What is a perimeter? How to find the perimeter? How is the perimeter of the shapes

Class: 2

Target: Learn how to find the perimeter of a rectangle.

Tasks: to form the ability to solve problems related to finding the perimeter of figures, to develop the ability to draw geometric figures, to consolidate the ability to calculate, using the commutative property of addition, to develop the skill of mental counting, logical thinking, to cultivate cognitive activity and the ability to work in a team.

Equipment: ICT (multimedia projector, presentation for the lesson), pictures with geometric shapes for a physical minute, a magic square model, students have models of geometric shapes, marker boards, rulers, textbooks, notebooks.

DURING THE CLASSES

1. Organizational moment

Check readiness for the lesson. Greetings.

The lesson starts
He will go to the guys for the future.
Try to understand everything -
And count carefully.

2. Mental account

a) The use of magical figures. ( Annex 1 )

- Let's fill in the cells of the magic square, name its features (the sum of the numbers along the horizontals, verticals and diagonals are equal) and determine the magic number. (39)

In a chain, children fill out a square on the board and in notebooks.

b) Acquaintance with the properties of magic triangles. ( Appendix 2 )

- The sums of the numbers in the corners that form the triangle are equal. Let's find the magic numbers in the triangle. Find the missing number. Mark it on the whiteboard.

3. Preparation for learning new material

- Before you geometric shapes. Name them in one word. (Quadangles).
- Divide them into 2 groups. ( Annex 3 )
What are rectangles. (Rectangles are quadrangles with all right angles.)
What can be learned by knowing the lengths of the sides of quadrilaterals? The perimeter is the sum of the lengths of the sides of the figures.
– Find the perimeter of the white figure, the yellow one.
Why are rectangles not known for all sides?
What are the properties of opposite sides of rectangles? (At the rectangle opposite sides are equal).
If opposite sides are equal, should all sides be measured? (No.)
- That's right, just measure the length and width.
- How to calculate in a convenient way? (Students work orally with comments.)

4. Study new topic

- Read the topic of our lesson: "Perimeter of a rectangle." ( Appendix 4 )
- Help me find the perimeter of this figure, if its length is - A, and the width is V.

Those who wish find R at the blackboard. Students write down the solution in their notebooks.

How to write it differently?

P = A + A + V + V,
P = A x 2+ V x 2,
R = ( A + V) x 2.

We have obtained the formula for finding the perimeter of a rectangle. ( Annex 5 )

5. Fixing

Page 44 no. 2.

Children read and write down a condition, a question, draw a figure, find P in different ways, write down the answer.

6. Physical Minute. signal cards

How many green cells
So many slopes.
We clap our hands so many times.
We stomp our feet so many times.
How many circles do we have here
So many jumps.
We will swear so many times
So let's pull up now.

7. Practical work

- You have geometric figures in envelopes on your desks. How shall we call them?
- What are rectangles?
What do you know about opposite sides of rectangles?
- Measure the sides of the figures according to the options, find the perimeter in different ways.
We check with a neighbor.

Mutual check of notebooks.

– Read: How did you find the perimeter? What can be said about the perimeters of these figures? (They are equal).
- Draw a rectangle with the same P, but different sides.

R 1 \u003d (2 + 6) x 2 \u003d 16 R 1 \u003d 2 x 2 + 6 x 2 \u003d 16
R 1 \u003d 2 + 2 + 6 + 6 \u003d 16
R 2 \u003d 3 + 3 + 5 + 5 \u003d 16 R 2 \u003d (3 + 5) x 2 \u003d 16
R 3 \u003d 4 + 4 + 4 + 4 \u003d 16 R 4 \u003d 1 + 1 + 7 + 7 \u003d 16

8. Graphic dictation

Left 6 cells. They made a point. We start moving. 2 - right, 4 - right down, 10 - left, 4 - right up. What figure? Turn it into a rectangle. Complete. Find R in different ways.

P \u003d (5 + 2) x 2 \u003d 14.
P \u003d 5 + 5 + 2 + 2 \u003d 14.
P \u003d 5 x 2 + 2 x 2 \u003d 14.

9. Finger gymnastics

They multiplied, they multiplied.
We are very, very tired.
We will interlace our fingers and connect our palms.
And then, as soon as we can, we squeeze it tightly.
There is a lock on the doors.
Who couldn't open it?
We knocked on the lock
We turned the lock
We twisted the lock and opened it.

(Words are accompanied by movements)

10. Drawing up and solving a problem by condition(Appendix 8 )

Rectangle length - 12 dm
Width - 3 dm m.
R - ?
In the first step, we find the width: 12 - 3 \u003d 9 (dm) - width
Knowing the length and width, we find out P in one of the ways.
P \u003d (12 + 9) x 2 \u003d 42 dm

11. Independent work

12. Summary of the lesson

- What did you learn. How was the P of a rectangle found?

13. Evaluation

Students' answers are evaluated at the blackboard and selectively in the process of independent work.

14. Homework

S. 44 No. 5 (with explanations).

Perimeter is the sum of the lengths of all sides of the polygon.

To calculate the perimeter of geometric shapes, special formulas are used, where the perimeter is denoted by the letter "P". It is recommended to write the name of the figure in small letters under the “P” sign in order to know whose perimeter you are finding.
The perimeter is measured in units of length: mm, cm, m, km, etc.

Distinctive features of the rectangle

A rectangle is a quadrilateral.
All parallel sides are equal
All angles = 90º.
For example, in Everyday life a rectangle can be found in the form of a book, monitor, table cover or door.

How to calculate the perimeter of a rectangle

There are 2 ways to find it:

1 way. Add up all sides. P = a + a + b + b
2 way. Add the width and length, and multiply by 2. P = (a + b) 2. OR P \u003d 2 a + 2 b. The sides of a rectangle that lie opposite each other (opposite) are called the length and width.

"a"- the length of the rectangle, the longer pair of its sides.

"b"- the width of the rectangle, the shorter pair of its sides.

An example of a problem for calculating the perimeter of a rectangle:

Calculate the perimeter of a rectangle, if its width is 3 cm and its length is 6.

Memorize the formulas for calculating the perimeter of a rectangle!

Semiperimeter is the sum of one length and one width .

Semiperimeter of a rectangle - when you perform the first action in brackets - (a+b).
To get the perimeter from the semi-perimeter, you need to increase it by 2 times, i.e. multiply by 2.

How to find the area of a rectangle

Rectangle area formula S=a*b

If the length of one side and the length of the diagonal are known in the condition, then the area can be found using the Pythagorean theorem in such problems, it allows you to find the length of the side right triangle if the lengths of the other two sides are known.

: a 2 + b 2 = c 2, where a and b are the sides of the triangle, and c is the hypotenuse, the longest side.

Remember!

All squares are rectangles, but not all rectangles are squares. Because:
- Rectangle is a quadrilateral with all right angles.
- Square A rectangle with all sides equal.
If you find the area, the answer will always be in square units (mm 2, cm 2, m 2, km 2, etc.)

In this lesson, we will get acquainted with a new concept - the perimeter of a rectangle. We formulate the definition of this concept, derive a formula for its calculation. We also repeat the associative law of addition and the distributive law of multiplication.

In this lesson, we will get acquainted with the perimeter of a rectangle and its calculation.

Consider the following geometric figure (Fig. 1):

Rice. 1. Rectangle

This figure is a rectangle. Let's remember what distinctive features rectangle we know.

A rectangle is a quadrilateral with four right angles and four equal sides.

What in our life can have a rectangular shape? For example, a book, a tabletop, or a piece of land.

Consider the following problem:

Task 1 (Fig. 2)

The builders needed to put up a fence around the land. The width of this section is 5 meters, the length is 10 meters. What length of fence will the builders get?

Rice. 2. Illustration for problem 1

The fence is placed along the boundaries of the site, therefore, in order to find out the length of the fence, you need to know the length of each side. This rectangle has sides equal: 5 meters, 10 meters, 5 meters, 10 meters. Let's make an expression for calculating the length of the fence: 5 + 10 + 5 + 10. Let's use the commutative law of addition: 5+10+5+10=5+5+10+10. In this expression, there are sums of identical terms (5 + 5 and 10 + 10). Let's replace the sums of identical terms with products: 5+5+10+10=5 2+10 2. Now let's use the distributive law of multiplication with respect to addition: 5·2+10·2=(5+10)·2.

Find the value of the expression (5+10) 2. First, we perform the action in brackets: 5+10=15. And then we repeat the number 15 twice: 15 2=30.

Answer: 30 meters.

Perimeter of a rectangle is the sum of the lengths of all its sides. Formula for calculating the perimeter of a rectangle: , where a is the length of the rectangle and b is the width of the rectangle. The sum of length and width is called semi-perimeter. To get the perimeter from the semi-perimeter, you need to increase it by 2 times, that is, multiply by 2.

Let's use the rectangle perimeter formula and find the perimeter of a rectangle with sides 7 cm and 3 cm: (7+3) 2=20 (cm).

The perimeter of any figure is measured in linear units.

In this lesson, we got acquainted with the perimeter of a rectangle and the formula for its calculation.

The product of a number and the sum of numbers is equal to the sum of the products of the given number and each of the terms.

If the perimeter is the sum of the lengths of all sides of the figure, then the semi-perimeter is the sum of one length and one width. We find the semi-perimeter when we work on the formula for finding the perimeter of a rectangle (when we perform the first operation in brackets - (a + b)).

Bibliography

Alexandrova E.I. Mathematics. Grade 2 - M.: Bustard, 2004.
Bashmakov M.I., Nefyodova M.G. Mathematics. Grade 2 - M.: Astrel, 2006.
Dorofeev G.V., Mirakova T.I. Mathematics. Grade 2 - M.: Education, 2012.

Festival.1september.ru ().
Nsportal.ru ().
Math-prosto.ru ().

Homework

Find the perimeter of a rectangle whose length is 13 meters and width is 7 meters.
Find the semi-perimeter of a rectangle if its length is 8 cm and its width is 4 cm.
Find the perimeter of a rectangle if its half-perimeter is 21 cm.

Lesson and presentation on the topic: "Perimeter and area of a rectangle"

Additional materials
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Teaching aids and simulators in the online store "Integral" for grade 3
Simulator for grade 3 "Rules and exercises in mathematics"
Electronic textbook for grade 3 "Mathematics in 10 minutes"

What is a rectangle and a square

Rectangle is a quadrilateral with all right angles. So the opposite sides are equal to each other.

Square is a rectangle with equal sides and angles. It is called a regular quadrilateral.

Quadrilaterals, including rectangles and squares, are denoted by 4 letters - vertices. Latin letters are used to designate vertices: A, B, C, D...

Example.

It reads like this: quadrilateral ABCD; square EFGH.

What is the perimeter of a rectangle? Formula for calculating the perimeter

Perimeter of a rectangle is the sum of the lengths of all sides of the rectangle, or the sum of the length and width multiplied by 2.

The perimeter is indicated by the Latin letter P. Since the perimeter is the length of all sides of the rectangle, the perimeter is written in units of length: mm, cm, m, dm, km.

For example, the perimeter of a rectangle ABCD is denoted as P ABCD, where A, B, C, D are the vertices of the rectangle.

Let's write the formula for the perimeter of quadrilateral ABCD:

P ABCD = AB + BC + CD + AD = 2 * AB + 2 * BC = 2 * (AB + BC)

Example.
A rectangle ABCD is given with sides: AB=CD=5 cm and AD=BC=3 cm.
Let's define P ABCD .

Solution:
1. Let's draw a rectangle ABCD with initial data.
2. Let's write a formula for calculating the perimeter of this rectangle:

P ABCD = 2 * (AB + BC)

P ABCD=2*(5cm+3cm)=2*8cm=16cm

Answer: P ABCD = 16 cm.

The formula for calculating the perimeter of a square

We have a formula for finding the perimeter of a rectangle.

P ABCD=2*(AB+BC)

Let's use it to find the perimeter of a square. Considering that all sides of the square are equal, we get:

P ABCD=4*AB

Example.
Given a square ABCD with a side equal to 6 cm. Determine the perimeter of the square.

Solution.
1. Draw a square ABCD with the original data.

2. Recall the formula for calculating the perimeter of a square:

P ABCD=4*AB

3. Substitute our data into the formula:

P ABCD=4*6cm=24cm

Answer: P ABCD = 24 cm.

Problems for finding the perimeter of a rectangle

1. Measure the width and length of the rectangles. Determine their perimeter.

2. Draw a rectangle ABCD with sides 4 cm and 6 cm. Determine the perimeter of the rectangle.

3. Draw a CEOM square with a side of 5 cm. Determine the perimeter of the square.

Where is the calculation of the perimeter of a rectangle used?

1. A piece of land is given, it needs to be surrounded by a fence. How long will the fence be?

In this task, it is necessary to accurately calculate the perimeter of the site so as not to buy extra material for building a fence.

2. Parents decided to make repairs in the children's room. You need to know the perimeter of the room and its area in order to correctly calculate the number of wallpapers.
Determine the length and width of the room you live in. Determine the perimeter of your room.

What is the area of a rectangle?

Square- This numerical characteristic figures. The area is measured in square units of length: cm 2, m 2, dm 2, etc. (centimeter squared, meter squared, decimeter squared, etc.)
In calculations, it is denoted by the Latin letter S.

To find the area of a rectangle, multiply the length of the rectangle by its width.
The area of the rectangle is calculated by multiplying the length of AK by the width of KM. Let's write this as a formula.

S AKMO=AK*KM

Example.
What is the area of rectangle AKMO if its sides are 7 cm and 2 cm?

S AKMO \u003d AK * KM \u003d 7 cm * 2 cm \u003d 14 cm 2.

Answer: 14 cm 2.

The formula for calculating the area of a square

The area of a square can be determined by multiplying the side by itself.

Example.
In this example, the area of the square is calculated by multiplying side AB by width BC, but since they are equal, side AB is multiplied by AB.

S ABCO = AB * BC = AB * AB

Example.
Find the area of the square AKMO with a side of 8 cm.

S AKMO = AK * KM = 8 cm * 8 cm = 64 cm 2

Answer: 64 cm 2.

Problems to find the area of a rectangle and a square

1. A rectangle with sides of 20 mm and 60 mm is given. Calculate its area. Write your answer in square centimeters.

2. A suburban area was bought with a size of 20 m by 30 m. Determine the area of \u200b\u200bthe summer cottage, write down the answer in square centimeters.

Class: 2

Target: Learn how to find the perimeter of a rectangle.

Tasks: to form the ability to solve problems related to finding the perimeter of figures, to develop the ability to draw geometric figures, to consolidate the ability to calculate using the commutative property of addition, to develop the skill of mental counting, logical thinking, to cultivate cognitive activity and the ability to work in a team.

DURING THE CLASSES

1. Organizational moment

Check readiness for the lesson. Greetings.

The lesson starts
He will go to the guys for the future.
Try to understand everything -
And count carefully.

2. Mental account

a) The use of magical figures. ( Annex 1 )

- Let's fill in the cells of the magic square, name its features (the sum of the numbers along the horizontals, verticals and diagonals are equal) and determine the magic number. (39)

In a chain, children fill out a square on the board and in notebooks.

b) Acquaintance with the properties of magic triangles. ( Appendix 2 )

- The sums of the numbers in the corners that form the triangle are equal. Let's find the magic numbers in the triangle. Find the missing number. Mark it on the whiteboard.

3. Preparation for learning new material

- Before you geometric shapes. Name them in one word. (Quadangles).
- Divide them into 2 groups. ( Annex 3 )
What are rectangles. (Rectangles are quadrangles with all right angles.)
What can be learned by knowing the lengths of the sides of quadrilaterals? The perimeter is the sum of the lengths of the sides of the figures.
– Find the perimeter of the white figure, the yellow one.
Why are rectangles not known for all sides?
What are the properties of opposite sides of rectangles? (A rectangle has opposite sides equal.)
If opposite sides are equal, should all sides be measured? (No.)
- That's right, just measure the length and width.
- How to calculate in a convenient way? (Students work orally with comments.)

4. Explore a new topic

- Read the topic of our lesson: "Perimeter of a rectangle." ( Appendix 4 )
- Help me find the perimeter of this figure, if its length is - A, and the width is V.

Those who wish find R at the blackboard. Students write down the solution in their notebooks.

How to write it differently?

P = A + A + V + V,
P = A x 2+ V x 2,
R = ( A + V) x 2.

We have obtained the formula for finding the perimeter of a rectangle. ( Annex 5 )

5. Fixing

Page 44 no. 2.

Children read and write down a condition, a question, draw a figure, find P in different ways, write down the answer.

6. Physical Minute. signal cards

How many green cells
So many slopes.
We clap our hands so many times.
We stomp our feet so many times.
How many circles do we have here
So many jumps.
We will swear so many times
So let's pull up now.

7. Practical work

Mutual check of notebooks.

– Read: How did you find the perimeter? What can be said about the perimeters of these figures? (They are equal).
- Draw a rectangle with the same P, but different sides.

R 1 \u003d (2 + 6) x 2 \u003d 16 R 1 \u003d 2 x 2 + 6 x 2 \u003d 16
R 1 \u003d 2 + 2 + 6 + 6 \u003d 16
R 2 \u003d 3 + 3 + 5 + 5 \u003d 16 R 2 \u003d (3 + 5) x 2 \u003d 16
R 3 \u003d 4 + 4 + 4 + 4 \u003d 16 R 4 \u003d 1 + 1 + 7 + 7 \u003d 16

8. Graphic dictation

Left 6 cells. They made a point. We start moving. 2 - right, 4 - right down, 10 - left, 4 - right up. What figure? Turn it into a rectangle. Complete. Find R in different ways.

P \u003d (5 + 2) x 2 \u003d 14.
P \u003d 5 + 5 + 2 + 2 \u003d 14.
P \u003d 5 x 2 + 2 x 2 \u003d 14.

9. Finger gymnastics

They multiplied, they multiplied.
We are very, very tired.
We will interlace our fingers and connect our palms.
And then, as soon as we can, we squeeze it tightly.
There is a lock on the doors.
Who couldn't open it?
We knocked on the lock
We turned the lock
We twisted the lock and opened it.

(Words are accompanied by movements)

10. Drawing up and solving a problem by condition(Appendix 8 )

11. Independent work

12. Summary of the lesson

- What did you learn. How was the P of a rectangle found?

13. Evaluation

Students' answers are evaluated at the blackboard and selectively in the process of independent work.

14. Homework

S. 44 No. 5 (with explanations).