What does this kid think “factoring” means? And, at least to me, the more interesting question is: where did that conception of “factoring” come from? Tease it out in the comments.

5 replies on “What does he think “factoring” means?”

Pretty sure he’s trying to find the “greatest common factor” (because it has the word factor in it) and failed?

He is typing the expression into his calculator. The calculator is giving the variables a value of zero.

Students need to do & draw before they are able to dream (work abstractly) to really have a robust understanding of maths. They need to experience factorising (I use squares which represent a^2, rectangles = a and units size 1) then you can see that if you had the 3 ‘a’ rectangles underneath each other there would be 2 units in each of the 3 rows (=6) so factorising it becomes 3 (rows) lots of a + 2 (columns) which we write as 3(a+2). It’s hard to describe in words but I hope you can get the idea.

I want to see the problem above, where 2 + 3(5) becomes 6(5) becomes 30…

[…] and determine what is happening conceptually or procedurally that would lead to that conclusion. This problem has an especially enlightening mistake that shows up in the second […]

## 5 replies on “What does he think “factoring” means?”

Pretty sure he’s trying to find the “greatest common factor” (because it has the word factor in it) and failed?

He is typing the expression into his calculator. The calculator is giving the variables a value of zero.

Students need to do & draw before they are able to dream (work abstractly) to really have a robust understanding of maths. They need to experience factorising (I use squares which represent a^2, rectangles = a and units size 1) then you can see that if you had the 3 ‘a’ rectangles underneath each other there would be 2 units in each of the 3 rows (=6) so factorising it becomes 3 (rows) lots of a + 2 (columns) which we write as 3(a+2). It’s hard to describe in words but I hope you can get the idea.

I want to see the problem above, where 2 + 3(5) becomes 6(5) becomes 30…

[…] and determine what is happening conceptually or procedurally that would lead to that conclusion. This problem has an especially enlightening mistake that shows up in the second […]