Context for this Lesson
Focus Questions: What are the differences between basic shapes? How do you find the area and perimeter of basic shapes? What are real-life applications of shapes?
Invite students to sit on the floor in a circle.
Good morning. Today, we have a special visitor, an architect. When you hear the word architect, what do you think of? (Take Brainstorm Responses) Eventually connect ideas to suggest that an architect designs buildings. Our architect guest is currently working on a special project, but she’s having some problems. In a moment, when I put on this belt and hat, I’m going to become an Architect who really needs your help. Do you have any questions? Great help me count down from 5 and I will step into role. 5-4-3-2-1.
(Teacher steps into role.)
Hello, kids! I’m Miss Buildsalot. Oh, it’s so nice to meet you. I have a question for you: what did the acorn say when it grew up? Geometry! Haha, oooh, that one cracks me up every time! But, well, you know, I came here for your help, and I hope you can help me out because your teacher says you’re real experts in Geometry. Every year I enter the International Geometric House Contest to measure and build the most beautiful house constructed from three different geometric shapes but... I’ve never won, and I really hope to this year with your help. Because, you see, I seem to have mixed up all my files and I can’t remember which shapes I was using to build my Geometric House for the contest! I do have these 3 measurements, and each one goes with one of the shapes, but I’m really having a hard time knowing which shapes these measurements represent!
(Post measurements on the board as you say the following dialogue: -- I used measurements in inches to help students make a connection to the inch graph paper at the end of the lesson)
SHAPE 1: 2 inches wide, 4 inches long, 2 inches wide, 4 inches long
SHAPE 2: 5 inches wide, 5 inches long, 5 inches wide, 5 inches long
SHAPE 3: 3 inches long, 3 inches long, 3 inches long
Do these measurements tell you anything? What predictions can we make about the shapes with this information? (make predictions based on information)
Hold onto those ideas, because I’m going to need you to tell me what you’re thinking in just a minute. You see, without the designs for these measurements, I can’t build anything for the contest. I’m hoping you geometry mathematicians can help me out. I’m so confused I can’t even remember any names of any of the 2-dimensional shapes these measurements belong to... She breaks down into overblown tears. Large nose blow. (an idea)
Oh perhaps you can help me. Can any of you name any two dimensional shapes? (Write responses on board. Square, Rectangle, Circle, Triangle, etc.)
Transition: Wow, that’s a lot of shapes. I’m really a visual learner. Do you think you could show me what they look like by building them with your bodies. I know if I see them again I’ll remember which design goes with which measurement. Here, I have an idea. I’ll pass around these pieces of string. Let’s see if we can make three/six? groups with each of you putting two hands on the string so you can help me visualize what these shapes look like.
Shapes with String/Solving Perimeter of a Polygon
I have to be able to concentrate to be able to visualize these shape, so I’d really like you to make your shapes without talking. I know you can do it., I really want you to show me what each of these shapes looks like using your string. Remember, you need to hold the string with two hands at your waist level. What’s a (looking at list on the board)….square? Please show me a square with your string. (Class makes a square.) Can you remind me, what is special about a square? If you have an idea, nod your head so I call on you - don’t let go of that string! (get answers about equal sides) What a beautiful square -- You’re right! I see four vertices and four sides. Let’s look at my measurements, which of my measurements do you think might be made for a square shape? Why? (identify SHAPE 2). Of course, that’s right, now I remember I was going to outline my entire square shaped house design with a single, long strand of spaghetti. That’s sure to impress the contest judges...but I need to figure out how long the spaghetti needs to be. How can we figure out how long the spaghetti will need to be to go all the way around the perimeter of my house? (work with students to solve the math problem) Students can also be used as units of measure (i.e., each student equals 1 ft) to create the perimeter of the square.
Looking at our list of shapes, I also seem to recall that a rectangle has four vertices and four sides – isn’t that the same as square? Are they the same thing? How is a square different? (Responses.) Oh, I see, a square has four equal sides. Just to be sure I know the difference, please make a rectangle. Ok, now I see – two sides are longer. And what kinds of vertices or angles are on rectangles? (Possible side-coaching: obtuse angles? acute angles?). A right angle? I happen to have some angles in my pocket (reveals large cut outs of acute, obtuse, and right angles), so let’s test them out. (Obtuse angle:) No, that’s too big. (Acute angle:) That one’s too small. (Right angle:) Aahh, this one’s the right angle - get it?; it matches this corner perfectly!
Let’s look at my measurements, which of my measurements do you think I was planning to use for my rectangle shape? Why? (identify SHAPE 1). Of course, that’s right, now I remember I was going to outline my entire rectangle shaped house in a giant yellow bow. That’s sure to win the prize, right...but I need to figure out how long that ribbon needs to be, how can we figure out how long the yellow ribbon will need to be to go all the way around the perimeter of my rectangular house? (work with students to solve the math problem) Students can also be used as a unit of measurement on the string shape of the rectangle.
Okay, so we have one measurement left, SHAPE 3, what shape do you think this measurement might be for? (take predictions) Why? Let’s see if each group can find a way to make a triangle that would represent these measurement. You can use the techniques we already tried. (groups do their work and then share out with each other)
Student Math Assessment and Design Shape House
You all are such incredible shape-makers that, well…I wasn’t going to tell you this before, but you’ve already helped me out so much, and you’re just so smart….I actually would really love your help making designs for the Geometric House Contest. If everyone can return to their seats by the count of 5 I could really use your expertise. (pass out shape pages) On your page are measurements for a shape house but some of the measurements are missing, including 2 sides and the perimeter of the house. Your job is to solve the geometric addition equation on your paper first, and then use the measurements you calculated to draw the shape house on the graph paper. After you’ve drawn the house, you can design whatever you think might be fun on the perimeter of the house. And then give your house a name relating to the perimeter of your house. For example here is my picture of the spaghetti house. Pretty cool, huh? (And for a special bonus, you can even find the area of the house!)
Does anyone have any questions?
(After a few minutes) Your designs are coming along so nicely. Remember that once you’ve solved your measurement equation and drawn a picture of your shape house, you get to design the perimeter. Don’t forget to name your house with a title that lets us know what is on the outside of your house.
Once students are finished. Everyone can leave their work on their desk and then silently walk around the room to look at each of the designs. Once everyone has gone all the way around the room they can return to their desks.
These designs are just spectacular! You have proven your skill at identifying, measuring, drawing, and designing with shapes, and I would be honored for you to be my teammates at the annual shape contest. It’s next week, and I’ll give (TIR’s real name) all the information so we can enter and win together! Say, what did the rectangle say to the triangle? I’m twice what you are! I’ll see you next week, and until then, keep practicing your geometry! (exits)
(Teacher re-enters) Hi class. How was your time with Miss Buildsalot?
D - What did you do with her? What are some of the 2D shapes in the contest she is entering? What was Miss Buildsalot’s problem? What were the geometric figures in Miss Buildsalot’s design?
A – How did you help her understand the shapes that her measurements represented? What sorts of designs did you create with your houses for the contest?
R – Where else in your life do you come across shapes? What jobs use shapes and need to understand measurement and perimeter?
Art – cut out basic shapes in construction paper. Glue the shapes onto a piece of paper to create pictures (buildings, landscapes, self portraits, etc.).
Social Studies – find shapes in the community – street signs, cars, etc. What symbols do shapes represent?
Math – continue with the grouping, creating groups of even/odd numbers of people, groups of people divisible by a certain number, or multiples of a certain number; put a sheet over a square and find the volume, etc. Also can apply to symmetry; build symmetrical shapes/mirror images. Extend applications/types of area, with shapes within shapes, etc.