Last week’s question on the area of a triangle brought up two key, but completely different misconceptions. And the one teachers felt was the most popular was in fact beaten into second place by another nasty one. Let’s have a reminder of the question, and then take a look at those two misconceptions:

Incorrect Answer C

Whilst it is pleasing to note that these students have clearly remembered the important fact that they need to divide the product of the base and the height by two, unfortunately they have chosen the wrong height. That becomes very apparent in their explanations:

I think this is the right answer because you can’t just times them without using a division because that would make a rectangle. I think you times the 8 and 7 because that would make like a parallelogram which fits two triangles in it that’s why you divide it by 2?

Because the formula for the area of the triangle is base x height divided by 2. 7cm is a base, 6cm is a height so the area of the triangle is 6×7 divided by 2.

as its not a right angled triangle you cant use base times height so you have to use base times length divided by 2

8×7 gives the total of the area of a square then divide that by 2 to get the area of a triangle

 

Incorrect Answer B

Students opting for this one could not resist the temptation to include every single number in their calculation of area:

because to work out an area of a shape you times the length of each side together

Base x Height x width is how u find out the area of an isosceles

It is necessary to include the six as it tells you the height

the other three answers simply don’t have enough information.

 

What can we learn from this? Well, firstly the specific answer the students give determines the support the support they need. Perhaps students who went for C) need a visual approach as to why the perpendicular height is needed. Whereas the students going for B) are showing a lack of deep understanding of area, and perhaps need to go back to square one. The bottom line is that both answers imply a misremembered or misapplied algorithm, which is one of the most common causes of misconceptions that I see across the website.