Intermath | Workshop Support
 Write-up

Title

Problem Statement
On a calculator, enter the number 0.1. Continue to add 0.1 until you get 0.9. When you add another 0.1, what do you think you will get? Why? Continue to count to 4 or 5 by tenths. How many times do you have to add 0.1 to get from one whole number to the next? Try counting by 0.01. How many times do you have to add 0.01 to get from 0.01 to 0.1? Which is faster, counting by tenths to 10 or counting by hundredths to 1?

What real-world application can we use as a context for this exploration?

Problem setup

This problem involves closure of addition using rational numbers.  We are exploring the addition of tenths and hundredths and how rapidly these numbers approach whole numbers.  For example, counting by tenths to 4 or 5.

Plans to Solve/Investigate the Problem

Because of my existing mathematical maturity (Thanks Sarah), I recognized right away that it is quicker to count by tenths than it is to count by hundredths. And then also because of this, I know that there are the same number of incremental steps when counting to 10 by tenths as there are counting to 1 by hundredths.  My plan to explore this includes an Excel spreadsheet to demonstrate the incremental increases.

Investigation/Exploration of the Problem

Extensions of the Problem

The problem asks where this type of exploration may be applied in a real-world application.  It would be very easy to ask students to make the connection of counting by tenths and hundredths using dimes (tenths) and pennies (hundredths).

Author & Contact
Teresa Johnson
Email me