4 mistakes learners make with loci and construction, each one named and explained.
A construction is built with compasses and left on the page, because the arcs are the evidence that it was built and not guessed.
You measure the angle, halve the number and draw the line, instead of constructing the bisector with arcs.
Measuring gets to the same line faster, and the finished page looks much the same.
Question. Construct the bisector of an angle. What do you use?
A common answer. a protractor, to measure and halve the angle
The answer. a pair of compasses, to draw the arcs
Why. A construction question is asking for the method, and the marks are for the arcs.
The word construct means compasses. A protractor answer scores nothing.
You answer 50 rather than 050, or measure from the nearest line instead of from north.
A bearing is an angle, so any correctly measured angle feels like a correct answer.
Question. A bearing is measured as fifty degrees. How is it written?
A common answer. 50 degrees
The answer. 050
Why. A bearing is always three figures, measured clockwise from north.
Check two things every time: measured from north, and written with three figures.
You tidy the diagram by erasing the arcs once the line is drawn.
The arcs look like rough working, and rough working is what you have always been told to rub out.
Question. You have bisected a line with compasses. What should you do with the arcs?
A common answer. rub them out so the diagram is neat
The answer. leave them on the page
Why. The arcs are the working. Without them the line is just a line you might have guessed.
Leave every mark. Marks are given for the arcs, not for tidiness.
You draw the set of points 3 cm from a line segment as a plain rectangle, with square corners at the ends.
The two long sides are easy to see, and the ends are easy to close off with a straight edge.
Question. What shape is the set of points exactly 3 cm from a line segment?
A common answer. a rectangle around it
The answer. two parallel lines joined by a semicircle at each end
Why. At the ends the nearest part of the segment is a single point, so the boundary curves round it.
Ask what the nearest point is. If it is an end, you are drawing part of a circle.
WAJD spots these patterns in your child's answers and names the one behind their wrong answers, instead of just marking them wrong.