In this lesson students will further their understanding of using fractions on a number line by completing a task that requires demonstrating knowledge of number line fractions. Students will also use number line fractions as a ruler to measure lengths.
To begin this lesson students will participate in an activity called On the Line. This activity and description are from activity 12.9 in the second edition of Teaching Student-Centered Mathematics by John Van de Walle.
Have two students stand and form the end points of a number line using a piece of rope. One stands at zero and the other student to the right at one whole(about 10 feet apart). Each student holding the rope will have a clothespin attached to the rope with a card marked 0 or 1 for the class to use as a guide. Give out a variety of fractions on cards with clothespins—one to each team of two students. Then ask for a volunteer team to place their fraction on the number line. The likely respondents to start may have a card with 1/2 or 1/4. Place those and then call on others to come up and locate their fraction on the number line. Make sure students talk to each other as they agree or disagree on a location or as they think aloud about their decision making. Ask students who are watching a placement why an estimate of a location is a good one. At first, you may want to give students with disabilities unit fractions. That will help them estimate the distances(even by folding the rope if needed).
The task for this lesson involves students using their knowledge of fractional parts and numbers to solve the problem. After introducing the task to the students I allow them to work in small groups to strategize a solution. As the groups are working I circulate the room and guide student thinking. I let them struggle a bit before guiding them too much(MP 1).
An inchworm is at the bottom of a 7 feet deep well. During the day he climbs up 3/4 of a foot but slips back down 1/4 of a foot at night. How many days does it take for the inchworm to get out of the well.
The goal is that students create a number line from 0 to 7 and divide each part into fourths(MP 4). They then could use curved lines or something similar to show the up and down of each day and night. The trick is that students must realize that on day 13 the inchworm actually reaches the top of the well. Some students might rationalize that each day he goes 1/2 foot so it would take him 14 days to get out but on day 13 he was already out of the well.
To wrap up this lesson I have students take an interactive quiz that I display on the document camera. I found this on Dad’s Worksheets under Mark the Ruler. I have the class complete this quiz as a group by displaying one of the questions and asking for a volunteer to come and show the answer by marking it on the whiteboard. Once the student has marked their answer I ask the rest of the class to evaluate the thinking of their peer(MP 3). I ask students to share their responses to first student. I do this for the next four questions.
I go through two interactive quizzes. The first one I do is wholes, halves, quarters. If the students do well with this one I move on to quarters and eighths. If they did not do well, I select a different version of the first quiz.