised that a line joining two adjacent dots diagonally (at an angle of 45^o to the horizontal) has length √2 then the following shapes should be included:

Square :: √2 by √2
Triangle :: √2 by 2√2
Parallelogram :: √2 by √2

Note that the discussion about a square being a parallelogram, rectangle and trapezium etc might come out of this activity.


	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).

Here a concise URL for a version of this page without the comments.

Transum.org/go/?Start=September10

Here is the URL which will take them to more traditional exercise on area and perimeter.

Transum.org/go/?to=areaperimf

Curriculum Reference

See the National Curriculum page for links to related online activities and resources.

Area Two

A Maths Starter of The Day

Answers

Curriculum Reference