Area and Perimeter of Complex Figures
State Standards Addressed:
The content standard that this
lesson will address will be taken from the fourth grade mathematics standards.
The class is designed to be an extra support element for students in grades 4
through 6. Due to the review and support nature of the class the standards
addressed may be below the grade level of individual students, but are relevant
to the content of the course.
4th Grade
Algebra and Functions
1.0 Students use and interpret variables, mathematical symbols, and
properties to write and simplify expressions and sentences:
1.1 Use letters, boxes, or other symbols to stand for any number in
simple expressions or equations (e.g., demonstrate an understanding and the use
of the concept of a variable).
Measurement and Geometry
1.0 Students understand perimeter and area:
1.4 Understand and use formulas to solve problems involving
perimeters and areas of rectangles and squares. Use those formulas to find the
areas of more complex figures by dividing the figures into basic shapes.
Content Standards can be found in
full detail on pages 16 and 17 of the Mathematics
Content Standards for California Public Schools.
Introduction:
Knowing how to calculate area is a
very important skill for all students to learn. Now that we have covered and
learned how to find the area of basic quadrilaterals, area= length x width, we
are going to learn how to apply this skill to more complex figures.
In many real world applications our
shapes will not be perfect squares and rectangles. In this lesson we will be
taking our understanding of calculating area and applying it to more complex
polygons.
A basic polygon is typically a
square or a rectangle. The formula for calculating the area of these shapes is
A=L x W.
For this basic polygon our formula
to calculate the area would be A= L x W. For this figure our length is 5 in.
and our width is 7 in. So our formula would be A= 5in x 7in, or A=35in^2.
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But what if the shape that you
wanted to calculate the area of was not a basic square or rectangle? We are
going to learn how to apply our newly learned skills to complex shapes. By the
end of the lesson you will be able to calculate the area of a shape like this
one with no problems.
Task/Process:
For this lesson you will be asked
to work both individually and in a pair.
Each individual will watch and respond to a video on how to calculate the area of complex figures. In your response please discuss what you learned from the video and what you still are unclear about. After posting your response to the video read through and respond to 2 classmates posts. Your responses should be relevant and if possible you should address issues that they are still having with the concepts.
Each individual will watch and respond to a video on how to calculate the area of complex figures. In your response please discuss what you learned from the video and what you still are unclear about. After posting your response to the video read through and respond to 2 classmates posts. Your responses should be relevant and if possible you should address issues that they are still having with the concepts.
Along with the discussion you will
be working in groups of 2, you will create a short power point presentation
similar to the teacher created one linked here: Finding the Perimeter and Area of Complex Figures.
Your presentation should follow the
progression of the teacher presentation. You and your partner must create a
complex figure, find and label all the sides and lengths on the figure, and
calculate the perimeter and the area of the figure. You will be graded on your
detail explanation of the steps needed in order to complete the problem. You
may choose to complete the problem together or you may choose two figures and
complete them individually. Even if you choose to do two problems both partners
should check the work and the calculations on the entire presentation. One
grade will be given for the group.
Resources:
To complete these assignments there
are some videos that you will need to watch.
To view the technological
components you will need to have access to you tube, an internet image search,
and Microsoft Power Point.
§
The
video to watch is Area of Complex Figures-Finding Missing Lengths (#3 and #4)
You can access them here:
§
The
power point example can be viewed here:
For
your power point you will need to access an internet search engine to find your
complex figure for your power point presentation. To aid your search I suggest
these search terms: perimeter and area of complex figures. After doing your
search choose a figure that does not already have the problem worked out and
copy and paste the image into your presentation. Please include the website
link for your image so that I may look at your source.
Rubric/ Grading:
Discussion Rubric
Category
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Description
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Points
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Initial Response
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Student clearly responded to the video. Student touched on both
required aspects of the discussion.
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10 points
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Response to Peers
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Student posted two additional posts to peer submissions. Responses were
relevant and meaningful.
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5 points for each response
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Total Points Possible
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20 points
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Power Point Rubric
Multimedia Project : Area of Complex Figures Presentation
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Teacher Name: Ms.
Brodie
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Student Name:
________________________________________
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CATEGORY
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5
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4
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3
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2
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Design
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Makes excellent use of font, color, graphics, effects, etc. to
enhance the presentation.
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Makes good use of font, color, graphics, effects, etc. to
enhance to presentation.
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Makes use of font, color, graphics, effects, etc. but
occasionally these detract from the presentation content.
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Use of font, color, graphics, effects etc. but these often
distract from the presentaion content.
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Requirements
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All requirements are met and exceeded.
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All requirements are met.
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One requirement was not completely met.
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More than one requirement was not completely met.
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Content
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Covers topic in-depth with details and examples. Subject
knowledge is excellent.
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Includes essential knowledge about the topic. Subject knowledge
appears to be good.
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Includes essential information about the topic but there are 1-2
factual errors.
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Content is minimal OR there are several factual errors.
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Organization
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Content is well organized using headings or bulleted lists to
group related material.
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Uses headings or bulleted lists to organize, but the overall
organization of topics appears flawed.
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Content is logically organized for the most part.
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There was no clear or logical organizational structure, just
lots of facts.
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Mechanics
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No misspellings or grammatical errors.
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Three or fewer misspellings and/or mechanical errors.
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Four misspellings and/or grammatical errors.
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More than 4 errors in spelling or grammar.
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Total Points: /25
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Conclusion:
At the end of this assignment you
should feel more confident in your area and perimeter skills. We have taken our
basic skills and learned to apply them to more complex and difficult problems.
In this lesson you have learned that problems will typically take multiple
steps that must be organized properly to successfully reach an answer. From
this lesson you should be able to correctly find the answer to any complex area
problem. If you do not yet feel fully confident in your new skills it is alright.
Keep practicing and please feel free to contact me with any questions or issues
that I can clarify. As an additional tool to keep practicing and sharpening
your skills visit this site, it will allow you to practice finding area in a
fun and easy way WWW.ixl.com
it is great for extra practice.
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