Mathematics K–6 · Years 5–6

Coordinates on the floor: the Cartesian plane in four quadrants

Measurement and space

Practical, model not builtLow risk

This site has no interactive model of its own. Where a step or a material names a Concept Studio model, simulation or tool, it has not been built; an external simulation a step names (for example PhET) is not part of this site.

The idea

A point is named by its distance right or left of the origin and then up or down, so negative coordinates place points in all four quadrants.

What you need

a floor grid of masking tape 11 by 11 squares with two axes through the middle, labelled minus 5 to 5
a set of coordinate cards, including negative values
4 cones and a length of string
grid paper with axes for recording

How to do it

Stand at the origin. A partner reads a card such as (3, 2); walk 3 squares along the first axis, then 2 up, and stop. Say which quadrant you are in.
Repeat for (minus 3, 2), (minus 3, minus 2) and (3, minus 2). Mark the four points with cones and stretch the string round them. Name the shape.
From (3, 2) walk 4 squares left and 3 down. Read your new coordinates and describe how each number changed.
Reflect (3, 2) in the vertical axis by walking to the mirror-image square. Read the coordinates. Repeat for the horizontal axis.
Record every point on the grid paper and draw the rectangle and the reflections.

What you should see

(3, 2) is in the first quadrant, (minus 3, 2) in the second, (minus 3, minus 2) in the third and (3, minus 2) in the fourth, and the four cones make a rectangle 6 squares wide and 4 squares tall. Walking 4 left and 3 down from (3, 2) ends at (minus 1, minus 1), so the first coordinate drops by 4 and the second by 3. The reflection of (3, 2) in the vertical axis is (minus 3, 2) and in the horizontal axis is (3, minus 2). A child who takes the first number as the up step and the second as the along step ends at (2, 3) instead, and the class sees on the grid that the order of the two numbers in the pair decides the point while the order in which the two moves are walked does not.

What changes

This activity lists no variables to change, measure and keep the same.

Common misconceptions

Each of these ideas is wrong, and the activity is a chance to test it.

The order of the two numbers in a coordinate pair does not matter.
Negative coordinates are impossible because you cannot walk a negative number of squares.

Safety card

Low riskLearners carry it out

Hazards

tape edges
cones on the floor

Controls

press tape flat; walk, do not run

Note

No chemicals or heat are used, so the NSW Department of Education Chemical Safety in Schools package is not needed; ordinary classroom supervision under the school's usual risk management.

Curriculum references

The NSW syllabus outcomes and Australian Curriculum v9 codes this activity supports. They are references, not a verified or complete curriculum alignment.

Mathematics K-10 Syllabus (2022), NSW Education Standards AuthorityMA3-GM-01 MAO-WM-01
Australian Curriculum v9AC9M5SP02AC9M6SP02AC9M6N01

Sources

The pages the author read to write this activity.

All Concept Studio activities