Logic

Estimation is an important skill in life and in math.  The critical question is: about how many _______ are there?

Students always want to count in order to figure out how many there are. The instinct is correct.  But, we also want to teach them to make a ballpark guess.  What does "about 2" look like?  What does "about 10" look like? What does "about 100" look like?

So much of math is patterns, from finding easy tricks for memorizing times tables to recognizing special products in algebra.

The first step of patterns is noticing repetition and being able to make predictions based on that repetition. 

Some patterns are very simple.  Some patterns are very complex.

For young students, start with simple graphical patterns.  What comes first? What comes next?  What do you think comes after that?

Logic and critical thinking skills are essential for math -- so we tend to teach a lot of basic thinking skills in math (although, they are not exclusively math skills).

One of those thinking tasks is the work of categorizing objects: what belongs? What does not belong?

In thinking about what belongs, students need to learn to think about the different qualities of objects, some of these qualities are related to math: