EMERGE LESSON: TOPPLING TOWER OF CUBES

Quadratic Functions – Suitable for grades 7-12

In this Emerge lesson, students compete in teams to uncover the relationship between the number of blocks in a tower and the distance the top block will travel if the tower is knocked over.  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 (20-25 minutes)

1. Play the video below, pausing and following the directions 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 distance.  Pause it when prompted again and announce the winner.  Have students record the distance and number of blocks (5 in the first case).

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

6. Continue to play more rounds of the game, following the video’s prompts each time.

PHASE 3: STUDENT PRESENTATION (10-15 minutes)

1. For the last round, ask the students to carefully record the method they are using.
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 distance the block travels for 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:

Middle School (Grades 6-8):  Have students predict the distance the block will travel using graphical analysis and rate reasoning.  Specifically, have them calculate the rate of change between relevant data points that are known.  Point out that the rate of change between data points is not consistent.  In general, the rate of change seems to be going up as the number of blocks increases.  To make a new prediction, calculate (or use the graph to find) what the distance would have been if the rate of change was constant.  Then, if the data point you are looking to find is between two data points that you’ve found the rate of change between, decrease the prediction a bit to account for the fact that the rate isn’t constant.  If the data point you are looking to find comes after or before two data points that you’ve found the rate of change between, increase the prediction a bit to account for the fact that the rate isn’t constant.  After a few data points have been revealed.

High School (Grades 9-12):  Have students use quadratic regression to find a quadratic function that describes the data.  As more and more data comes in, students can update the regression and use it to make their predictions. 

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.

VIDEO COMING SOON