Year 6, Term 1: Cartesian geometryFocus: CoordinatesScope and sequence: Algebra 

Learning intention: Students explore the Cartesian coordinate system linking geometry with algebra. 

NSW Syllabus

Australian Curriculum
(version 9.0)

"A student locates and describes
points on a coordinate plane." (MA3GM01)

"Students learn to recognise
situations, including financial contexts, that use integers;
locate and represent integers on a number line and as
coordinates on the Cartesian plane." (AC9M6N01)

René Descartes
René Descartes (1596 – 1650) could be described as a 'triple threat' as he made significant contributions to science, philosophy and mathematics. This unit is about Cartesian geometry which is also known as as 'analytic geometry'. Analytic geometry is the study of geometry using a coordinate system.
(https://commons.wikimedia.org/wiki/File:Frans_Hals__Portret_van_Ren%C3%A9_Descartes.jpg)
Science
“It was René Descartes in 1637 who initially described the heart as a mechanical pump and the body as a machine” (Loxley, et al., 2018, p. 253).
Philosophy
Descartes is probably best known for his statement, “I think; therefore I am” which means we cannot doubt our existence while we doubt.
https://www.pinterest.com.au/pin/71353975316940566/
The following 10 x 10 grid is labelled with letters from left to right and numbers from top to bottom. Using a letter and number specifies particular square on the grid. For example the square in the topleft corner is A 1. Coordinates are often written in brackets and separated with a comma so that would be (A,1). The square at the bottomright would be (J,10).
Battleship game
This same grid can be used for the game Battleship. This
game is commonly available as a board game with holes and pins or as a
computer game where you play your opponent or the computer. It also
works well on paper too. You can print an A4
page here which is double sided so you can play two games. Each
player will need their own page.
Rules
The photo below shows how some clips and a piece of stiff board or cardboard can enable the paper pages to fit together as a twoplayer board game.
This introduction to coordinates will be extended into Cartesian geometry after looking at Euclidean geometry and algebra.
Plane geometry
The following video (3:19) is a lighthearted
look at the origins of Euclidean geometry.
What's in the black box?
The following video (8:59) provides another introduction
to algebra using boxes.
The following video (2:04) recounts a story
about how Descartes devised his coordinate system while watching a fly
on his ceiling. The story is considered to be a 'legend' as it might not
have actually occurred in this way. Other versions of the legend mention
square tiles on the ceiling which would help explain the layout of the
grid.
Cartesian coordinates
(https://socratic.org/questions/whereisthexaxisandyaxislocated)