Many Mathematics Teacher Educators (MTEs) teach about other number systems/different bases to help prospective teachers (PTs) learn about our own Base 10 system better  by reflecting on digits, place value, and counting in a new way. Is it possible to truly understand our current decimal system if we do not compare it to other systems? I think this lesson works well for elementary or middle school prospective teachers. Because of my love of number, I also think it would be great for students of any age really  particularly for middle school and high school students to reflect on how they might take our number system for "granted." Although this is not a new concept, I present my introduction lesson to different bases for this blog. This task is one that we used at Illinois State University in Math 130 (a first content course for elementary PTs); I have modified it a bit and used this week at George Fox University in Math 211 (a first content course for elementary PTs). Week 4 of the #MTBoS Blogging IntiativeIntroduction & discussion.If our ancestors had decided to count and group only by the fingers and thumb on one hand, what would our place value system be? Sometimes I rephrase the question  What if instead of using two hands to count, our society decided to use only one hand? How would that change our number system? Task 1.Make up names for the groupings in this place value system, and then develop a counting chart for the numbers up to the 3rd place value. Questions to help facilitate discussion: How many digits would be in your place value? (Typical misconception is the confounding of digits and numbers.) How many digits do we have now? What are they? (Typical misconception is that "10" is a digit.) How would this compare to our place value system now? Task 2.Discuss the meaning of each of the following numbers in this place value system: 241(five) 26(five) 304(five) Teacher moves to help facilitate discussion: When students get frustrated Pass out Katy cubes or grid paper. If we can model Base 10 numbers with our blocks? What would Base 5 pieces look like? Task 3.Have students practice counting on and counting back from the following numbers. 14(five) 224(five) 443(five) 204(five) Teacher moves to help facilitate discussion: Consider asking students to make a counting chart similar to The Hundred Chart. Closure.Pick one of the jokes below and explain the mathematical pun. Joke A Joke B Why do mathematicians always confuse Halloween and Christmas?
Because 31 Oct = 25 Dec Joke C
3 Comments
Moving to the context of a new number base is such a perfect opportunity to revisit those "elementary" concepts  if you can't do long division in base 8, do you really know how to do long division?
Reply
Nicole
2/10/2016 10:33:15 pm
That's a great idea! I didn't know about the Yuki Native Americans!
Reply
2/7/2016 06:54:00 am
I've done some similar things with high school students. It really helps them to understand place value and how to work more flexibly with numbers.
Reply
Leave a Reply. 
Nicole M.

Powered by