Concepts and memorizing facts

I know that many students in the class already know multiplication facts. Knowing the facts is important and useful. Knowing the concepts is vital for further learning.

This Monday I asked the students to model what multiplication means. We have modeled addition and subtraction earlier. I asked them to use colored pencils to draw models of what they know.

Majority of the papers looked colorful like this:

There is clear evidence of knowing multiplication facts. These however are not models.

The next math lesson I modeled various multiplication problems. The students had to find what each model represented and figure out what types of models ( not materials) there were.

After this lesson the students began creating pictures like these:

Knowing these different models and meaning of multiplication will help the students later when they learn multiplication of larger numbers or division.