LESSON PLAN

 

Name:  Terry Mulhollan

 

Title of lesson:

     Origami water bomb: confirm mathematical volume by experiment

 

Date of lesson:

 

Length of lesson:  Two 50 minute sessions

Description of the class

                          Course Title: Geometry

                          Grade level: 10th grade

 

Source of the lesson: Self

 

TEKS addressed: 111.34. Geometry

(e)1. The student extends measurement concepts to find area, perimeter, and volume in problem situations. 

             

The Lesson:

I.     Overview

The surface area of an origami water bomb (balloon) is much less that the surface area of the paper sheet from which it has been constructed, the paper difference being found in the folds of the construction.  Because the excess paper folds are on the outside of the water bomb, mathematically calculated volume should be very close to experimentally measured volume.  The purpose of this lesson is to have students brainstorm about how they would design an experiment to verify the volume calculated by their derived formula.

 

II.  Performance or learner outcomes

*Students will be able to design an experiment that independently confirms balloon volume.

*Students will be able to constructively discuss the pros and cons of alternate experimental designs presented to the class.

 

III._Resources, materials and supplies needed

origami paper

construction blueprint for water bomb

 

 

 

 

 

 

 

 

Five-E Organization

 

Teacher Does                                                             Student Does

Engage:

Mathematics frequently describes a perfect world.

 

For example, the water bomb (balloon) construction from an earlier lesson identified a mathematical relation between the side length of the balloon and the length of the paper used to construct it.

 

But how close is the mathematical expression to the real world?

 

You are going to design your own experiment to estimate the level of accuracy between your own water balloon and the mathematical expression,

cube side = (1/4)a, where a is the length of the side of a perfectly square piece of origami paper.

 

 

Students are listening.

                                                                                Evaluate

*Check that students have notes covering the earlier water bomb construction.  If not, then have them pair up with someone who does have notes.

 

Explore:

There are many ways to verify volume.  Here is one suggestion:  there is a blowhole built into the construction of the balloon, so perhaps the balloon could be filled with a known measurable substance, such as water or plastic micro-beads.

 

Work in teams of two.  This is a very quick 2- day project, so think simply rather than elaborately.

 

Your project will be graded by the following rubric which requires you to:

1. keep a journal which will contain:

(a)     a preliminary experimental design with diagram(s),

(b)    noteworthy computations required by the experiment, and

(c)     an informal but cleanly written discussion comparing the mathematical model with your experimental model and

2. actively participate during tomorrowÕs discussion session.

 

 

 

 

 

 

 

Students will have to brainstorm how to design an experiment based on limited equipment available to the average high school student:  rulers, graduated cylinders, mass scales, etc.

     Evaluate

*Students will turn in a preliminary experimental design idea by the end of the class.

*END OF LESSON DAY 1

 

Explain:

Each team will require individual attention tailored to their experimental design.

 

 

Experimental volume vs. Mathematical volume

 You will find that your experimental values for volume do not exactly match your calculated volume taken from the formula, cube side = (1/4)a.  This is because there are real world conditions affecting your calculations. 

 

Example 1:  if we chose to fill the water balloon with water, the paper would absorb some of the water.  The water absorbed by the paper should not be included in the experimental volume.  Q1: How do you separate the two numbers?

 

Example 2: if we chose to fill the water balloon with plastic micro-beads, there would be air space between the beads.  Q2: Would this cumulative air space cause your experimental volume to be significantly less than your mathematical volume?  Q3: How much less?

 

Notify students that their experimental designs will be collected 40 minutes after class begins. 

 

The class will then informally discuss the pros and cons of their experimental designs.

 

 

Students are working in teams.

 

 

 

 

 

 

 

 

 

 

 

 

 

1. Use waterproof paper rather than regular paper.

2. If regular paper is used, then determine its water soaked weight prior to folding. 

 

 

Students could build a large scale model of the stacked micro-beads to determine the air space between the beads, then scale their model down to determine the actual volume not filled by the beads inside the water balloon.

 

 

 

Students will quiz each other about their chosen experimental methods and remain open to suggestions from their classmates.

 

     Evaluate

*Score students for worthwhile active participation during group discussion.

 

Extend / Elaborate:

Have students write a few paragraphs about the other experimental methods revealed during class discussion.

 

Students will refer back to their notes for specific details regarding the other experimental methods outlined in the discussion.

 

     Evaluate

*Collect student journals the following day for evaluation.

*END OF LESSON DAY 2

Scoring Rubric:  Journal evaluation of experimental designs

                                                                                          No work                Modest work         Elaborate work

1. Diagram of experimental set-up

 

2. Short description of procedure

 

3. Possible pitfalls (sources of error) introduced

    by experimental procedure

 

4. How pitfalls (errors) can be eliminated or reduced.