Divide Fractions with Number Lines

In math we are currently learning how to take a whole number and divide it by a fraction...actually a decimal fraction.  Today we thought about how we can break down a fraction in terms of what it equals to 1.  For example, how many tenths = 1? 10...so 10/10 = 1...got me?  

We figured out then that if 1 is made up of 10/10s, then 0.1 x 1 = 10.  

So...we can quickly then figure out that 3 x 0.1 = ___ (using the above idea that 0.1 x 1 = 10) simply multiply the answer by 3...so 3 x 0.1 = 30.  This means that 30=tenths make up the number 3.

Our final problem today asked the following:

Amber bought a 6-meter roll of ribbon.  She needs pieces that are 20 centimeters long.  How many pieces will she be able to cut from the roll?  Show your thinking.

This problem assumes something significant...that students know how much of a meter 1 centimeter equals (1/100) OR how much of a meter 10 centimeters equals (1/10).  

A couple of my students figured this problem out using a number line version by taking meter sticks and determining the answer...great way to show their thinking:

Another group of students determined the answer by using what they already knew about meters, centimeters, and newly acquired information about division (and multiplication) of fractions and decimal fractions.

This is exciting to see students really using what they have learned throughout the school year in order to solve one problem.  COOL!