Grade 9: Algebra

Warm up with a few quick algebra warm-ups on the board while the class settles, so every child starts thinking about the skill.

This unit covers three related coordinate-geometry skills, all computed from two points on the Cartesian plane: the gradient (steepness) of the line between them, their midpoint, and the straight-line distance between them. Model the method clearly, thinking aloud:

• Teach gradient as 'rise over run': the change in y divided by the change in x, using a graphed example first.
• Introduce midpoint as simply averaging the x-coordinates and the y-coordinates separately.
• Connect the distance formula directly to Pythagoras' theorem: the horizontal and vertical gaps are the two legs of a right triangle.
• Use Pythagorean-triple coordinate pairs (e.g. a horizontal gap of 3 and vertical gap of 4) so distance answers come out as clean whole numbers while the method is new.
• Practise all three skills on the same pair of points so students see they are three separate, related questions about the same two points.

Work this through step by step on the board, then have the class talk you through a second one.

• Find the gradient, midpoint and distance between (1, 2) and (4, 6)
• Gradient = (6-2)/(4-1) = 4/3
• Midpoint = ((1+4)/2, (2+6)/2) = (2.5, 4)
• Distance = sqrt((4-1)^2 + (6-2)^2) = sqrt(9+16) = sqrt(25) = 5

Do the first few questions of the practice worksheet together, one child explaining each step. Check for understanding before releasing the class to work alone.

Students complete the practice worksheet independently while you circulate and support.

Circulate and look for these, they are the usual sticking points:

• Subtracting the coordinates in the wrong order for gradient, e.g. mixing (y2-y1) with (x1-x2).
• Adding the coordinates instead of averaging them when finding a midpoint.
• Forgetting to square root the final sum in the distance formula, leaving the answer as a squared distance.
• Mixing up which coordinate pair belongs to which point when substituting into a formula.

Pull the class back together. Ask one child to explain algebra in their own words, pose a single check question everyone answers on a mini whiteboard, and name what you will build on next lesson.

Use the independent worksheet as the evidence. A child who can complete it accurately and explain one answer has met the objective; anyone who cannot needs the easier level and a short reteach next session.