3 mistakes learners make with gradient from two points, each one named and explained.
Gradient is the change in y divided by the change in x, in that order.
One of the numbers from the two points is offered as the gradient.
Four numbers are in the question and any of them is a candidate if the method has not landed.
Question. (1, 3) to (4, 12)
A common answer. 4
The answer. 3
Why. The 4 is where the second point sits, not how steep the line is.
A gradient always comes from a subtraction and a division, never straight off the page.
From (1, 3) to (4, 12) the gradient is given as 9.
Nine is the difference the question is really about, and it is the harder step.
Question. (1, 3) to (4, 12)
A common answer. 12 - 3 = 9
The answer. 9 / 3 = 3
Why. The line rose 9 while moving 3 across, so it rises 3 for every 1 across.
A gradient is always a rate. It has to be divided by the run.
The change in x is divided by the change in y.
Both differences are worked out and only the order of the division separates the two answers.
Question. (1, 3) to (4, 12)
A common answer. 3 / 9 = 1/3
The answer. 9 / 3 = 3
Why. Gradient is how much it rises for each step across, so the rise is on top.
Say the words: change in y over change in x. Y is on top because y is up.
WAJD spots these patterns in your child's answers and names the one behind their wrong answers, instead of just marking them wrong.