# Relating factored equations to the area of a rectangle

### Cecilia Russo, Universidad de Cantabria, Spain

STACK offers the possibility of immediate formative feedback. It's great to have everyone in a class of 100 students know they would be able to get feedback even if you are away. The teacher's presence is vital, but it is impossible to be there all the time, and AuthOmath is the perfect teaching assistant combining STACK and GeoGebra.

This example is a task sequence to help the student relate factored equations to the area of a rectangle. The first task asks the student to factorise a square of binomial.

If students write an incorrect answer, they are get the following feedback:

Now, a student can drag point to observe the area of square and try to find a relation between the expression, the area and the length of the sides. When they drag point , they get a square composed of rectangles. The area of each rectangle is shown in the applet. The idea is for the student to add these areas, and obtain the expression needed as the answer to the task. STACK and GeoGebra help the student during the feedback.

Then, the second part of the sequence is related to expressions. Where "" and "" are different natural numbers. In this second part we don't have a square.

Again, if students write a wrong answer, they get feedback with a GeoGebra applet. This applet lets the student try out the relation between the length of the sides of the rectangle and the area of it. In that case, they can drag points and to get a rectangle composed of four rectangles. The area of each one is shown.

This feedback allows the students to interact with a geometric polynomial representation. At the same time, they can find out a strategy to find a factorized expression. In this way, the geometry and the algebra reinforce each other.