Using coordinates and drawing basic shapes

Coordinate grids can provide a quick and easy way to draw shapes with a class, as a starter or a general activity.

Drawing and labelling axes is a necessary skill, but if it is not the main point of the lesson then it can be sidestepped by providing pre-drawn grids with axes. If the results need to be checked or marked, printouts are a good option. If not, whiteboards are less threatening, allowing students to make errors without any stigma and without being marked down.  A standard A4 whiteboard, with a 1 cm square grid already printed on the surface, can be cut up into four or even six grids and axes can be drawn on them with permanent marker.  Depending on the age and knowledge of your students they can be positive only or negative and positive. This also depends on whether the intention is to practice plotting points or to discuss the properties of shapes.

Students can get quite excited by point-plotting games involving verbal instructions.  I think it is something to do with anticipation, and guessing what someone else is thinking.  How much or how little you tell them depends on what your goals are.

Here are just a few examples using a rectangle. One of the good things about this kind of exercise is that you don’t need any preparation – you can draw the shapes along with the students, going with the flow and awareness of the students.

Join these four points: (1, 2); (5, 2); (5, 4). What next?  Why? 
Usually students will pick the fourth corner of a rectangle with little or no prompting, and without mentioning rectangles.  Ask others in the class why the student responding chose their point.



Try another: (2, 5); (5, 1); (5, 5). What’s the next point?

Same result.  It is good to pick fourth points where y ≠ x, to ensure students are getting their coordinates the right way round.



How about this one: (1, 0); (5, 2); (4, 4)? Next point?



Can you guess the rectangle if you only know two points? How about (2, 2) and (5, 2)?

Invite offers of points for the other 2 corners.



How about just two points if you know they are opposite corners of a rectangle? Say (2, 1) and (6, 4).  What are the other corners?



Parallelograms offer two choices for the fourth corner. For example: (1, 0); (2, 2); (-2, 0). The fourth point could be (-3, -2) or it could be (-1, 2).



We could start with three points: (0, 1); (1, 2); (2, 1) and ask for a fourth to make a square (1, 0), a kite (1,-1) or others such as a trapezium (2, -1).



Hopefully these few examples illustrate an idea.  The intention here is not to provide a comprehensive list of possible exercises.  Obviously the different types of triangle could also be explored, (although an equilateral triangle could provide some interesting attempts).  Rather, it is to suggest playing with coordinates to explore shapes, or playing with shapes to practise coordinates, or both.

All the best,

Steve Fearnley

Steve Fearnley, MA MEd PGCE, has been a maths teacher for over 30 years as well as being a deputy headteacher. He is now a private maths tutor, covering KS3 up to A Level, as well as an author for both and our new AQA GCSE Maths Student Books.

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