On the this lesson students are given the opportunity to get acquainted with another unit of area measurement, a square decimeter, learn how to translate square decimeters in square centimeters, as well as practice doing various tasks to compare values and solve problems on the topic of the lesson.
Read the topic of the lesson: "The unit of area is a square decimeter." In the lesson, we will get acquainted with another unit of area, a square decimeter, learn how to convert square decimeters to square centimeters and compare values.
Draw a rectangle with sides 5 cm and 3 cm and label its vertices with letters (Fig. 1).
Rice. 1. Illustration for the problem
Let's find the area of the rectangle. To find the area, multiply the length by the width of the rectangle.
Let's write down the solution.
5*3=15(cm2)
Answer: the area of a rectangle is 15 cm2.
We have calculated the area given rectangle in square centimeters, but, sometimes, depending on the task being solved, the units of area may be different: more or less.
The area of a square whose side is 1 dm is a unit of area, square decimeter(Fig. 2) .
Rice. 2. Square decimeter
The words "square decimeter" with numbers are written as follows:
5 dm 2, 17 dm 2
Let's establish the ratio between square decimeter and square centimeter.
Since a square with a side of 1 dm can be divided into 10 strips, each of which has 10 cm 2, then there are ten tens or one hundred in a square decimeter. square centimeters(Fig. 3).
Rice. 3. One hundred square centimeters
Let's remember.
1 dm 2 \u003d 100 cm 2
Express these values in square centimeters.
5 dm 2 \u003d ... cm 2
8 dm 2 = ... cm 2
3 dm 2 = ... cm 2
We reason like this. We know that there are one hundred square centimeters in one square decimeter, which means that there are five hundred square centimeters in five square decimeters.
Test yourself.
5 dm 2 \u003d 500 cm 2
8 dm 2 \u003d 800 cm 2
3 dm 2 \u003d 300 cm 2
Express these quantities in square decimetres.
400 cm 2 = ... dm 2
200 cm 2 = ... dm 2
600 cm 2 = ... dm 2
We explain the solution. One hundred square centimeters make up one square decimeter, which means that in the number 400 cm 2 there are four square decimeters.
Test yourself.
400 cm 2 = 4dm 2
200 cm 2 \u003d 2 dm 2
600 cm 2 \u003d 6 dm 2
Take action.
23 cm 2 + 14 cm 2 = ... cm 2
84 dm 2 - 30 dm 2 \u003d ... dm 2
8 dm 2 + 42 dm 2 = ... dm 2
36 cm 2 - 6 cm 2 \u003d ... cm 2
Consider the first expression.
23 cm 2 + 14 cm 2 = ... cm 2
Add up numerical values: 23 + 14 = 37 and assign the name: cm 2. We continue to reason in the same way.
Test yourself.
23 cm 2 + 14 cm 2 \u003d 37 cm 2
84dm 2 - 30 dm 2 \u003d 54 dm 2
8dm 2 + 42 dm 2 = 50 dm 2
36 cm 2 - 6 cm 2 \u003d 30 cm 2
Read and solve the problem.
mirror height rectangular shape- 10 dm, and width - 5 dm. What is the area of the mirror (Fig. 4)?
Rice. 4. Illustration for the problem
To find the area of a rectangle, multiply the length by the width. Let's pay attention to the fact that both values are expressed in decimeters, which means that the name of the area will be dm 2.
Let's write down the solution.
5 * 10 = 50 (dm 2)
Answer: the mirror area is 50 dm 2.
Compare sizes.
20 cm 2 ... 1 dm 2
6 cm 2 ... 6 dm 2
95 cm 2 ... 9 dm
It is important to remember that in order for values to be compared, they must have the same name.
Let's look at the first line.
20 cm 2 ... 1 dm 2
Convert square decimeter to square centimeter. Remember that there are one hundred square centimeters in one square decimeter.
20 cm 2 ... 1 dm 2
20 cm 2 ... 100 cm 2
20 cm 2< 100 см 2
Let's look at the second line.
6 cm 2 ... 6 dm 2
We know that square decimeters are larger than square centimeters, and the numbers for these names are the same, which means we put the sign “<».
6 cm 2< 6 дм 2
Let's look at the third line.
95cm 2 ... 9 dm
Note that area units are written on the left, and linear units on the right. Such values cannot be compared (Fig. 5).
Rice. 5. Various sizes
Today in the lesson we got acquainted with another unit of area, a square decimeter, learned how to convert square decimeters into square centimeters and compare values.
This concludes our lesson.
Bibliography
- M.I. Moro, M.A. Bantova and others. Mathematics: Textbook. Grade 3: in 2 parts, part 1. - M .: "Enlightenment", 2012.
- M.I. Moro, M.A. Bantova and others. Mathematics: Textbook. Grade 3: in 2 parts, part 2. - M .: "Enlightenment", 2012.
- M.I. Moreau. Mathematics lessons: Guidelines for teachers. Grade 3 - M.: Education, 2012.
- Regulatory document. Monitoring and evaluation of learning outcomes. - M.: "Enlightenment", 2011.
- "School of Russia": Programs for elementary school. - M.: "Enlightenment", 2011.
- S.I. Volkov. Mathematics: Testing work. Grade 3 - M.: Education, 2012.
- V.N. Rudnitskaya. Tests. - M.: "Exam", 2012.
- Nsportal.ru ().
- Prosv.ru ().
- Do.gendocs.ru ().
Homework
1. The length of the rectangle is 7 dm, the width is 3 dm. What is the area of the rectangle?
2. Express these values in square centimeters.
2 dm 2 \u003d ... cm 2
4 dm 2 \u003d ... cm 2
6 dm 2 = ... cm 2
8 dm 2 = ... cm 2
9 dm 2 = ... cm 2
3. Express these quantities in square decimeters.
100 cm 2 = ... dm 2
300 cm 2 = ... dm 2
500 cm 2 = ... dm 2
700 cm 2 = ... dm 2
900 cm 2 = ... dm 2
4. Compare the values.
30 cm 2 ... 1 dm 2
7 cm 2 ... 7 dm 2
81 cm 2 ... 81 dm
5. Make a task for your comrades on the topic of the lesson.
(primary school teacher, secondary school No. 17)Chuvashova Nina Alexandrovna
PHYSICAL AND MATHEMATICAL SCIENCES
"SQUARE DECIMETER"
math in 3rd grade
Primary school teacher
MOU Secondary school No. 17 "city of Serpukhov
Math lesson script
using a media product.
Class. Third.
Topic. : Square decimeter. Explanation of the new
Educational and methodological support. Traditional school. Mathematics Moreau.
Necessary equipment and materials for the lesson. Computer, multimedia projector, presentation screen, pen, pencil, notebook, ruler, squares.
The time of the implementation of the lesson. 40 minutes.
Media product. Visual presentation of educational material.
(Wednesday: Windows XP SP2 Pro , Editor: POWER POINT)
technology scenario. (serial model)
Lesson Objectives:
1. Introduce students to a new unit of area measurement for them - a square decimeter.
2. Strengthen the ability to find the area of a rectangle and a square
3. Improve mental counting skills, knowledge of the multiplication table, the ability to solve simple and compound problems.
4. To develop attention, ingenuity, ingenuity.
5. To cultivate discipline, independence.
During the classes:
1. Message of the topic and purpose of the lesson SLIDE 2
Stage I of the lesson. Self-determination for activity (org.moment).
The purpose of the stage: the creation of an emotional mood for joint collective activity.
Forms, techniques, methods. Purpose of application.
1. The psychological mood of children for the lesson
The math lesson begins.
Guys, what mood are you in before the lesson?
(On the table of each child are cards with the image of the sun, the sun behind the cloud and the clouds.)
And today I am in a joyful mood, because we are going with you on another journey through the Great Land of Mathematics. Good luck and new discoveries!
Znayka will accompany us on the journey.
Znayka and I, we are glad to meet you, friends!
And we think we met for a reason.
We will learn to decide today
Explore, compare, reason.
Znayka offers to warm up
"GYMNASTICS FOR THE MIND"
What is today's date?
Increase it by 17.
How many dm in 1 m?
What number follows the number 59,88,99?
Increase 9 by 6 times
Increase 9 by 6
Decrease 42 by 7
Reduce 42 by 7 times
How many cm in 1 m?
How many cm in 1 dm? Activation of mental activity of students.
II stage of the lesson. Knowledge update.
The purpose of the stage: the development of skills to group figures, justify your opinion
Znayka's next task. slide 3
Children have geometric shapes on the board and on the desk.
What figures are missing here? (1 and 3)
Why?
(Figures 2,4,5 have right angles, opposite sides, equal in pairs, they are rectangles).
Find its area of rectangle 2.
What do you need to know for this?
Is there a square among the rectangles? (Yes).
Name it (5).
What is the main property of a square? (all sides are equal).
Measure the side of the square in front of you.
What is its area? (1 cm2)
Who also thinks?
The development of students' logical thinking, the ability to compare and
analyze
III stage of the lesson. Statement and solution of a problem situation.
The purpose of the stage: to repeat the material and prepare students for the assimilation of new material.
Znayka has prepared a figure for you, it is on your desks. slide 4
Measure the sides of this figure (10 cm) click
What can be said? (this is a square, with a side of 10 cm)
- 10 cm is a linear unit, a unit of length.
Let's replace it with the largest linear unit.
10 cm = 1 dm click note in notebook
- So you have a square with a side of 1 dm.
How to find the area of this square? (Length times width)
click
S \u003d 1 dm * 1 dm \u003d 1 dm2 entry in a notebook
-
this is the new area unit - 1 DM click
SQUARE DECIMETER
We found the area of the square in decimetres.
Flip your square. What did you see? (divided by cm2)
How many squares can be laid in 1 dm2
How to find the area of this square?
(Recalculate all the squares, count the squares by length and width and multiply them)
How to write it down?
S \u003d 10 cm 10 cm \u003d 100 cm2 entry in a notebook
Which way is shorter?
In what units is area measured?
How many square centimeters are in 1 dm2? CLICK
.
- in 1 dm2 = 100 cm2 - entry in a notebook
Who doesn't understand what? Development of cognitive activity.
Developing the ability to make inferences based on previously acquired knowledge.
Fizminutka.
Purpose: to avoid overload and overwork of students, to maintain motivation for learning.
"Calm"
The teacher says the words and the children do the actions. reflecting the meaning of the words.
Everyone chooses a comfortable sitting position.
We are happy, we are happy!
We laugh in the morning.
But now the moment has come
It's time to be serious.
Eyes closed, hands folded,
Heads lowered, mouth closed.
And quiet for a minute
To not even hear a joke,
To not see anyone, but
And only one myself!
IV stage. Primary fastening
The purpose of the stage: repeat the algorithm for finding the area.
Znayka has prepared the following task for you.
Open the textbook p.60, No. 3 slide 8
Finding the area of a mirror
- The length of a rectangular mirror is 10 dm, and the width is 5 dm. What is the area of the mirror?
Read the task.
-What will we measure?
What units are used to measure the length and width of a mirror? (in dm)
What is known?
What length?
What is known?
What's the Width?
What should be found?
How to do it?
As the task is parsed, data is displayed on the screen when clicked.
Write down the solution yourself,
1 student on the blackboard on the back
S \u003d 10 5 \u003d 50 (dm 2)
Answer: 50 dm 2.
V-th stage of the lesson. Independent work with self-test
The purpose of the stage: consolidation of the studied material.
Znayka has prepared a task for you. Slide 9
Read the task.
Draw a rectangle with sides 1 cm and 3 cm.
Find area.
-What need to do?
-What is known?
- What length? Width?
What units are used to measure length and width?
(In different: dm and cm)
-What do you need to find? (find area)
Can you do it right away? (No)
What should be done first? (Convert dm to cm)
Make a plan for solving the problem.
1. Convert to dm to cm
2. Find area
3. Write down the answer
Decide on your own plan.
slide self test
Who hasn't made a single mistake?
Formation of practical skills for finding the area
VI-th stage of the lesson. Inclusion in the system of knowledge and repetition.
The purpose of the stage: the formation of skills for solving problems for repetition and consolidation of the studied material.
Znayka has prepared a short note for you.
Make a task for it.
Length 8 dm
Width-? 2 times less
Find S.
Can we immediately answer the question of the problem? Why?
Who can explain her decision?
(1 child at the blackboard explains the solution to the problem and writes it down.)
on your own with cards
(Solution of examples by options,
followed by self-test
(checklist on slide)
8 7 + 5 6
9 9-28: 7
63: 7 + 54: 6
9 (38-30)
65-(49-19)
28 + 45: 5
8 8
56: 8
49: 7
Who hasn't made a single mistake?
Promotes the development of skills to establish cause-and-effect relationships.
Application of previously acquired knowledge in practice.
Actualization of acquired knowledge.
VII-th stage of the lesson. Reflection of activity (the result of the lesson).
The purpose of the stage: Generalization of the entire work. The evaluation itself.
You have been very productive in class today.
- Our lesson is over.
- What topic were you working on?
In what units is area measured?
How many square cm are in 1 square DM?
-What did you achieve the most?
What can you praise yourself for?
-What didn't work?
- Guys, since we have reached the goal of our lesson,
then what mood are you in?
Homework: p.60, No. 2. Slide 11
slide 12
Znayka and I want to tell you
The lesson is over and the plan is done.
Thank you guys very much.
For the fact that you worked hard and together,
And the knowledge will definitely come in handy for you
Thank you for the lesson!
Method of stimulation and motivation
Target: to promote the development of the ability to find the area of \u200b\u200bgeometric shapes using a square decimeter
Tasks:
Educational:
determine a visual image of a new unit of area - a square decimeter;
Developing:
set the ratio between square centimeter and square decimeter as units of area
Educational:
learn how to calculate the area of rectangular figures using a square decimeter
Planned results:
Hello guys, my name is Kristina Evgenievna, today we will have a lesson in mathematics.
And first, let's answer the questions with you:
How can you compare figures by area?
(on the "eye" and superimposing one figure on another)
What does it mean to measure the area of a figure?
(measure how many squares fit in it)
What common unit of area do you know?
Areas, what figures can you find by the value of lengths?
(Square, rectangle)
You answered all the questions very well, - It was not by chance that we remembered with you about named numbers, units of measurement for length and area, this knowledge will be useful to us in the lesson.
and now I'll tell a story. But first, tell me, guys, what holiday will we have this week? Are you already preparing gifts for your mom?
At school, all the students were preparing for the upcoming holiday, Mother's Day. Pupils of class 3 A decided to make invitation cards for their mothers. To do this, they needed colored cardboard with sides of 6 and 9 centimeters. What is the size of the invitation card? (54 cm)
And the students of grade 3 B decided to prepare a rectangular ad with sides equal to the width and height of the desk, 30 centimeters and 4 decimeters. What will be its area? and what size sheet of colored cardboard will they need?
Were you able to complete the task?
Why doesn't it work? What is the difficulty? (we don’t know how to count, for a long time).
It turns out? What is the problem?
A problematic situation arises - how to multiply 30 cm by 4 dm - children do not know the methods of out-of-table multiplication (they only learned the table up to 9).
Can we find out the area of the figure in cm2?
What to do?
We need a different unit of measure for area.
Which? Children will guess that it will be dm 2.
Guys, we also prepared a figure for you, get it under number 1
Measure the sides of this figure (10cm)
What can be said about her? (this is a square, with a side of 10 cm)
10 cm is linear unit, unit of measure for length.
Let's replace it with the largest linear unit.
10 cm = 1 dm writing in a notebook
So you have a square with a side of 1 dm.
So, on your tables is a square with a side of 1 dm. This is a new unit of area. Who guessed what it's called? (sq. dm)
How to find the area of this square? (Length times width)
S\u003d 1 dm * 1 dm \u003d 1 dm 2 writing in a notebook
What is its area?
What discovery have we made now? (We found the area of the square in decimeters)
Formulate the topic and objectives of the lesson.
Let's return to the desired problem, and solve it. Let's draw a conclusion according to the task.
To do this, they may suggest expressing 30 cm as 3 dm. And find the area of the figure.
Take the second square #2. What did you see? (divided by cm2)
How many squares can you put in 1 dm 2
How to find the area of this square?
How to write it down?
S\u003d 10 cm 10 cm \u003d 100 cm 2 writing in a notebook
Which way is shorter?
In what units is area measured? (In dm 2)
How many in 1 dm 2 square centimeters? (click)
AT 1 dm 2 \u003d 100 cm 2
Color one square centimeter green.
- And why did people need to use a new unit of measurement of 1 sq.dm, if they already had a unit of 1 sq.cm?
What items can be measured using this yardstick? Look around and name such objects (the surface of a desk, table, books, notebooks, etc.)
We have made another discovery.
And now let's open the textbook on page 144 and complete tasks No. 351
Which segment has a different length? Prove your answer.
Download:
Preview:
Target: to promote the development of the ability to find the area of \u200b\u200bgeometric shapes using a square decimeter
Tasks:
Educational:
determine a visual image of a new unit of area - a square decimeter;
Developing:
set the ratio between square centimeter and square decimeter as units of area
Educational:
learn how to calculate the area of rectangular figures using a square decimeter
Planned results:
Hello guys, my name is Kristina Evgenievna, today we will have a lesson in mathematics.
Updating students' knowledge. Motivation for activity.
And first, let's answer the questions with you:
- How can you compare figures by area?
(on the "eye" and superimposing one figure on another)
- What does it mean to measure the area of a figure?
(measure how many squares fit in it)
- What is the common unit of area?
(cm 2 )
- Areas, what figures can you find by the value of lengths?
(Square, rectangle)
You answered all questions very well.- It was not by chance that we remembered with you about named numbers, units of measurement for length and area, this knowledge will be useful to us in the lesson.
and now I'll tell a story. But first, tell me, guys, what holiday will we have this week? Are you already preparing gifts for your mom?
At school, all the students were preparing for the upcoming holiday, Mother's Day. Pupils of class 3 A decided to make invitation cards for their mothers. To do this, they needed colored cardboard with sides of 6 and 9 centimeters. What is the size of the invitation card? (54 cm)
And the students of grade 3 B decided to prepare a rectangular ad with sides equal to the width and height of the desk,30 centimeters and 4 decimeters. What will be its area? and what size sheet of colored cardboard will they need?
Were you able to complete the task?
Why doesn't it work? What is the difficulty? (we don’t know how to count, for a long time).
Would you like to know how to complete this task?
It turns out? What is the problem?
A problematic situation arises - how to multiply 30 cm by 4 dm - children do not know the methods of out-of-table multiplication (they only learned the table up to 9).
Can we find the area of the figure in cm 2 ?
Not?
What to do?
We need a different unit of measure for area.
Which? Children will guess that it will be dm 2 .
Guys, we also prepared a figure for you, get it under number 1
Measure the sides of this figure (10cm)
What can be said about her? (this is a square, with a side of 10 cm)
10 cm is linear unit, unit of measure for length.
Let's replace it with the largest linear unit.
10 cm = 1 dm writing in a notebook
So you have a square with a side of 1 dm.
So, on your tables is a square with a side of 1 dm. This is a new unit of area. Who guessed what it's called? (sq. dm)
How to find the area of this square? (Length times width)
S \u003d 1 dm * 1 dm \u003d 1 dm 2 writing in a notebook
What is its area?
What discovery have we made now? (We found the area of the square in decimetres)
Formulate the topic and objectives of the lesson.
Let's return to the desired problem, and solve it. Let's draw a conclusion according to the task.
To do this, they may suggest expressing 30 cm as 3 dm. And find the area of the figure.
Take the second square #2. What did you see? (divided by cm 2 )
How many squares can you put in 1 dm 2
How to find the area of this square?
How to write it down?
S=10cm 10cm=100cm 2 writing in a notebook
Which way is shorter?
In what units is area measured? (In dm 2 )
How much in 1 dm 2 square centimeters? (click)
In 1 dm 2 \u003d 100 cm 2
Color one square centimeter green.
Compare measurements with each other. What can you say?
- And why did people need to use a new unit of measurement of 1 sq.dm, if they already had a unit of 1 sq.cm?
What items can be measured using this yardstick? Look around and name such objects (the surface of a desk, table, books, notebooks, etc.)
We have made another discovery.
And now let's open the textbook on page 144 and complete tasks No. 351
Which segment has a different length? Prove your answer.
