Singapore Math Drills Team · 6 November 2026
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Every reality show needs a set. This one is a bedroom: a bedsheet pegged to a string for a backdrop, a desk lamp for a key light and a boom mic that is a sock on a broom. A cardboard slate lettered BEHIND THE SCENES, STARRING: ME snaps shut in front of the lens. The Mastermind drops onto the edge of his bed for his first confessional: "Lights." Then, leaning in to the camera: "This is my show."
The show is called "Behind the Scenes", and on a walk-and-talk down the hallway he explains the format: "Five questions a day." The Partner, who is the whole film crew, juice box in hand, is not convinced. "...Five?"
That is Behind the Scenes, the ninth episode of our comedy series, The Mastermind, and our third Secondary episode. Watch it first (it is under a minute), then read on. What hangs behind the bedsheet is a Secondary 3 idea.
In the practice montage, each ordinary question card held up to the camera gets the same full-intensity confessional: "Plot twist." On the fifth one, the Partner pulls the bedsheet down. Taped to the wall behind it is a sheet of graph paper with a straight line through the points (1, 2) and (4, 8), and the camera follows the line: run 4 − 1 = 3, rise 8 − 2 = 6, gradient 6 ÷ 3 = 2. The Partner sums up the show: "He does five questions. That's the show."
The working on that graph paper is one of the most useful ideas in Secondary 3 coordinate geometry.
The gradient of a straight line tells you how steep it is, and which way it slopes. It is the number of units the line rises for every one unit it runs across to the right.
On a graph you can count squares to find the rise and the run. From two points, you subtract instead:
Written as a formula, for points (x₁, y₁) and (x₂, y₂), the gradient is (y₂ − y₁) ÷ (x₂ − x₁). The two words that matter most are "same order". Whichever point your child starts from for the rise, they start from the same point for the run.
In the MOE teaching sequence, the gradient of a straight line from two points is part of coordinate geometry, which comes in Sec 3 and Sec 4 for G2 and G3 Mathematics; it is not part of G1 Mathematics. Students taking G3 Mathematics first meet positive and negative gradients in Sec 1 graph work, so for them Sec 3 is where gradient is worked from coordinates. If you are not sure which subject level your child takes, our guide to G1, G2 and G3 Mathematics explains the difference.
Find the gradient of the line through (1, 2) and (4, 8).
Step 1: Sketch it. From (1, 2) to (4, 8), x goes up and y goes up, so the line goes up to the right. Expect a positive gradient.
Step 2: Find the run. Subtract the x-values, second point first: 4 − 1 = 3.
Step 3: Find the rise. Subtract the y-values in the same order, second point first: 8 − 2 = 6.
Step 4: Divide. Gradient = rise ÷ run = 6 ÷ 3 = 2.
Step 5: Check. The answer is positive, as the sketch said. A gradient of 2 means the line rises 2 for every 1 it runs. Start at (1, 2) and take three steps of "1 across, 2 up": (2, 4), (3, 6), (4, 8). That lands exactly on the second point. The gradient is 2.
Find the gradient of the line through (2, 7) and (6, 3).
Step 1: Sketch it. From (2, 7) to (6, 3), x goes up but y goes down, so the line goes down to the right. Expect a negative gradient.
Step 2: Find the rise. Subtract the y-values, second point first: 3 − 7 = −4.
Step 3: Find the run. Subtract the x-values in the same order, second point first: 6 − 2 = 4.
Step 4: Divide. Gradient = −4 ÷ 4 = −1.
Step 5: Check. The answer is negative, as the sketch said. A gradient of −1 means the line drops 1 for every 1 it runs. From (2, 7): (3, 6), (4, 5), (5, 4), (6, 3). Four steps, and it lands on the second point. The gradient is −1.
Starting from the other point gives the same answer, as long as both subtractions start there: rise 7 − 3 = 4, run 2 − 6 = −4, and 4 ÷ (−4) = −1.
3 − 7 = −4 with the run 2 − 6 = −4 gives −4 ÷ (−4) = 1. The sign is wrong: the line goes down, so the gradient must be negative. Pick a starting point and use it for both subtractions.3 ÷ 6 = 0.5. That line would climb only half a unit per step, and three steps from (1, 2) would reach (4, 3.5), not (4, 8). Rise goes on top: "rise over run".4 ÷ 4 = 1 for the second example loses the direction. If the sketch slopes down, the answer needs a minus sign.A sheet of squared paper and a pencil are enough.
One player marks two points where the gridlines cross and labels their coordinates, such as (1, 1) and (3, 5). Before anyone calculates, the other player looks at the sketch and calls it: "up" or "down". Then they work out the rise, the run and the gradient by subtracting. Last, they check by drawing the staircase from the first point: across 1, then up or down by the gradient, until they reach the second point. If the staircase lands on the point, the answer stands.
For (1, 1) and (3, 5): the call is "up", the rise is 5 − 1 = 4, the run is 3 − 1 = 2, and the gradient is 4 ÷ 2 = 2. The staircase goes (2, 3), then (3, 5). It lands.
Swap roles each round. Five rounds is plenty, one for each "Plot twist."
Make one house rule for every gradient question: sketch first, sign second, numbers last. A ten-second sketch says whether the answer should be positive or negative before a single number is written.
Keep each session short and stop while your child still wants to play. When your child is stuck, ask "Which way does it slope?" before "What is the answer?", and praise the method rather than the speed.
In the episode, the whole show is five questions a day, each one greeted by "Plot twist.", while the day card in the corner goes Day 1, Day 7, Day 30. It only ever goes up. Gradients become comfortable the same way: one idea, met often and checked every time.
That is the idea we built Singapore Math Drills around:
Coordinate Geometry is one of the Secondary 3 topics in our collection, alongside Indices & Standard Form and Quadratic Equations, the other two cards on the episode's THIS SEASON guide. Our Secondary 3 set currently has 10 selected G3-tagged topics. Secondary coverage does not claim complete syllabus coverage or track-specific coverage.
Holding the sock boom over the Partner's confessional, he whispers to the lens: "Act natural."
Try a free interactive Secondary 3 worksheet and see how calm practice feels, with no signup or credit card required.