ORIGAMI: LESSON PLAN 2

Name: Baburam Kharel (BK)

Title of lesson: minimizing and maximizing of surface area.

Date of lesson:

Length of lesson: 50 minutes

Description of the class:

                          Name of course: Geometry

                          Grade level: 9th and 10th

                          Honors or regular: Pre-AP

Source of the lesson:

               Original

TEKS addressed:

      Geometry (e).1(D) Students find surface areas and volumes of prisms,                                                               pyramids, spheres, cones, and cylinders in problem situations.

I.             Overview

Students will develop a very useful concept of how the same volume can be enclosed by different surface areas and apply their knowledge in solving word problems, for example, involving  the total cost of painting, wrapping, carpeting, tiling, etc.

II.   Performance or learner outcomes:

Students will be able to:

á        Find the minimum and the maximum surface area for a given volume of rectangular prism.

á        Calculate the total cost of painting or wrapping a rectangular prism when the dimensions of the object and per unit cost are given.

III. Resources, materials and supplies needed

 Eight origami cubes per group made in last class, calculators, rulers are optional.

IV. Supplementary materials, handouts.

                 Work sheets.

Five-E Organization

Teacher Does                      Probing Questions                                     Student Does      

Engage:

Talk about the mistakes, if any, from previous classes work sheets.

Last time, you learned about surface areas. Today you are going to find out how volume and surface area of a rectangular prism are related.  You might want to talk with Robert about this lesson.  He, too, has an introductory lesson on volume – although it's volume of a cube.

Do you have any questions from your last class?

Can any one tell me what volume is? Or give me an example of volume.

How do you find out how much water a rectangular swimming pool can contain?

If any, then will be redirected to the class.

Amount of water in a swimming pool?

l×b×h

Explore:

Pass out the work sheets and the origami boxes they made last time and form groups of 4 students for the activity. Supply additional boxes if not enough from last time.

Guide their activities with the help of work-sheet and supervision.

      Group the given eight blocks (cubes) I'm confused, which size of blocks are they using?  The really big boxes they folded last time or smaller cubes?  If they are using big blocks and only have four blocks there are only two arrangements they can make – that seems kind of boring.  Where will they get the additional 4 blocks – do they make them or you? in many different ways to come up with different rectangular prisms of different dimensions. Make sure that all eight boxes are used every time and that one face of one box covers a face of another box completely. Partial contact is not wanted. Note down the dimensions and calculate the corresponding surface areas and the volumes.

Work in groups of 4, and come up with results/data.

Explain: 

Acts as a discussion leader, help different groups reach to the conclusion that enclosing the same volume you can have different surface areas.

What is the volume in each case?

 Surface areas?

Tell me the situations when the surface area is minimum and maximum.

What did you learn?

Different groups will present their findings.

Extend / Elaborate:

Asks further.

1. Suppose those eight boxes are blocks of ice. How would you stack them in order to minimize their melting process?  This is a great question! 

Which of the positions in your work sheet will maximize the melting process? Why?

2. If the cost of wrapping is 10 cents per square inch, how much will you have to spend on wrapping those eight boxes?

Cubic position.

When all of them are stacked in a row or a column. Because that's when the surface area is maximum.  Nice.

2.  6 (2.2 + 2.2) ^2 * 10 cents.

  Evaluate:

 Wrap-up:

Revise the student's explanation if needed.

Quiz;

  1. What are some units of surface area?
  2. Calculate the surface area and volume of a rectangular water tank of dimensions 4 feet × 3feet × 5 feet. This sort of question just seems way too easy – maybe ask something about advertising and if they would want to min/max surface area and what effect that would have on the volume of their product packaging.

Can some one explain what you learned today?

 

Name:                                                                                                   Date:

Surface Area Work Sheet

Group/stack the given eight blocks in many different ways to come up with different rectangular prisms of different dimensions. Note down the dimensions and calculate the corresponding surface areas and the volume.

Do you need a ruler to find the dimensions? Why or why not?

Shape Dimensions

Surface area

(Do not forget units)

Volume with units

(Do not forget units)

Shape 1:

l =

b =

h =

   

Shape 2:

   

Shape 3:

   

Shape 4:

   

Shape 5 :

   

1. What remains unchanged?

2. What is changing?

3. When is surface area the minimum?

4. When is surface area the maximum?

5. What did you learn from the activity?