To begin the lesson, I show the students the image that's used here as the lesson image. I ask them to consider our snowfall this year. Did they think it was more, or less than the amount shown in the image? Actually, we received approximately 93.6 inches this winter in Michigan!
I then ask what the "point 6" meant to them. I explain it means more than 93 inches, but not a whole inch more. This decimal number means 6/10 of the next full inch and it is just like talking about fractional parts. The ruler helps us determine more closely a measurement.
Next, I show the students a set of number lines that run from 0 to 1. Some are partitioned, and some are not. They are asked to figure out the intervals on the first page (twelfths) with their partner. I then ask them if they can use 12 as a number to figure out equal intervals, like the ones labeled to the side of each line. You may want your students to place the pages side by side in order to see the pattern.
As they work on this, with or without the Cuisenaire Rods, I travel around the room listening for precise vocabulary, and asking questions to take the children's thinking deeper. When you ask children to discuss their understanding and to look for patterns outside of the basic outcome of the lesson, you raise the rigor of the task. This is critical and a part of the Mathematical Practices.
In this clip, you hear my student looking for a pattern on the page, which causes him to look at all the information, rather than each question or task as an isolated incident.
Also, during the activity, the students are asked to interact with various questions about the same number line, partitioned the same way, but with different tools. Each page takes away one "guide" and has the students making sense of the number line with fewer visual clues. On the last page, they must find the Cuisenaire rods that make the partitions equal on the line.
This student, in these two clips, is explaining what each of the numbers mean, and how she makes sense of 2/2 equaling 1.
This student explains what each fraction means on the number line. It is important to make sure the students know what these numbers represent.
You might want to place the pages found in the resource section side by side in order to compare twelfths to the other fraction names. If this comes up with the students, definitely begin a chart of equivalent fractions.
As a wrap up, I ask student teams to talk with another team about what was tricky today. Specifically, I ask them to share strategies with each other that they used to figure out the open number line for the sixths.
Many teams discuss that they divide the thirds in half (which was wonderful) as they were unable to find a Cuisenaire rod that equaled 1/6.
One student shows me how he learned the the number of "lines" to partition was one less than the unit fraction denominator. He also is able to locate some equivalent fractions, as seen in the reflection video.