EMERGE LESSON: STRING ON A TAPE ROLL

Linear Function – Suitable for grades 5-11

In this Emerge lesson, students compete in teams to uncover the relationship between the number of times a roll of tape turns and the length of an attached string.  Game on!

THE LESSON

PHASE 1: INTRODUCTIONS

1.  Explain the game to students.  Make sure they are grouped into teams and that each team has a whiteboard.

PHASE 2: EXPLORATION (10-15 minutes)

1. Play the video below and pause it when prompted.

2.  Explain that each team will be responsible for guessing the length of the string.  The team with the closest guess wins that round.

3.  Give each team a small amount of time (30 seconds to 2 minutes) to discuss and agree on a guess, write it on their team whiteboards, and hold it in the air so that it cannot be changed.

4.  Play the video again, revealing the length.  Pause it when prompted again and announce the winner.  Have students record the length and number of tape roll turns (0) on their handout.

5.  Ask students to discuss, in their groups, what they notice and wonder about the situation.  Have a few students share.

6. Play four more rounds of the game, following the video’s prompts each time.

PHASE 3: STUDENT PRESENTATION (10-15 minutes)

1. Play one last round, but this time, ask students to carefully record the method they are using on their whiteboards.
2. After the final length is revealed, have some of the student teams present their methods.  Summarize and consolidate some key information that will connect with the Formal Learning Phase, which comes next.

PHASE 4: FORMAL LEARNING (30-45 minutes)

In this phase, the teacher introduces a specific, formal mathematical method for guessing the length of the string after each round.  The method that is taught will depend on the course and grade level.  Each teacher will have to determine what the appropriate method is for their course.  Here are the suggested methods based on general grade level ranges:

Elementary (Grades 5-6):  Have students determine the unit rate using decimal subtraction and division (if 1.5 turns made the string 30 sm shorter, how much shorter would 1 turn make it?)  Then have students apply that unit rate to future rounds.  Finally, have the students find the mass of the cup and cubes using decimal multiplication and subtraction (How long would the string be after 2.25 turns?  Well, since 1 turn reduced the string length by 30, 2.25 turns would reduce the string length by 30*2.25 = 67.5.  Subtracting this number from the original length of the string gives us the current length of the string.

Middle School (Grades 6-8):  Have students determine the length of the string using proportional reasoning (if 1.5 rolls shortened the string by 30 cm, then 2.2 rolls would shorten the string by how much?)

High School (Grades 8-11):  Have students write a linear function that describes the data by calculating its slope and y-intercept.  Then have students use the linear function to determine the length of the string during each round.

Regardless of the method taught, the steps of this phase are the same:

Modeling and Guided Practice

1. Using the Phase 4 section of the lesson handout, model the method you are teaching on the first set of data.
2. Allow students to try to recreate the method on the second set of data.  Guide them where needed.
3. Allow students to try to use the method on the third set of data independently.

Independent Practice in Context

Play the video below and allow students to use it to practice their new skills on another concrete context.