Stage 3 - number – cartesian coordinates

Develop efficient strategies for numerical calculation, recognise patterns, describe relationships and apply algebraic techniques and generalisations.

Strategy

Students can:

• recognise that the number plane (Cartesian plane) is a visual way of describing location on a grid
• recognise that the number plane consists of a horizontal axis (x-axis) and a vertical axis (y-axis), creating four quadrants
• plot and label points, given coordinates, in all four quadrants of the number plane

Activities to support the strategy

Activity 1 – creating a cartesian/number plane

Teacher gives each student a sheet of 1 cm grid paper. The students fold the paper in half horizontally and then fold the paper in half again, so that when it is opened it is divided into four quarters/quadrants. Have students draw a green line over the horizontal fold and a red line over the vertical fold.

At the point where the two lines intersect (origin) write zero. Instruct students to write the numbers 1, 2, 3 …… on the line to the right of the zero, one number per line as shown and -1, -2, -3 …… on the line to the left of the zero.

Teacher explains that what we have now is called a "number line" or "coordinate line." It can be used to describe where a point is on the line. To give the exact "address" of a point, we just look at how far the point is from zero, using a minus symbol for numbers to the left of zero. These numbers are ‘negative’ numbers. Teacher explains that to give an address for the points that are not on the number line we will need to label the vertical line with positive numbers above the horizontal number line and negative numbers below the horizontal number line. Explain that the horizontal number line is called the x-axis and the vertical number line is y-axis. The teacher explains that the mathematical term for the address of a point is called coordinates.

The ‘coordinates of a point' refers to the ordered pair (x,y) describing the horizontal position x first, followed by the vertical position y.

In pairs, students use the coordinate plane they have drawn to play ‘Sharks and Seagulls’ (an adaptation of ‘Battleships’).

Partners sit opposite each other. Each student draws three sharks below the x axis and five seagulls above the x axis. Each shark is to be drawn within four grid spaces and each seagull drawn within two grid spaces.

Partners alternate turns calling out one coordinate. If you call out a coordinate location that is occupied by a shark/seagull, your opponent tells you whether you have located a shark or a seagull. Record your hit by drawing a red dot in the corresponding coordinate on your grid. Your opponent places a cross on their shark/seagull you have located. If you call out a coordinate location that is not occupied by a shark/seagull on your opponent’s grid, it’s a miss. Record your miss by drawing a black dot in the corresponding coordinate on your grid (this avoids you calling this coordinate location again).

Remind students when calling their coordinate that they call the x position first then the y (x,y).

Continue until one player has located all their opponent’s sharks and seagulls.

Activity 2

Students practise their point plotting skills playing the Simple Coordinates Game. The game allows users to figure out and to practice using the coordinate plane for giving the “address” or exact location of particular points.

Activity 3

Students complete the worksheet and interactive whiteboard activity below.

References

Australian curriculum

ACMMG143: Introduce the Cartesian coordinate system using all four quadrants.

NSW syllabus

MA3-8NA: Analyses and creates geometric and number patterns, constructs and completes number sentences, and locates points on the Cartesian plane.