I ask students to think about what other fractions there might be besides halves, fourths, and eighths. I'm always hopeful that someone will say tenths!
First I have them share their thoughts with a neighbor and then call on a few students to share with the class. In this part of the lesson, I emphasize their willingness to stretch their thinking rather than getting into the details of any particular fraction.
I tell them that today we will work with thirds, sixths, and tenths.
Today we go through the same process with thirds, sixths and tenths that we did with halves, fourths and eights. Dividing a line segment into thirds is more difficult than dividing it in half. Here is how I teach it:
I like to have my students work through this on whiteboards because it gives them practice dividing the number lines into thirds but I provide a page for students with handwriting challenges or an overwhelming desire to make "the perfect line".
I observe how students are processing the idea of thirds and sixths and if it seems that the majority of them can move to ninths without being discouraged or confused, I do so. Then I move to tenths and for that I draw the line or project it on the board myself. They don't need to write out the number line with 12 marks at this point. (zero, the 9 dividing lines, and 1).
If students made a constructive choice yesterday, I let them choose their "level" again today. Often students who choose the "easier" list will ask if they can also do problems from the more difficult list. What teacher would ever say, no?!
I project Fractions on Number Line (thirds, sixths differentiated) independent practice on the board and students draw the number lines on their whiteboards. I have students work with "teacher" partners, some self-selected and some teacher chosen. As they are working, I walk around to discuss their thinking with them. Here is a Student Thinking about Thirds.
I have students write an answer to this prompt in their journals OR ask them to think about it and then write it up at home. Any answer is okay as long as they make an attempt.
What pattern did you see with sixths and thirds that was similar to a pattern you observed with eighths, fourths and halves?