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Letter to
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| Grant |
Name: Rebecca Johnson
Title of lesson: A Pen for Penny
Length of lesson: 50 minutes
Description of the class:
Name of course: 6th grade Math
Grade level: 6th
Honors or regular: Regular
Source of the lesson:
Original, but based loosely upon an activity done in a past high school math class.
TEKS addressed:
6.8A Estimate measurements (including circumference) and evaluate reasonableness of results.
6.8B Select and use appropriate units, tools, or formulas to measure and to solve problems involving length (including perimeter) and area.
I. Overview
Students will learn to create different shapes with the same perimeter and compare their areas. This is important to understanding why some shapes are more commonly used in architecture than others.
II. Performance or learner outcomes
Students will be able to:
- Construct regular shapes with a perimeter of 20 inches
- Measure and compare the area of the constructed shapes
III. Resources, materials and supplies needed
ê 20 inch strands of yarn (Class set)
ê Rulers (Class set)
ê Pencils
IV. Supplementary materials, handouts.
§ Pen Dimension Chart
Five-E Organization
Teacher Does Probing Questions Student Does
Engage: The Austin Zoo has just received news that they will be receiving a new guest—Penny the Penguin! The Austin Zoo has a job for you. You have just been hired as an architect! |
Does anyone know what an architect does? What types of skills would an architect need to have? |
Students will probably respond that an architect is someone who builds buildings. Students may or may not know that architects need to know formulas like perimeter and area to know how much of materials to buy. |
Evaluation: Check to see that students understand what an architect does and which formulas they might be using today.
Explore: The teacher will introduce the challenge: The Zoo needs to build a pen for Penny the Penguin. They would like the pen to be as big as possible for her so that she has lots of room to play; the only catch is that they have already purchased the building materials. You have only 200 feet of fencing to work with, but you may make the pen in any des ign that you want.Your challenge is to build a pen for Penny the penguin that maximizes the area of her pen. You may use the yarn to model different pens. Please work in partners and measure and record your attempts on the handout. Once you have found your best design, please tape it to a sheet of white paper with your name, the name of the exhibit, the perimeter, the scale, and the area. |
Who can tell me what the formula for perimeter is? (for different shapes such as squares, rectangles, triangles, circles, etc.) What do we already know about the perimeter of Penny’s pen? If I give you 20 inches of yarn, how could that represent 200 feet? Who can tell me what the formula for area is? Which shape pen do you think will produce the greatest area? (i.e. the most room for Penny to play.) What makes you think that? |
Students should be able to give formulas easily, possibly needing some reminders about the formula for the area of a triangle. Students recall that they only have 200 feet of fencing. Students may or may not come up with the idea of letting 1 inch of yarn=10 feet in real life. Students will work in partners with their string to model different sizes of pens. Students will record their attempts on the data sheet. |
Evaluation: Formative assessment, the teacher will walk around checking to see that each group is modeling different areas and recording them.
Explain: The teacher will let students present their ideas and facilitate discussion. |
Which type of design maximized area? Why do you think this is? Is that what you expected? Would this still be the best design if you had 1,000 feet of fencing instead of 200? What are the advantages to choosing this type of design? What are the disadvantages to choosing this type of design? |
Students will present their designs, especially those that maximized area and those that minimized area. Students will explain how they arrived at the presented areas. Students will discuss as a class, advantages and disadvantages of each design. |
Evaluation: Students will be assessed on how well they presented, on how well they listened appropriately to other groups’ ideas, and if they are able to participate in discussion.
Extend / Elaborate: Write a letter to the director of the Austin Zoo. |
What would the zoo director be interested in when picking a pen design? |
Cost, attractiveness, size, etc. Students will write a brief letter to the director of the Austin Zoo in partners stating why their design is best for the Zoo; the letter will also include a sketch of their pen and a description of the perimeter and area of the pen. |
Evaluation: Teacher will check to make sure the students argument makes sense and includes a description of how the student came about their choice. (i.e. how they measured the area and perimeter.)