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.) |