Mathematics
Intermediate
50 mins
Teacher/Student led
+80 XP
What you need:
IWB/Projector/Large Screen

The Full Four-quadrant Co-ordinate Plane

Learn to navigate the full four-quadrant coordinate plane. Explore what happens when we extend the axes left and down past zero, discover how each quadrant is numbered and signed, and practise identifying which quadrant any point lands in.

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    1 - Getting Started ~4 mins

    You already know how to plot points like (3, 4) by going along and then up. But what if a place is below the start line, or to the left of it? Look at our grid as the two lines stretch out past zero, in every direction. What appears down here, below zero? And what about over there, to the left of zero?

    2 - Watch and Notice ~9 mins

    Illustration for Watch and NoticeWatch the grid carefully. The two lines crossing at the centre meet at a special point called the origin, written (0, 0). The lines split the whole plane into four regions, called quadrants. We number them I, II, III and IV, starting in the top-right corner and going anticlockwise.

    Now watch one point land in each region: (4, 3) up in the top-right, (−4, 3) in the top-left, (−4, −3) down in the bottom-left, and (4, −3) in the bottom-right. Look at the signs each time. What do you notice about whether each number is positive or negative as we move from one region to the next?

    3 - Try It Together ~11 mins

    Today we work through this together: I will name a point and you tell me which quadrant it lands in, just from its signs. Then a pupil will come up and plot it to check. We'll do points like (5, 2), (−3, 4), (−6, −1) and (2, −5).

    Which quadrant does it land in?

    4 - Sketch the Quadrants in Your Copy ~3 mins

    COPYBOOK MOMENT

    Illustration for Sketch the Quadrants in Your CopyIn your maths copy, sketch the four-quadrant plane with the axes running from −6 to 6 on each side. Label the four quadrants I, II, III and IV in the right corners. Then write the sign pattern beside each one:

    • Quadrant I: (+, +)
    • Quadrant II: (−, +)
    • Quadrant III: (−, −)
    • Quadrant IV: (+, −)

    5 - Class Challenge ~8 mins

    Today we work through these challenges together: first, name the quadrant for a given point. Then give me a point that lives in quadrant III. Then the trickiest one — give me a point that sits on an axis and lands in no quadrant at all.

    Name it, place it, trick it

    6 - What Did We Notice? ~3 mins

    MATHS TALK

    Where do points sit when one of their co-ordinates is zero — not in any quadrant, but somewhere special? A zero means no step in that direction (no step left or right, or no step up or down), so the point stays on a line. Have a think about why that happens.

    7 - What's Next ~2 mins

    Today we learned

    • The two axes cross at the origin, (0, 0), the centre of the plane
    • The four quadrants are numbered I, II, III, IV, anticlockwise from the top-right
    • Each quadrant has its own sign pattern: (+,+), (−,+), (−,−), (+,−)
    • A point with a zero co-ordinate sits on an axis, in no quadrant

    Coming up

    Next we'll plot and read points with negative co-ordinates anywhere on the plane, going left and down from the origin with confidence.

    Pupil practice
    Module 8 · Location, Transformations and Scale Algebra
    Lesson 83 · The Full Four-quadrant Co-ordinate Plane
    Download Activity Book page (PDF)
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