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?
Display a first-quadrant grid as pupils settle, then extend both axes through zero live on the IWB — push both lines out past zero so the new regions appear. Take two or three hands-up answers, not open call-outs. Don't name the word "quadrant" yet — let pupils describe "below" and "to the left" in their own words first.
Watch 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?
Reveal one term at a time, pausing visibly before each so the three ideas don't arrive at once. First point to the origin and say its name and co-ordinate aloud: "zero, zero — the very centre." Pause.
Next, trace the quadrant numbering with your finger: top-right is I, then sweep anticlockwise. Pause. Then walk the four points one at a time, reading the signs: quadrant I is (+,+), quadrant II is (−,+), quadrant III is (−,−), quadrant IV is (+,−). Pause before each reveal and ask the class to predict the signs.
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).
This round is for talking it through together — pupils take turns at the board and the class agrees or corrects out loud.
Ask the class to read the signs before the point is plotted, then plot to confirm. Revoice a strong answer: "both numbers negative, so it has to be quadrant three." Watch for the common slip of reading the y sign first — keep saying x sign, then y sign. Rotate four pupils to the board.
In 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:
Walk the room glancing at the quadrant numbering direction (anticlockwise from top-right) and the sign pairs — this is whole-class copybook practice, not marking. A quick scan for the (−,+) vs (+,−) mix-up tells you who needs a nudge.
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.
This round is the practice bank — pupils take turns at the board, check each answer, and the class confirms before moving on. Keep the board work brisk rather than over-explaining.
The final challenge is the high-ceiling one: a point on an axis (like (0, 4) or (−3, 0)) belongs to no quadrant because one co-ordinate is zero. Let the class debate it before checking. Revoice: "if a number is zero, the point sits on the line, not in a corner."
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.
Listen for pupils connecting a zero co-ordinate to sitting on an axis rather than in a region. Revoice a strong answer: "a zero means no step in that direction, so the point stays on the line." Head off the misconception that (0, 4) must belong to quadrant I just because 4 is positive — the zero overrides it.
Next we'll plot and read points with negative co-ordinates anywhere on the plane, going left and down from the origin with confidence.
Recap the sign patterns quickly by pointing to each quadrant and taking hands-up answers for the signs. Flag the next lesson moves from naming quadrants to plotting negative points precisely.
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