Students select graphs on a Cartesian plane when their gradient and y-intercepts are given.
Answers/responses:
Y10 (04/2016)
a)
difficult
b)
difficult
c)
very difficult
d)
moderate*
a) - d)
3-4 correct
2 or more correct
1 or more correct (students who get just 1 correct, may be guessing**)
very difficult
difficult
easy
Based on a representative sample of 132 Y10 students.
NOTE
* It is interesting that question d) was the easiest. It seems that a) should be easiest, with both the slope and the intercept being positive. It may be that they choose correctly because both the x- and y-intercept are negative.
** It may also be that a number of students in the sample were unfamiliar with the concepts involved, and were guessing. Note that the resource was trialled in Term 1, and many students may have not covered the concepts involved, particularly gradient.
Teaching and learning:
The key concepts involved in this resource are intercept (specifically the y-intercept) and gradient (slope).
Diagnostic and formative information:
Common error
Likely misconception
a) - d)
Lack of knowledge about gradient
Students select a graph with the correct y-intercept, but not gradient, i.e., where the intercept is the same sign (positive or negative) as the one with the correct answer.
Students may know how to find the intercept, but not the gradient (slope).
Next steps:
Lack of knowledge about gradient
Students could explore linear equations with positive gradients greater than 1, and then with gradients that are between 0 and 1.Repeat using negative gradients. Technology can be good for demonstrating this.
