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What are the major misconceptions students have when combing algebra with geometry? Specifically, what misunderstandings do students reveal when attempting to work out the area of a simple shape, but with the sides containing unknowns?

Using real life data and student explanations from my Diagnostic Questions website, we can find out! :-)

Have a look at the question below.

What percentage of students do you think get it correct?
What is the most popular incorrect answer?
What explanations do students give for the incorrect answers?

Give the question a go yourself, and try to come up with an explanation of the correct answer that would make sense to students:


At the time of writing, this question has been answered 152 times, and has been answered correctly 65% of the time. Thw two most popular incorrect answers are A and C.

Now, looking at the alternative answers, we can probably hazard a guess as to why students have gone wrong. But why do that when we can read actual student responses? :-)

Visiting the Data Question page (which is also accessible to all who have answered the question by clicking on the small graph icon in the bottom-right corner of the question window) is very revealing.

Correct Explanations for B

Scrolling down the page, we can see some beautiful correct explanations, submitted by students from all over the world:

it would be written like (x+5)(x+5)

(X+5)(x+5) Expands to x^2+5x+5x*25 Goes to x^2+10x+25

Area=wxh so (x+5)(x+5) expands to x^2+10x+25

Please “like” your favourite on the site, as it gets recorded in the student’s records.

As ever, the incorrect answers are incredibly revelaing. You can access these by clicking on the drop-down menu and selelcting a different letter. Reading them can help us feel more prepared as teachers as we deliver the topic of algebra and geometry.

Explanations for A

The classic trap of forgetting to expand the double brackets, and instead just multiplying the xs and 5s together.

X * X = X squared 5*5 = 25

X +5 times itself

Explanations for C

Students muddling up area and perimeter.

4(x+5) because square has four sides 4 times x=4x and 4×5=20 4x+20

there are 4 sides so 4 x x = 4x and 4×5=20

Explanations for D

I find this partricuarly interesting. Some students are not happy leaving an answer with a letter in it, possibly beleiving that answers in maths most have a numeric solution

We need to know the length and width, but we don’t know the value of x

To follow up this question, you might want to assign your students the Algebra Skills quiz below




And here is a video, just taking you through how you can access the pages discussed in this article:



Finally, click here for a link to all the How To pages, where you can find out how to import your students, assign quizzes, and analyse their responses.