Context for this Lesson
TOPIC: Finding the perimeter of polygons
GRADE LEVEL: 4th Grade
- What are different attributes of polygons?
- How can we solve for the perimeter of different polygons?
- Why is perimeter important in work settings?
§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.
CRM Vocabulary (Fourth Quarter)
Angle vertex, acute angle, right angle, obtuse angle, triangle, rectangle, square, quadrilateral, parallelogram, trapezoid, polygon, customary measurement, pentagon, hexagon, octagon, rhombus, trapezoid
MATERIALS NEEDED: Ball of yarn cut, worksheets with different-shaped polygons as described in lesson (approximately 6, depending on size of class)
1. STRING SHAPES
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 create a triangle 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.
- Right Triangle
- Acute Triangle
- Obtuse Triangle
Once students have practiced making shapes, ask them to find a way to measure the perimeter of the shape they create. They get to choose how they do this; they might use a form of standard measurement (if they want to get a ruler or yardstick, or measure by tiles on the floor) or nonstandard measurement (using pencils, fingers, feet, etc.).
- How did you work together to make the shapes?
- How did you prove that you had created each shape?
- What is good about nonstandard measurement? Why might we use standard measurement instead?
2. PERSON IN A MESS
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.
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?
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, your teacher 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.
3. DESIGN PITCH
Goodness, you all are really good at this! I think you might be better at it than our old supplier. Your teacher just mentioned to me that you are also excellent artists; while I'm here, I'd love to get your thoughts on some new designs for the rugs!
Now that you've solved for the perimeter (so I know exactly how much trim to buy), could you design the kind of rug you'd like to see? You can choose the color of trim that will go around the rug, as well as the design. If you could also write a suggestion for where you think these rugs might go (in someone's house, in a classroom, outside, etc.), that would be great! You all are inspiring me to start a new marketing campaign! You can create your designs right over those drawings, because I'm going to come around and collect the amounts of trim I need to buy and write them here on my purchase order (clipboard). You can also write your recommendations for the uses of the roles there in the margins.
Give students time to create their designs, while checking for their understanding of perimeter (in role).
Transition: Thank you so much for your help today! I would love to collect all of your designs to take them back to my team at Plush Polygons. I need to run to make sure I can put in these orders for the trim by the end of the business day. Thank you again so much for your help! And now I'll step out of role in 3-2-1. Take off costume piece.
4. REFLECTING ON THE LESSON
- What were some of the things you had to do to help Shelley with her problem?
- How did you know how to solve for perimeter when information was missing?
- You could you tell which shapes were which based on the measurements?
- When else might you need to solve for the perimeter of a polygon?
- What careers might require you to make design choices as well as solve math problems?
- Ask students to solve for the area of the polygons as well (so Shelley knows how much material, as well as trim, she needs to order).
- Give students materials like felt, yarn, and fabric and ask them to create the rugs they have drawn on paper.
- Construct rugs that are composite shapes and ask students to solve for perimeter and/or area.