Exploring Other Bases

Recently, a teacher asked me why other bases are explored in Bridges. I could relate to her question, as I wondered the same thing when I first encountered the lessons with Base 5 in third grade and Base 4 in fourth grade. While at some level I understood that exposure to other bases would lead children to a deeper understanding of place value and our Base 10 system, it wasn't until I saw it in action that I could fully appreciate the results.

Using the lessons from the beginning of Unit 2, Grade 3, I led a group of students through an exploration of Base 5. They manipulated Base 5 pieces, found "minimal collections," and played games in the Base 5 counting system, thoroughly immersing themselves in a new number system. On the last day of the sequence, I asked students to imagine... "Picture base ten. What would a unit look like? A strip? A mat?" The quietest child in the class couldn't hold back... "100!!!" They immediately told me that base ten would have a unit of 1, a strip of 10, and a mat of 100! I gave them base ten pieces and asked them to create a stripmat. With wide grins they asked me for TEN MATS and told me that a stripmat would have 1000 units. They built a strip mat and then proceeded to tell me what the next piece would look like and that it would have 10,000 units. "And then 100,000 and then 1,000,000....!!!!!!"

The "base" understanding increased exponentially!

Do you have stories about using other bases in your classroom? Please comment or send an email.