Understands empty and full. Volume comparisons as well as the grouping of objects to fill a volume.
Understands more and less. The foundation of ordering numbers and understanding relations.
Position and Direction
Understands up and down. Forerunner of the number line.
Understands in and out. This preschool math concept gets them into early set theory.
Understands front and back. More number line stuff.
Understands over (on) and under. The math concepts here get them ready for setting up fractions.
Understands top, bottom, middle. Standard preschool readiness and also the basics of ordering.
Understands beside and next to. Gets them ready to multiply a number by a variable by just standing the number next to the variable: 3x means 3 times x.
Understands hot and cold. Getting ready to measure temperature.
Understands fast and slow. Getting ready to measure speed as well as rates.
Understands day and night. This preschool math concept gets them ready to expand into bigger and bigger time units – which will allow them to eventually understand the ideas of infinity and infinitely small. Curiously, this is also pattern recognition – every day you get day and every day you get night!
Knows age and birthday. This seems to be another “good to know” thing. However, it is another forerunner to big time units.
There are many more preschool math concepts that can be spun off from the other lists, like Reading and Social-Emotional Development. I’ll be writing up how to integrate math in those in a few days!
Am I missing anything? Let me know in the comments.