2019 MidSchoolMath National Conference

Why does 9 + 1 = 10? Of course we can count out nine objects, add one more the pile, recount and see that there are now ten in the pile. But why do we use the symbol “10” to represent this amount that is one more than nine? Many of our symbols are arbitrary, scratches on paper that have been passed down and altered through time from ancient scripts. But the symbol “10” is not random--there is a very good reason that we use the symbol “10” to represent ten instead of some other symbol, say ^ or }. “10” means, one group of a full set of fingers, with zero fingers left over. And in that way, “11” means one group of a full set of fingers, with one extra finger. So if humans had four fingers on each hand, for a total of eight fingers, the number “10” could presumably mean what we call eight.

In this session, we will explore what mathematics would look like on an alien world where people have only four fingers on each hand (but somehow still use the same written system we do). I will lead the participants through a session I have done several times with 4th-6th grade students, where we start in Alien Kindergarten, counting to 100. We will progress through the elementary grades, performing grade-level arithmetic in this different system. If time and interest permit, we will discuss decimals and fractions as well. We will discuss how they see the solutions and different ways that students in various grades might visualize solutions. We will work in this alien system while also repeatedly relating it to our base ten system: our number “34” means three groups of a full set of fingers with four fingers leftover, but our quantity thirty-four is actually four groups of eight with two leftover, so the aliens would write it as 42.

We will primarily be using paper and pencil (and fingers!) in this session, but we will also discuss what common elementary school manipulatives would look like in this alien world--rods that are eight blocks long instead of ten, for example.