Context for this Lesson
TOPIC: Area, Perimeter, and Volume
GRADE LEVEL: 5th Grade
- How do find area, perimeter, and volume?
- What mathematical considerations are needed to design a room?
§111.7. Grade 5
(B) Knowledge and skills.
- (4) Algebraic reasoning. The student applies mathematical process standards to develop concepts of expressions and equations. The student is expected to:
o (H) represent and solve problems related to perimeter and/or area and related to volume.
- (6) Geometry and measurement. The student applies mathematical process standards to understand, recognize, and quantify volume. The student is expected to:
o (A) recognize a cube with side length of one unit as a unit cube having one cubic unit of volume and the volume of a three-dimensional figure as the number of unit cubes (n cubic units) needed to fill it with no gaps or overlaps if possible; and
o (B) determine the volume of a rectangular prism with whole number side lengths in problems related to the number of layers times the number of unit cubes in the area of the base.
Common Core State Standards:
Mathematics Grade 5
Measurement and Data:
- CCSS.Math.Content.5.MD.C.3 Recognize volume as an attribute of solid figures and understand concepts of volume measurement.
- CCSS.Math.Content.5.MD.C.4 Measure volumes by counting unit cubes, using cubic cm, cubic in, cubic ft, and improvised units.
- CCSS.Math.Content.5.MD.C.5 Relate volume to the operations of multiplication and addition and solve real world and mathematical problems involving volume.
- Name Tags
- Graph Paper
“Please come join me in a standing circle. We are going to play a game called Donkey. Donkey is a game where you will have to work with your classmates in order to create a shape with your body. The person in the middle of the circle is the caller. To start out I will be the caller. The caller will point to one student and say a specific word. The student that is pointed to and the student to his or her right and left will have to help create the shape within a quick count to three. Let me show you what elephant looks like.” Model the person pointed to is the trunk using their hands, the other two students create ears by making a C shape with their hands.“Great let’s practice.” Practice a few times until students feel comfortable. “Let’s add two other animals and then we can play.” Model horse (hands like teeth for the center person and outside two people are the ears) and donkey (freeze). “Let’s play a round. If you do not make the animal before the caller counts to three you will sit down.” Play a round of the game.
"Great job. What did we do that made us successful?" Allow students to share what they did to make the game successful. “Now we are going to add in some math vocabulary. Our first is going to be area. What is area?” Discuss and create an action involving three students. “Great let’s practice that one.” Teacher is the caller and students practice area. “We are going to add in one more vocabulary word, perimeter. What is perimeter?” Discuss and create an action involving three students. “Great let’s practice that one.” Teacher is the caller and students practice perimeter. “We are going to play a round of Donkey now where the caller can say donkey, elephant, horse, area, or perimeter." Play a round of Donkey. Remind students to pay attention because they will have to notice if someone is out and jump in on the left or right to make the shape.
“Great job. For our final round we are going to add in one more vocabulary word, volume. What is volume?” Discuss and create an action involving three students. “Great let’s practice that one.” Teacher is the caller and students practice volume. “We are going to play a round of Donkey now where the caller can say donkey, elephant, horse, area, perimeter, or volume. This time the caller will make sure we are using more math vocabulary than animals.” Play a round of Donkey.
Transition: “Thank you for playing. We are going to use the three math words (area, perimeter, and volume) we just used in Donkey in our lesson today. You may sit down.”
2. ROLE PLAY
(Teacher #1 is the design firm owner Mr. Frank, Teacher #2 is the client Mrs. Smith. Change names as needed based on gender.)
Put students into collaborative groups of three to four students. Getting into Role: “I’m going ask you to close your eyes. When I ask you to open your eyes I will be a different character. Open your eyes.”
Teacher #1: “Hello friends. I am so glad that you could all join me today. Thanks for carving out some time in your busy schedules to meet with me first thing this morning. I am so stressed I almost forgot to tell you who I am. My name is Mr. Frank and I work for Austin Home Designs. I am working for this client, Mrs. Smith. She is building this huge new house up in North Austin. She is asking that I have different designers work on plans for their new house. I called all the designers I knew and they were all busy. So, I am so glad that you are available and able to help me out. Before I give you the task I need to tell you a little bit about what I do. I work with design teams all over the country. My design teams create the plans for rooms in a house- they figure out what the room looks like, how many doors, any windows, how big the room is, etc. They also get to decide if the room will have wallpaper, paint, carpet, or tile. And lastly they get to decide what furniture goes in the room. I see you are already sitting in groups so you must be ready to work and help me out. Why don't we begin with having your group come up with a name for your design team.”
Allow students to create their design team nametags. Walk around and help students as needed. Ask the groups to share with you their team name. Remain in character while doing this.
Teacher #1: “Great I am so glad to meet all your teams. Because this is a giant house I think the best way for you to help me out is that each design team will get a room of the house to design. This house is huge and I think this is the best way for us to work! Each design team is going to design a room for my client and have to pitch their room to the client. You will have a design papers here that you need to fill out. I will be here to answer any questions you have about the project as well as your teacher.”
Each group will be assigned a room to design using graph paper. For each room the group of students will need to find: the length and the width of your room and then find the area and the perimeter of the room. If time: students can decide how the room will be covered and find the cost of needed supplies. Students may need reminded that they will share this information along with their team’s design with the client during the presentation pitch. Walk around and assist students as needed.
Teacher #1: “Sorry to bother you. I see that you all are working really hard on these rooms for Mrs. Smith. They look great! But, I just got a text message from my client. They started ordering stuff for the house from Amazon.com and we have nowhere to put this stuff, but the garage is built and we can probably store the boxes in there. I need to figure out how many boxes we can store in the garage so I make sure we have enough room and don’t need to make other arrangements. I am really not the best with this kind of math- I just run the design company. Designers are much better at math than I am. I hate to do this to you, but I am going to need each design team to figure out how many boxes the garage can hold. I have the dimensions of the garage and all the boxes from Amazon.com will be the same size. So, stop your room design for just a second because I’m going to need your help with this.”
Each group will be given the dimensions of the garage and the size of the boxes. The groups of students will need to find: volume of the garage, the volume of each box, and how many boxes will fit into the garage. Walk around and assist students as needed.
Teacher #1: “Great work today design teams. Our client will be here shortly and I wanted to go over with you the way you can pitch your design to our client. She can sometimes be picky, but she is really nice. First you will do is come up front and tell us your design team name. And then give us the information about your room. Let me model it for you.”
Model the design team pitch. Support students as needed.
Teacher #1: “Be prepared though the client might ask you some questions about your design or comment on it. The client only has a few minutes; she is really busy so we will get this underway. Let me get my client, Mrs. Smith.”
Teacher #2: “Hi designers. I’m Mrs. Smith. I am so excited to see the rooms you have designed for my new house.”
Teacher #1: “Do we have any groups that would like to go first?”
Groups of students present their work to the client and the rest of the design teams. Support students as needed in character
Teacher #1: “Thanks so much for all your hard work design teams. I think you have really impressed our client and you have most defiantly helped me out. You all had creative ideas and so much knowledge about calculating area, perimeter, and volume.”
Teacher #2: "Wow. I was so impressed with all the ideas you had about how I can design my house. Thank you so much for also helping me figure out how many boxes can fit in my garage."
Transition: Teacher steps out of role. “Please close your eyes. Thanks for your willingness to think and play with me today in math class. When you open your eyes I will no longer be the character from the math lesson. Please open your eyes. Let’s talk a little bit about our work together. ”
- What did we do in our work together today?
- What skills did you have to know in order to complete the task?
- What did you do to be successful in your work?
- What other jobs might require someone to find area, perimeter, and/or volume?
Transition: “That is all for our math lesson. Great job today.”