cartesian

Cartesian Co-ordinate Practice

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“The coordinate system we commonly use is called the Cartesian system, after the French mathematician René Descartes (1596-1650), who developed it in the 17th century. Legend has it that Descartes, who liked to stay in bed until late, was watching a fly on the ceiling from his bed. He wondered how to best describe the fly’s location and decided that one of the corners of the ceiling could be used as a reference point.” ~ https://wild.maths.org/ren%C3%A9-descartes-and-fly-ceiling

Since 1650, the Cartesian plane has been the model for almost all mapping systems and enabled a connection between algebra and geometry. Using such a coordinate system it is possible to solve geometric problems using algebra, and vice versa.

To better understand the co-ordinate plane system we are going to practice plotting points in a few different ways. Cartesian Co-ordinate Battleships is a game you can play to ‘sink’ an opponents ships, by calling out a series of cartesian co-ordinate pairs, while  they try to ‘sink’ your ships.

Maths Nook has some online games to draw suprise shapes by plotting points on a cartesian plane:

https://www.mathnook.com/math2/graphing-puzzle.html

https://www.mathnook.com/math2/graphing-puzzle-2.html

https://www.mathnook.com/math2/graphing-puzzle-christmas.html

More cartesian coordinate games here: https://www.mathnook.com/math/skill/coordinategridgames.php

More about Cartesian Co-ordinates

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Learning Intention:
To understand how cartesian coordinates are used on maps and in mathematics to describe locations and linear equations. Also to understand the relationships between co-ordinates that are reflected across the x and y axis.

Success Criteria:
Students will be able to draw up a cartesian plane, correctly locate and plot coordinates on the plane, as well as be able to identify where points exist using cartesian coordinates. They will complete the games and activities above and identify what they have learnt from each of the interactives.

Maths is Fun – Cartesian Co-ordinates

Shodor Interactives – General Co-ordinates

The links above take you to several activities to help you learn about Cartesian coordinates. Go to the first activity (Interactive cartesian co-ordinates) and plot three points to form an equilateral triangle in one quadrat. Write the co-ordinates down in your book, then reflect the triangle into each of the three other quadrats. List the plotted points in your book. What do you notice about the relationship between the plotted points?

Now. draw a shape of your own choice in one of the quadrats – it could be a simple polygon, a star, heart or more complicated original design. Then write down the co-ordinates of it’s vertices (in order). Reflect the shape into each of the quadrats and write down their co-odinates. Give a partner your list of co-ordinates and see if they can determine the shape you have created using the co-ordinates given.

Rene Descartes and the Cartesian Plane

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Find out the answers to the following questions using your netbook for research:

  1. What is Descarte’s most famous saying?
  2. What did he see on a placard in the town of Breda, that challenged him?
  3. What branch of mathematics is named after Descartes?
  4. What habit did he give up up in the last year of his life?
  5. Now find a map of the school and create a set of cartesian co-ordinates on it. Work out the co-ordinates of the most important places in the school.