# No Series: Table for 22: A Real-World Geometry Project

Math.3.MD.C.7b

Common core State Standards

• Math:  Math
• MD:  Measurement & Data
• C:  Geometric measurement: understand concepts of area and relate area to multiplication and to addition
• 7b:
Relate area to the operations of multiplication and addition.

a. Find the area of a rectangle with whole-number side lengths by tiling it, and show that the area is the same as would be found by multiplying the side lengths.
<br />
b. Multiply side lengths to find areas of rectangles with whole-number side lengths in the context of solving real world and mathematical problems, and represent whole-number products as rectangular areas in mathematical reasoning.

c. Use tiling to show in a concrete case that the area of a rectangle with whole-number side lengths a and b + c is the sum of a × b and a × c. Use area models to represent the distributive property in mathematical reasoning.

d. Recognize area as additive. Find areas of rectilinear figures by decomposing them into non-overlapping rectangles and adding the areas of the non-overlapping parts, applying this technique to solve real world problems.

|
Math.3.MD.D.8

Common core State Standards

• Math:  Math
• MD:  Measurement & Data
• D:  Geometric measurement: recognize perimeter
• 8:
Solve real world and mathematical problems involving perimeters of polygons, including finding the perimeter given the side lengths, finding an unknown side length, and exhibiting rectangles with the same perimeter and different areas or with the same area and different perimeters.

## Table for 22: A Real-World Geometry Project

Lesson Objective: Apply knowledge of area and perimeter to solve real-world problems
Grade 6 / Math / Geometry
Math.3.MD.C.7b | Math.3.MD.D.8

## Discussion and Supporting Materials

### Thought starters

1. Why does Ms. Park go back to 3rd grade content standards?
2. How does she ramp up to teaching 6th grade content?
3. When Ms. Park says that you create your practice by knowing the content first, what does this mean?
4. How does Ms. Park ask students to reflect on their learning?
5. Why is this reflection important?

I just looked at the different comments, I hope these people are not teaching any type of math. No one has mentioned that her definition for rectangle is wrong.

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I really like the concept! But, the definition for rectangle is WRONG. A square is a rectangle. Rectangles do not have to have different lengths. The incorrect definition is shown at least 4 times. I'm really shocked that this video is on The Teaching Channel.

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What a great way to connect math concepts to everyday situations! Great job.
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Great classroom management and instruction. You're also very enthusiastic, which the kids (especially sixth graders) still need! Awesome lesson all around! :)
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Sheryl Dasinger, there are transcripts available. You have to sign up and have an account. After which, you will find the transcripts on the right hand side under supporting materials.
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### Transcripts

• Transcript of “A Table for 22”

My name is Sunny Park and our lesson is on area and perimeter. A table

Transcript of “A Table for 22”

My name is Sunny Park and our lesson is on area and perimeter. A table for 22.

Teacher: Math spiral, open to a clean page.

Teacher: Students enter the room and you start with a whole group lesson just so that you can get them all on the same page and they’re all listening, and you start with a challenge.

[00:00:30]
Teacher: We’re going to pretend that we all want to sit together for a Thanksgiving dinner, and I want the table to be rectangular. The challenge is this: I want you to figure out what does a table look like if it must be rectangular and if everybody must sit at the table. And what’s the biggest table I can have so that I could put the most food in the middle. After you figure that out I have another challenge for you. With everybody sitting at the table again what’s the shape of a table that’s going to have the smallest amount of space? So what’s the biggest table going to look like where everybody sits, and what’s the smallest table going to look like where everybody sits.

[00:01:15]
Teacher: The kids knew perimeter and area as isolated topics for geometry and of doing something with shapes and so what this lesson really did was to take it to another level of critical thinking where you can see both of them happening at the same time simultaneously.

[00:01:32]
Teacher: And your place at the table is going to be this piece ….this yard of poster paper. Now this is 3 feet long, this is your seat at the table. There’s 22 of us and everybody must sit there. No overlap. Nobody sitting on each other’s lap. Side by side and this is your chair and so when you put your place down you put it down like that and that’s your place and you just stand behind it.

[00:02:02]
Teacher: The practice standard vs. the content standard, they’re equally important. You create your practice by knowing the content first.

Teacher: Chlorisa, what do we know about rectangles?

Student: They have four sides

[00:02:17]
Teacher: Yes, a rectangle has four sides so we want to make sure that our table has four sides. What else do we know about rectangles that’s going to help us brainstorm it?

Student: All sides are straight, there’s none that are curved.

[00:02:33]
Teacher: OK, so we have straight, the lines are straight. Vanessa?

Student: The lines are parallel from each other and the same length

[00:02:42]
Teacher: OK. So the opposite sides are parallel and they’re the same what, everyone?

Students: Length

[00:02:50]
Teacher: Same length. But right now we’re not going to design anything, we’re only going to talk about it. So in a second nobody is going to get this yet, you’re just going to get into your groups, you’re going to sit down and you’re going to have a discussion for about 5 minutes OK, and then after that we’re actually going to see if it works.

[00:03:07]
Teacher: We could have gone straight from the whole group where I introduce the activity to the activity itself, but it would have been mayhem. It would have been chaos. Everyone would want to speak over each other and when you have them divided into groups you’re giving all a chance to say something because they all want to say something.

[00:03:24]
Teacher: And you guys are so good at working in groups, I know that you’re going to come up with really good ideas and then we’ll share them out and then we’ll actually try it. Do you think you can do the challenge?

Students: Yes

Teacher: OK, so on the count of three – one, two, three

Student: Each side will be 11 so we’ll have 22 people but then we’ll have space for four more at the ends of the table

Student: How many tables or how many seats?

[00:04:20]
Today I was very pleased when I visited each group and every group was engaged in math conversation about area and perimeter without knowing it.

[00:04:36]
Teacher: _____ When Alex, he made the connection, I’ve seen something like this. It’s when in the renaissance time when the king and queen would sit at the dinner table. There was all this room between them and they didn’t talk very much, and that connection was great.

Teacher: Is that the biggest table that I could fit the most food on, or is it the smallest table that I can put the least food on because I don’t have enough.

Student: I think it’s that one

[00:05:05]
During the lesson I was thrilled when the students made the connection between the activity and area and perimeter.

Teacher: What is the most space possible in terms of a table?

[00:05:21]
And it just kind of came up in one of their groups.

Teacher: So what’s the area of this table?

Student: inaudible

Teacher: 10 square yards. What’s the area here?

Student: inaudible

Teacher: What is ____________? That’s a bigger area, but is that 22 people?

Student: Yeah

[00:05:49]
Teacher: OK, everyone, back to your seats. With your ideas. Everyone come on back. This started out as a challenge problem but then as you were talking in your groups a lot of you actually had a light bulb go off, ding, where you said oh my gosh, this is math. I’m using math to figure out this real-world problem.

[00:06:16]
If there’s no application the students will think of area as multiplying the length times the width, and that’s it.

Teacher: But what is it really?

Student: There’s one person right here and there’s one person right here and there’s people right here

[00:06:33]
It’s the space inside and not everyone knows that it’s the space inside. OK, space inside, well what do you mean?

Student: At first we studied the rectangle and the possible ways you could do and so we wrote down all the possible ways and then we found the area of them and we found what was the largest and what was the smallest, and so we made our rectangle based on it.

[00:06:52]
Teacher: When you talk about a table then, the space inside becomes how much space is there for food plates?

Student: So basically what we’re doing here is finding the area which is how much food could fit in. So 10 by 1. The area would be 10. Then if the table was 9 by 2 ….

[00:07:21]
Some groups had decided to go straight away into the diagram and to draw a picture. Another student chose to do the table, the data table, where they had the different values on either side.

Student: The area would be 18. This area would be 24. This area would be 28, and this area would be 30. So then we see that this is the largest and this is the smallest.

[00:07:45]
Teacher: A mathematical connection. What we’re going to do now is we’re going to actually put your design to the test

[00:07:51]
Usually the objective is the content standard. Now how do you teach it is the practice standard and that’s where the teacher has a choice to teach it a traditional way or to teach it in a way that you feel will provide relevance and experiential knowledge for the kids.

[00:08:10]
Teacher: I want your crates and I want your desks pushed out toward the perimeter so that there’s a big empty space in the middle. Once you get your ____can you sit down on the floor.

[00:08:28]
Teacher: When I turn around you’re going to have probably a minute to get yourselves in order. Try to do your best with right angles. And no overlaps and first we’re going to do the big table. On your marks, get set, go ….

[00:09:00]
I had the option of using rope and having them just kind of do something with string but I think that them becoming part of the perimeter had a lot of value.

Teacher: I’m about to turn around

[00:09:28]
And so if I was just watching them the whole time they wouldn’t think …they wouldn’t find any satisfaction of the finished product. So I do that a lot. I say I’m going to turn around and close my eyes and when I turn back around I should see it, and they’re like oh yeah.

Teacher: My eyes are still closed, and now they will open. Wow, wow, wow. One, two, three, four, five, six; one, two, three, four, five, six; one, two, three, four, five; one, two, three, four, five. What is the perimeter of this rectangle?

Students: 22 yards

[00:10:11]
Teacher: 22 yards. And what is the area?

Students: 30 square yards

[00:10:18]
Teacher: 30 square yards, interesting. Task #2. I’m going to turn around again and I don’t know how but I want the smallest renaissance table because the king and the queen are in a fight and do not want to speak with each other.

[00:10:32]
One of the bullet points under the modeling mathematic standard is application to real-world situations and that’s valuable in my teaching because I feel that that’s one of the main ways that kids learn, is they make connections based on their experiences.

Teacher: Go!

[00:11:00]
Teacher: One, two, three. Wow. Wow. This is very, very, very, very different from what we had before. What is my perimeter?

Student: 2
[00:11:20]
Teacher: What’s my area?

Student: 10

Teacher: What?

Student: 10 square yards

[00:11:26]
Teacher: 10 square yards. What a humongous difference from before

[00:11:31]
It was student generated discovery and I think in a lesson you have to make those connections and you have to instead of it being just like this playtime you have to bring it back to the scholarly, the math academic part of it.

[00:11:44]
Teacher: Can somebody come up with a statement using the word area and perimeter in it, that would describe what we just discovered through this activity. Eric?

Student: The perimeter can be the same but the area can change

[00:12:02]
Teacher: Can you say that in your own words, somebody else. Melvin.

[00:12:08]
Student: So if we had the same amount of people the perimeter would stay the same, but if we move the shape the area would be a different number

[00:12:18]
And so I think that concept that they were able to verbalize that themselves, was really exciting for me and I felt therefore the lesson was successful – because that was the jest of it, that was the content standard that needed to be met.

[00:12:53]
I think part of good teaching is to take what they give you and then go with that, and it’s not going to follow your lesson plan but again I think the objective is the most important, that the objective is being met and your path might go a different way – I mean we had kids dancing – but I think that’s going to be the thing that sticks in their head, the visual that they’ll have, more than doing it on graph paper.

² end of transcript

### School Details

Eastside College Preparatory School
1041 Myrtle Street
East Palo Alto CA 94303
Population: 336

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### Teachers

Alma Suney Park
English Language Arts Math Science Social Studies / 6 / Teacher

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