The students have had experiences dividing a number line into fractional parts in order to make one whole. Today, I will begin to work with them on going beyond one whole.
To begin, I place a number line on the board with divisions labeled to 5/2. I then ask the students to turn and talk about what they notice and what they understand.
This clip sums up the students' beginning understanding, and is the jumping off point of our lesson.
After listening to some ideas, I place the Cuisenaire rod that I had used (red) to create the 1/2 unit fraction. I ask the students to tell me how many of those rods I need to create a whole. I was not surprised that they knew it was 2. I ask them to explain to their partners why 2 is the correct number.
I then put 2 up and label its end mark as 1 Whole and discuss the fraction 2/2. Next, I place 3 more rods on the line and ask the students to remind each other what the unit fraction name is that we are working with and to count how many we have on the line. I then ask them to share with each other what 4/2 would equal in terms of wholes. (Every 2/2 is one whole). By this point they are able to recognize that we have 2 Wholes on the line and 1/2 "remaining".
In order to give the students practice in iterating unit fractions and naming more than one whole, I supply them with strips of adding tape and Cuisenaire Rods. I also place the following scenarios on the board.
If the purple rod equals 1/2, label the intervals from 0/2 to 9/2. Find and label the wholes.
If the light green rod equals 1/2, label the intervals from 0/2 to 9/2. Find and label the wholes.
If the brown rod equals 1/4, label the intervals from 0/4 to 9/4. Find and label the wholes.
If the brown equals 1/3, label the intervals from 0/3 to 8/3. Find and label the wholes.
I ask the students to work through the list at their pace, using a different strip for each activity. As they work, I circulate the room and watch for correct labeling. I also frame my questions to prompt the appropriate use of our mathematical vocabulary terms as well as elicit student understanding of how more than one whole can be made using unit fractions.
In this clip, my student explains what her interval is and how she knows where to label the whole numbers.
My close today is a bit different. Instead of pulling the entire class together, I ask students at different times to come to the board to examine the number line we started at the beginning of the lesson. I ask each of them a different question based on what I learned from them during the active engagement.
Some are asked to recreate the iteration of the unit fraction, some are prompted to explain why the 2 is placed where it is, and some were asked to describe patterns that they noticed.
This student is noticing a pattern in the numerators and denominators, so he's asked to explain his thinking.