The first questions: digits and base-ten

The first two questions for my sixth-graders:

1. How many digits do we have in our system of numbers and what are they?
2. What is the "main thing" about our numbering system?

    A note about the awkward nature of this question.

    If I ask, "What is the basis of our system of numbers?"  or, "On what is our numbering system based?"; students will not understand the use of the words "basis" and "based".  So, I will use "main thing" and we will talk about what I mean:
            main idea
            the foundation
            main concept

Some examples from students' experience:
            something can sit on its "base"
            being "safe" in tag is touching a "base"
            being "safe" in baseball is being on "base"

Ultimately, students will understand that:
Our system of numbers is based on groups of ten.  We work in a base-ten numbering system.  Furthermore, each place value has a base of 10 with an exponent.
                10^3                  10^2            10^1                        10^0
            thousands      hundreds        tens                 ones or units
These are called "powers of 10".  In other words, exponents all with a base of ten.

We have ten fingers called digits.  Long ago, when people counted things, they counted on their fingers and kept track of groups of ten.  Symbols were developed for each of the number of things.  Ten symbols were developed: 0, 1, 2, 3, 4, 5, 6, 7, 8, and 9. When all their fingers, or digits, were used up, they recorded the number as 1 group of ten, or 10.  Notice that the 1 moves to the next higher place value, which became the tens. I am not sure how much I will discuss zero as a place holder and a symbol for an empty set, but the invention of zero was a significant advancement in the development of number systems.

From this, our system of numbers was developed based on groups of ten.  This became our base-ten system of numbers.

For years, teachers have used "base-ten blocks" or "base-ten drawings" to help students understand the idea of base-10 in our system, particularly how it is related to place-value.  Each symbol represents a ten-fold (ten-times) difference in size or value.  At this time, we will use the symbols for 100s, 10s, and 1s.

A couple of examples of base-ten drawings:



Homework is to make a base ten drawing for each of these eight numbers:

23
89
217
454
34
72
232
877

• Posted at Saturday, August 23, 2008 11:08 PM
• In General Category | Permalink