Speaker A
Hello, respected members of the jury. I will now present to you a third-grade math lesson on the perimeter of a polygon. This topic is not new to the children. They were already introduced to perimeter in the second grade. In
A third-grade math lesson on polygon perimeter using practical examples, games, and spatial thinking to engage students.
Key Takeaways
- Using real-world professions helps students understand the practical importance of math concepts.
- Interactive games and hands-on tools like geoboards enhance engagement and spatial reasoning.
- Reinforcing prior knowledge with new formulas solidifies understanding of perimeter.
- Logical thinking and memory are critical skills developed alongside computational abilities.
- Connecting math lessons to large-scale projects inspires student interest and motivation.
What the video covers
- The lesson focuses on teaching third graders about the perimeter of polygons, reinforcing prior knowledge from second grade.
- It introduces formulas for finding the perimeter of squares and rectangles.
- The lesson incorporates practical examples related to professions such as engineering designers and construction workers.
- Game elements like a 'Lottery' scratch game are used to motivate and engage students.
- Students practice mental math, logical thinking, and memory through interactive tasks.
- A geoboard is used to build geometric shapes and understand perimeter measurement in arbitrary units.
- The lesson emphasizes the importance of multiplication in calculating perimeter.
- Students derive formulas for perimeter and apply them to real-world inspired problems like building cable cars.
- The teacher connects math concepts to spatial thinking and practical applications in engineering and architecture.
- The lesson concludes with reflections on student performance and the integration of theoretical and practical tasks.
Chapters
- 00:00Introduction and Lesson Overview
- 03:22Regional Context and Professions Related to Math
- 05:39Lottery Game to Introduce Mathematical Concepts
- 08:07Mental Math and Logical Thinking Exercises
- 11:10Using the Geoboard to Build Shapes
- 16:56Calculating Perimeter of Squares
- 18:45Deriving Formulas and Working with Rectangles
- 32:24Applying Knowledge to Real-World Problems
- 38:09Lesson Summary and Reflections
Full Transcript — Download SRT & Markdown
Speaker A
the third grade, they generalize, reinforce, and systematize their knowledge of perimeter and add the formulas for finding the perimeter of squares and rectangles. The lesson is built in a practice-oriented format with game elements. Throughout the lesson, we will look at the practical
Speaker A
significance of the topic by using examples of professions. A special feature of this lesson is the inclusion of elements that develop spatial thinking. They didn't lay it out for me. Just a second. If you happened to want to...
Speaker A
For you too, right? How... If you... Just one? Okay, I am ready to invite the children in.
Speaker A
Excellent. Alright, kids, come on in. Take your places by the desks. Hello, kids. My name is Konstantin Romanovich. We will have a math lesson together today.
Speaker A
Please be seated. Uh-huh. I traveled here from the Amur Region, having covered over 8,000 kilometers. Our land is known for being located on the border with China. On one side of the river is the city of Blagoveshchensk, and on the other is the Chinese city of
Speaker A
Heihe. And these two cities are separated by just 800 meters of the Amur River. We have many Chinese tourists because the two countries are connected by an international bridge.
Speaker A
And we are also a space-faring region. The Vostochny Cosmodrome is located on our territory, from where space rockets are launched. And recently, the largest Amur gas processing plant was built, which produces things like fuel for spaceships. Please look at these
Speaker A
large-scale structures. What professions do you think were involved in building these projects? Engineers. What else?
Speaker A
Architects. Well done, Katya. Construction workers. That is all correct. Indeed, an engineering designer took part in the development phase. Does anyone know what kind of profession that is? An engineering designer. Do you know what they do?
Speaker A
Well then, I will tell you. An engineering designer is a specialist with a technical education. They design future structures, create blueprints on paper, build models, and the builders then begin work on a specific object based on their plans. What math
Speaker A
knowledge and skills do you think an engineering designer must possess? Good. Anything else related to math?
Speaker A
I don't know. What kind of math knowledge and skills? To find things. Well done. Anything else? I wanted to say, to not find the per...
Speaker A
Our thoughts coincided. Something... So, you have to be able to calculate well, right? You just named one of the skills that an engineering designer actually needs today. I suggest we find out who was right by playing a game
Speaker A
called "Lottery." Please open your notebooks. On the last page... A lottery is a game of luck. Take a coin, it's on your desk, and actively scratch off the silver layer.
Speaker A
Uh-huh. Yes. Actively, actively, faster, it will scratch off better that way. Uh-huh. Put the coin down, read which mathematical concept a design engineer must know how to work with. Go ahead, Eleonora.
Speaker A
The perimeter of a polygon. That's right, perimeter. And why does a design engineer need the knowledge and ability to find the perimeter? Uh, well, to build something, to construct, to fence off what?
Speaker A
Uh-huh. That will be the topic of our lesson today. And we'll test your assumption. Guys, you are already familiar with perimeter, so please recall, what is a perimeter? Oh, Egor, a perimeter is the sum of the sides of
Speaker A
a polygon. Well done. And what is perimeter measured in? In what units? Sasha, centimeters, meters.
Speaker A
Indeed. Tell me, does a design engineer need to have good calculation skills, logical thinking, and a good memory?
Speaker A
Are they necessary? They are, Andrey, I suggest we test how well your calculation abilities, logical thinking, and memory are developed. Our notebooks will help us with this, with numbers written on the pages. Now, here is a task for you, you solve it, and
Speaker A
without speaking aloud, show the answer like this using your notebook. Let's try. If you add three identical numbers, the sum is six. What number is covered by the square? Show it. The first one.
Speaker A
Uh-huh. Good. You are all showing me the number two. It really is the number two. By the way, pay attention that for everyone, or almost everyone, your number two is written in black, but only for one person is it written in blue. Who? Who?
Speaker A
Oh, Masha. Congratulations. You are a lucky one. You will have a separate task, but a bit later. And by the way, do you remember the lottery game? We had a lucky winner there too. A game of chance. And who had the lesson topic
Speaker A
title written in blue? Take a look. Oh, Zlata remembered. You are a lucky one too. You will have a separate task, but later on. So, I will also ask you to memorize the numbers hidden behind the geometric shapes. So, remembering what
Speaker A
number is hidden behind the square, calculate and show me the number covered by the triangle. The first one is there. Keep flipping, keep flipping, maybe it's hard to turn the pages. Like this. Found it. So, you are all showing
Speaker A
me the numbers. I see, three. Indeed, that's it. Correct, lucky one, we congratulate you. You will have a separate task, but later, did you memorize the number hidden behind the triangle? Show what number is covered by the rectangle. Uh-huh. I see. So,
Speaker A
this number, if the triangle is 3, then it's 4. And the last task. You all remember the numbers hidden behind the geometric shapes. Calculate the value of the equation, remembering the order of operations. And show the answer. Saw
Speaker A
it. Uh-huh. So, stand, stand, the tables. Most of you are showing the answer 10. Please explain, which operation did you perform first, Dima?
Speaker A
The first one. First, I performed the multiplication. Because multiplication and division come before addition and subtraction, right? In this case, we indeed perform multiplication first, and then we add.
Speaker A
So the correct answer is 10. Now, put down your notebooks. For those who made no mistakes or only one mistake while doing this task, we can say you have well-developed computational skills and logical reasoning. Those who made two
Speaker A
or more mistakes should pay closer attention to math lessons. After all, this is all about math. Today in class, we will be helped by this board, a geoboard. Without closing your notebooks, move it closer to you. Move the geoboard closer to you. And the
Speaker A
notebook is nearby. We will need it nearby. And also open the notebook to the last page. Uh-huh. Here. On this one. Using the geoboard, we can build various geometric shapes using rubber bands. Today we will focus on such
Speaker A
types of polygons as squares and rectangles. And in later lessons, we will look at other types. Please, build this square on the geoboard using a rubber band. We can start building it.
Speaker A
We have just built a shape whose perimeter we can determine. Well, guys, you told me that the perimeter is measured in centimeters or meters, but on the geoboard, there are no such units. Let's agree that the distance between two pegs will be denoted as one
Speaker A
unit, as one arbitrary unit. The next distance between two pegs is one more arbitrary unit. What is the side of the square equal to? Wait, 2 units.
Speaker A
Two. Units, arbitrary units. Today, this is our working value for the lesson. Knowing the side of the square, we can find its perimeter. Please find the perimeter of the square and write it down, using only addition, in the first line under
Speaker A
the square. Who is ready to dictate their solution to me? Raise your hand, Dima. 2 + 2 + 2 + 2 = 8. Uh-huh.
Speaker A
Guys, an arbitrary unit is not a standard unit, so we don't write anything after the eight. Now replace this sum of addends with multiplication. Who guessed how to do it? 2 x 4.
Speaker A
Good, let's write that below. Guys, what does the number two show? Masha, the number two shows the number that we will multiply. Uh-huh.
Speaker A
And what does the number two sh
Speaker A
The number that, uh, we will take. Oh, well done. Multiplication. You remember well, and for the square How many sides is that?
Speaker A
The number of square sides. Indeed, that's exactly why we multiply 2 by 4 and get the perimeter. Now, a square doesn't always have a side of two units . Let's use this multiplication method to fill in the table. We'll find the
Speaker A
perimeter of a square with a side of 3, 5, and a variable A, which can represent any other number. I'll ask the first lucky volunteer to come up.
Speaker A
Zlata, please, you have the topic title . We solve it mentally and write only the answer in the cell. Using multiplication. So, what do we do?
Speaker A
Multiply, tell us. Aha. What do we need to multiply by, guys? By how much?
Speaker A
By four, because because in a square remembered. Aha, she says. Oh, I remembered. Okay, narrate it. 3 x 4 is 12, written down. Those who figured it out, solve it yourselves and write it down, then we'll check.
Speaker A
So, narrate it, Zlata, please. 5 x 4 is 20. And that's why I wrote 20. Next.
Speaker A
6 x 4 is 24. Guys, here we will write an expression. So, now instead of So, now instead of 6, 5, and 3, we have the variable A, but nothing has changed.
Speaker A
Let's write not the answer, but the expression. Did you guess? Go on, say it. Aha, that would be the answer then, right, some kind of B. Well, logical, Andrey, what expression would be the solution itself, how to find the
Speaker A
perimeter of a square with side A? By multiplication. Well done. That's correct. By multiplication, Eleonora.
Speaker A
A plus A. by multiplication. A times 4. There. That is correct. Good. Let's write it here in the cell. A times 4.
Speaker A
Okay, thank you. Take a seat, guys. We have just derived a formula with which we can determine the perimeter, find the perimeter of any square. After all, the letter A represents any other number. I suggest we record this formula now so we don't
Speaker A
forget it. Let's repeat it together in chorus. A times 4. That will be our square perimeter. I suggest highlighting the cell with the formula so we don't lose it. Do you have a colored pencil for this? Uh-huh. Now I
Speaker A
suggest using this knowledge in a game. Stand up, please. Okay, I'll put my pencil down. If Look at the square, if the perimeter of the square is stated correctly, clap. If it is incorrect, stomp. So, the perimeter of this square
Speaker A
is four units. If it's right, we clap; if it's wrong, we stomp. Oh, you can do that. Correct. Look at the square again . The perimeter of this square is eight units. If it's correct, clap; if it's incorrect, stomp. Well done. Correct.
Speaker A
Take a seat. So, now take off the rubber band. We handled the square. It turned out quite easily, right?
Speaker A
Easy. Well then, we'll handle the rectangle even more so. Build a rectangle like this. A rectangle like this. Oh. Uh-huh. Just [unintelligible] . Good. Uh-huh. Uh-huh. Now let's find the...No, not yet. What is the width of the rectangle?
Speaker A
Masha, the rectangle's width is one unit. Well done. What is the length of the rectangle, Sasha?
Speaker A
Let's use arbitrary units. Uh-huh. The distance between two pins. The distance, don't mix it up, we aren't counting the pins, that is one arbitrary unit. And Sasha, how many such distances are there? Four.
Speaker A
Well done. Four arbitrary units. Now, what other property of a rectangle do you already know? Katya, all of its sides are equal in pairs.
Speaker A
Indeed, opposite sides are equal. This property will help us today in one way of finding the perimeter. Let's find the perimeter of this rectangle using only addition. And let's write the first line below the rectangle. So, who is ready to dictate their solution to
Speaker A
me? Yes, please, Vasilisa. The perimeter is 4 + 4 + 2 + 2. So, who disagrees? Sasha.
Speaker A
Uh, my answer is 4 + 1 + 4 + 1. That is also possible. But why one or two?
Speaker A
Why, Sasha? Because its width is one arbitrary unit . Yes, the width is not two arbitrary units. You know what you're confusing?
Speaker A
You probably counted the two pins, right? That's why two arbitrary units. The distance between the pins, Vasilisa , okay, is one arbitrary unit. So, equals equals 10 arbitrary units.
Speaker A
So, now let's replace the sum of identical addends with multiplication where possible. Who has guessed and is ready? Andrey, my solution is 4 x 2 + 1 x 2.
Speaker A
So, 4 x 2 + 1 x 2. Guys, does anyone see another solution? Eleonora.
Speaker A
The sum of the numbers 4 + 1 x 2 = 10 arbitrary units. Uh-huh. Guys, why do we multiply by two in this way?
Speaker A
Are you doubting, Katya? Well, go ahead . You know, we add, well, we find the semi-perimeter and multiply it by two.
Speaker A
What did you tell me today? Because they are in pairs, yes, opposites are equal. Okay, don't doubt yourself, you actually know everything. Now let's use this method and find the perimeter of a rectangle with the length and width
Speaker A
specified in the table. I'll ask the next lucky one to come to the board.
Speaker A
Masha, please. So, we use this method and provide commentary. What are we doing? So, look. Length, width, yes, 4 and 1 are our length and width in arbitrary units. 1 equals there. Next, okay, please, can you explain using the
Speaker A
second method? 4 times 2 will be 12. 1 + 5 So, and now instead of length we have the variable A, under which any other number can also be hidden.
Speaker A
Instead of width we have the variable B , also hiding any other number. Let's create an expression, not the answer, but an expression to find the perimeter of a rectangle with sides A and B.
Speaker A
We can. A + A + B + You can do it this way. A + A + B + with multiplication. Guys, let's try. Go ahead.
Speaker A
A + B x B. Write it down. And what about this, Zlata? We needed the sum of numbers A + B, so we wouldn't get 18 as the answer in mental math today. Correct. We put A and B in brackets as the sum of numbers
Speaker A
A and B. Well done, Sla. Here, Masha, have a seat. Thank you, guys. We also derived a formula that allows us to find the perimeter of any rectangle.
Speaker A
After all, the letter A represents any other number depending on the length. The letter B represents any number, just like the width. And we multiply that by two. So, let's repeat it all together in chorus. The sum of numbers
Speaker A
A + B multiplied by 2, and let's highlight this cell with the formula so we don't lose it. Okay. Uh-huh. Show me your readiness. Or something like this.
Speaker A
In the Amur Region, another large-scale project is currently under construction . The world's first international cable car that will connect Russia and China.
Speaker A
A design engineer must know how to work with models. And I suggest we take on the role of a design engineer now and build a cable car model. To start, let's determine the banks of the two countries 'positions, and I will ask
Speaker A
the third lucky one to come up. Oh, guys, and the lucky one. Katya, what can serve as our rope?
Speaker A
Of course, let's stretch our rope between the two countries. And you stretch a rope between the two countries as well. Uh-huh. So that the cabins don't collide on their way along the rope, I suggest increasing it. So, now a question. But how? Come on, I'm
Speaker A
holding it. Pull the rope. How do we find the length of the rope used for building the cable car? What, what needs to be done? What can we do?
Speaker A
Vasilisa measure it, right? Find the perimeter, accordingly. Of course. Let's find the perimeter of this rope, please. Multiplication.
Speaker A
Write down your solution in the last remaining line as well. Uh-huh. Take a seat. Thank you.
Speaker A
Good. The length of the cable car line is 14 conventional units. Guys, we've taken on the role of a design engineer.
Speaker A
Tell me, why did we need the knowledge and ability to find perimeters? What for, Vasilisa? to build a bridge and stretch stretch a rope. And also Andrei, and we also need to, well, make the rope visible, so it's larger and
Speaker A
smaller, yes, to determine, find this rope length and determine the necessary one to connect two countries. It's not just for this that a design engineer uses knowledge, knowledge of the perimeter.
Speaker A
It could also be to determine, for example, the width of a fence, how much material is needed for a fence. And here, too, the design engineer will use their knowledge and ability to find the perimeter. Now let's complete another
Speaker A
task. I suggest adding a landing pad to the cable car model on each side of the bank. But the client has set some conditions for us. The perimeter of the landing pad must be 20 m. You have pre-made models of landing pads. Unpack
Speaker A
them. They are presented to scale. 1 m equals 1 cm. Using a ruler, find which pads fit the client's requirements. 20 m must be the perimeter of the pad. If you are ready and have found them, hold your card up. Each pad is an individual
Speaker A
landing pad. And the models, the models are right here, right? So, the orange one will indeed fit the condition. Any more? Hold them up. The purple one actually fits. Turn the card over. Oh, the purple one. It fits correctly.
Speaker A
Right. Which other cards—or rather, which other pads meet the client's conditions? Okay, the orange one, yes, the light blue one, yes, any others?
Speaker A
And which one? The green one. It will indeed fit. Okay, let's place the landing pad that meets the criteria.
Speaker A
Mhm. On that side. Mhm. Our cable car model is complete. As a keepsake. Today we have seen for ourselves that math knowledge is needed in real life, using the profession of a design engineer as an example. And in memory of our
Speaker A
meeting, I would like to give each of you a postcard with engineering projects implemented in our Amur Region and a badge with the flag of the Amur Region, just like mine. Come visit the Amur Region, and perhaps you too will
Speaker A
be design engineers implementing grand projects. And do admire the border river. So, please, Sasha, Eleonora, Vasilisa, Semyon, Zlata, Dima, Matvey, Sasha. Polina, Egor, Andrey, and Masha.
Speaker A
Thank you for the lesson, guys. Goodbye . Dear Konstantin Romanovich, thank you for the lesson. In memory of this event , we want to give you a badge with the symbol of the Academic Gymnasium No. 56 named after Maya Borisovna Pildees.
Speaker A
Thank you very much. I will wear it. Do not forget your writing supplies. Here is your ruler, pencil case, pens, pencils. You can take your worksheet with you, but everything else—the pencil case—should stay on the desk.
Speaker A
And, of course, the gift. Let's pack up . Thank you, guys. Thank you for the lesson. Goodbye.
Speaker A
Thank you. Goodbye. Goodbye. Thank you, goodbye. Good- bye. Goodbye. Thank you. Good- bye. Thank you. Goodbye. Goodbye.
Speaker A
Goodbye. Goodbye. You may conduct your self-analysis standing up. You may sit. Whatever is comfortable for you. Sitting. Calmly.
Speaker A
So, the main goal of the lesson was to reinforce knowledge about perimeter and lead to the discovery of formulas for finding it, in particular for a square and a rectangle. The lesson was structured in a practice-oriented format with the resolution of
Speaker A
theoretical and practical tasks. I saw that game elements at the start of the lesson—the lucky ones. the lottery helped motivate the kids to study the topic and create an atmosphere of interest. At the beginning of the lesson, mental math tasks were used.
Speaker A
This is logical thinking combined with a reflective stage on the level of development of logical thinking and computational skills. Most of the children have well-developed computational skills. For the next lesson, in that case, I would plan more complex tasks. But one person made a
Speaker A
mistake with the order of operations in calculation, which means it still requires reinforcement. The geoboard became a visual tool that allows for building geometric shapes and finding their perimeter. There was a big risk here in that this is a tool the
Speaker A
children had not used before. First-time use. And another risk was seeing the distance between two pins and taking it as a conventional unit.
Speaker A
This serves as a propaedeutics of knowledge for using conventional units when a ruler is absent, but measurement is still necessary. Well, the risk generally did not materialize, so a more frontal form was chosen. And for the next lesson, we could try more
Speaker A
group and individual work if the kids were to work with geoboards again. The educational potential of the lesson was presented through an introduction to the profession of a design engineer.
Speaker A
And the kids saw that knowledge in mathematics does not end with mathematics; it finds reflection in real life as well. At the end, we performed a reverse task. Here, we did not have time to conduct the reflective stage. With this same task, when the
Speaker A
children raised their cards, I should have asked: "Who found three sites? Who found two sites? One site. The children were raising these cards. A third raised two or three cards. Three is high, two is average. One card, I
Speaker A
noticed, meant about a third of the children. This means they found the perimeter, remembered it, and reinforced it. Well, practice, reinforcement, and practice are required. Ah, honestly, I didn't pay attention and didn't ask. This requires a question. Who could not find a single
Speaker A
one, who did not manage the reverse task, could not find the perimeter: neither by addition nor by multiplication and, accordingly, well, I couldn't ask, I didn't see anyone like that. But I think there were no such children, because I saw everyone
Speaker A
measuring, and they measured and, accordingly, then chose the necessary, suitable layout. In many ways, the children who raised a card were also measuring the same layout on the other side, and so, I had measured it and was just about to say it, but someone else
Speaker A
already said it. That also happened. Therefore, I think all the children found at least one card with the required perimeter. Overall, I consider the goal achieved. A question, of course.
Speaker A
Konstantin Romanovich, were there any moments during the lesson when the children surprised you, and could that have influenced you to change anything in your lesson? I don't remember the name, I've already forgotten. A child surprised me, she put her hand down,
Speaker A
and I thought, something's not right here. It can't be that the child knew it and then put her hand down. I thought, let me ask her. I asked, she answered:" Correct. "That was probably not a surprise; I assumed she would
Speaker A
answer correctly. I was surprised that they found a second solution right off the bat. It is quite difficult to see two solutions. Um, and during the lesson, when the children, um, referred to formulas, um, when they derived the
Speaker A
formulas, I was also surprised that, um , they were able to quickly find a solution, and if they made a mistake, well, they corrected themselves and helped each other. Well, to fix something based on what I was surprised
Speaker A
by? I don't think there's anything to fix. You can't change the lyrics of a song. That would have been a different lesson.
Speaker A
Konstantin Romanovich, as a mathematician, I have a few questions. The children referred to the concepts of a square and a rectangle as polygons . Was it worth updating or defining these geometric shapes?
Speaker A
Sure, why not? Also. But how important is that when studying perimeter? The children have been familiar with them since the first grade, so no additional review is needed.
Speaker A
Only the properties, the properties of a square, the properties of a rectangle . Well, with the property of the square , um, although some difficulties arose, in fact, they remembered it. With the property of the rectangle, no difficulties arose either.
Speaker A
And a small question. Thank you. You mentioned that the distance between the banks is 800 meters, but when the problem was about the cable car, we worked in arbitrary units. Would it have been an over-task to solve it in
Speaker A
real dimensions? 800. Oh, yes. And unfortunately, here too, at the end when we built the cable car, we were a little short on time, um , but it was assumed that the cable car length would be 976 meters. And this is
Speaker A
a propaedeutics of knowing how to use arbitrary units. And then, for the next lesson, how much will it be in standard units, is there any connection? We will find out about this in subsequent lessons. And in the third grade, when
Speaker A
they solve problems involving reduction to a unit, we could return to this, but not in this lesson, but in a later one.
Speaker A
We have no time, 2 minutes, started at 42 minutes. Konstantin Romanovich, tell me, can I ask another, he won't make it, Colleagues, a quick question for Konstantin Romanovich. Could you please tell us what markers of success you saw
Speaker A
in the children during today's lesson? Just briefly, a couple of quick markers . When did you see that they felt this sense of success, what were they able to do?
Speaker A
I think the mental math went very well when they raised their cards." I got this task right. "Yes, there were many such markers. Each task was a success, the children completed them, so to single out something specific...
Speaker A
Well, time is up, the glass. Time has run out. Well, since time has run out, thank you very much.
Speaker A
Thank you.
Topics:third grade mathperimeter of polygongeometry lessonspatial thinkingeducational gamesengineering designinteractive learningmath formulasgeoboardteacher presentation
