Topic: Perimeter and Polygons
Focus Questions:
- What are different attributes of polygons?
- How can we solve for the perimeter of different polygons?
- Why is perimeter important in work settings?
CRM Vocabulary (Last Quarter) Vocabulary
Angle vertex, acute angle, right angle, obtuse angle, triangle, rectangle, square, quadrilateral, parallelogram, trapezoid, polygon, customary measurement, pentagon, hexagon, octagon, rhombus, trapezoid
TEKS
§111.6.(b)(6) Grade 4, Adopted 2012
(6) Geometry and measurement. The student applies mathematical process standards to analyze geometric attributes in order to develop generalizations about their properties. The student is expected to:
(A) identify points, lines, line segments, rays, angles, and perpendicular and parallel lines
(B) identify and draw one or more lines of symmetry, if they exist, for a two- dimensional figure;
(C) apply knowledge of right angles to identify acute, right, and obtuse triangles; and
(D) classify two-dimensional figures based on the presence or absence of parallel or perpendicular lines or the presence or absence of angles of a specified size.
STRING SHAPES (25 MINS)
Divide students into groups of 3-4 students and have them find a relatively open space in the room. Let students know that they will have several tasks as a group. The first task is to great a triangle [or other shape] using their string. All students should be part of the triangle (touching the string) one way or the other.
Once students have made their triangles, ask them to “prove it,” or how they know that they’ve made a triangle.
Repeat this process with other shapes. Some suggestions are below:
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Parallelogram
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Rhombus
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Right Triangle
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Acute Triangle
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Obtuse Triangle
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Square
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Rectangle
Once students have practiced making shapes, ask them to find a way to measure the perimeter of the shape they create. This could take the form of standard measurement (if they want to get a ruler or yardstick) or nonstandard measurement (using pencils, fingers, feet, etc.).
Reflection Questions:
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How did you work together to make the shapes?
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How did you prove that you had created each shape?
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What is good about nonstandard measurement? Why might we use standard measurement instead?
PERSON-IN-A-MESS (20 MINS)
We’re going to use all of the skills you’ve been practicing. To do that, we’re going to do some imagining and use our theatre skills. When I put on this [costume piece] I am going to step into the role of someone who needs help finding the perimeter of shapes to do a project for her job. You’ll know I’ve stepped into role because I will have that costume piece on and will be “in role,” or playing the character. Any questions about that?
Okay great. Here we go. 3-2-1...
Hi, I’m Miss Sullivan, or you can call me Shelley. I work for the Plush Polygons, which is a company that makes rugs in fun shapes and colors, ready-to-order! I love my job, because I love making big comfy rugs, and I love helping people pick out the shape of rug that’s just right for them.
But I’m afraid I’m in pretty big trouble…you see, the most important feature of our rugs is that they are 100% guaranteed to last for life, and they last because they have this super-strong trim around the outside that makes them both pleasing to look at and really strong. But our distributor went out of business, so I had to find a NEW distributor to sell us the trim. I found one, and everything was going fine, but then I realized that the OLD distributor had all the records of how much trim we needed for each shape of rug stored in their system, and I can’t find any of my old notes about how much we ordered. We also just had an ENORMOUS order of rugs of all different shapes that came in, so I have to figure this out really fast.
While I was tearing my office apart looking for the order information, I did find these old drawings of our rugs. I remember that I have to find the perimeter of each rug to know how much trim to order, but I don’t know how to do that! I heard from Ms. Ward that you all were experts at solving for perimeter of polygons, so I thought I would come and ask you. Do you think you could help me?
[Take student answers].
Oh really, that’s excellent! Thank you so much!
So the first thing I need to know is, “What does perimeter mean?”
[Take student answers, scribe on the board.]
Oh, so you’re saying we have to take the lengths of each side of the shape and add them all together? Well that shouldn’t be too hard…what if we look at this one first?
[Look at SQUARE, which only has one side labeled.]
But wait, there’s information missing! I only have the length of one side. It looks like I must have spilled my coffee on the plans while I was rushing to get here to ask for your help. What are we going to do now?
[Take student answers, add together all four of the same number to get the perimeter.]
Oh, excellent! Now, what about this one? [Look at RIGHT TRIANGLE, which has all of the side measurements, but doesn’t have a label.] Well, that’s good, this one has all of the sides, so I know you can help me find the perimeter, but its label is missing! I don’t know what shape to call this order of trim! Do you know what kind of shape this is?
[Guide students toward the idea of a “right triangle.” Ask them to prove how they know that, take diligent notes, and write out “Right Triangle” on the drawing.]
Wow, Ms. Ward was right. You all are really good at polygons! I have some more shapes here…do you think you could help me find either the perimeter or the name of the shape based on this information? Make sure to show your work really well so I can take your notes back to my team at Plush Polygons so we know how to do it in the future.
Pass out a sheet to each group and ask them to solve for the perimeter based on the information given, and, if they are missing the title, to write that in as well and write down how they know the rug is that shape. Give groups time to work (5 minutes?), and have them share out their answers with the other groups.
Well, thank you so much for your help! I’m going to collect your papers and take them back to my office with me so that I can know how much total trim I need to order. I don’t know what I would have done without you!
- What were some of the things you had to do to help Shelley with her problem?
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How did you know how to solve for perimeter when there was information missing? How did you know which shapes were which?
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What other situations might require you to solve for the perimeter of polygons?
DESIGN PITCH
Out of role, either later, or through taking a phone call, let students know that Shelley was so impressed with their work that she has another project for them. She would like them to create a design pitch for what each of their groups’ rugs might look like (colors and patterns) and suggestions for what rooms they might be best in.
Students can work on large pieces of paper to re-create the shapes they had and design them, as well as create a short presentation about why they designed their rug the way they did, how much trim (perimeter) they will need to purchase, and why they think she shape of rug they have is appropriate for the room they chose.