It all starts in first grade when we want the children to understand that the digits used to create a number actually stand for groups of things rather than the digit itself.  Sound confusing?  It simply means that in the number 537 the 3 stands for three sets of ten - not just 3, while the 5 stands for five sets of 100.   This is a rather abstract concept to a first grader so to make this a more concrete idea, Ms. Meland gets out her snap cubes and starts with a base four system.  If we were working in base-four, you could snap cubes together in the ones place until you had four together - then you trade them for a four cube.  The same thing happens in the fours place; once you get four 4s you trade them for a 16 cube.  So the place values in a base four are 1, 4 and 16.  The first graders aren't expected to be able to translate numbers into different bases but just to realize that the place values could stand for different groups of numbers depending on what base system we were in.

 When the students get to fourth grade, they study other base systems in depth as part of their math enrichment class.  They are expected to translate from another base system to base ten.  Many mathematicians feel that we ended up with a base ten system because we have ten fingers.  So the question is posed, "What if we only had five fingers.  What might our base system have been?"  Of course, the answer is base five!  In that case, the number 432 would stand for two 1s, three 5s and four 25s, or 117 in base ten!

Eventually, each fourth grader chooses a base that they want to work with.  Integrating math with language arts, they write a story about an animal or creature that might count in a different base.  (Dogs might use their paws to count in base four or ants might use their antennae to count in base two.)  Then they create their own abacus that depicts that base and create word problems that require conversion to base ten.  Middle School students are invited into the fourth grade classrooms so the fourth graders can demonstrate their new base systems.  Students work together to try and convert a variety of numbers from other bases to base ten.  It is a challenging hands-on project that brings students to that higher level of thinking that we are so proud of at MPA.

Nansee Greeley

Lower School Director