Finding a number by a given value of its fraction. Finding a number by a given value of its fraction presentation for a lesson in mathematics (grade 6) on the topic. Finding a number by its fraction
"Finding a number by its fraction"
[Technology of the activity method and developmental learning, using digital technologies]
Lesson type: a lesson in the discovery and application of new knowledge in solving problems.
Lesson objectives: Teach to findthe number by its fraction and the number by its percentage to form the skills of solving problems through the joint discovery of new knowledge with students. To develop cognitive activity, attention, abstract thinking, interest in the subject of mathematics. Education of cognitive interest, elements of the culture of communication.
Equipment : computer (PowerPoint presentation), Internet resource.
During the classes.
I. Motivation for learning activities(Organizing time). Target: inclusion of students in activities at a personally significant level.
Motivational conversation."Good morning!" - we say to each other and smile. "Good morning!" and the sun smiles. "Good morning!" and the heart is filled with joy. And so that the muscles are filled with strength and vigor, in the morning we do what? Right! Charge! Exercise is necessary for everyone: both young and old. And especially it is necessary for our brain. As the great Russian commander Alexander Vasilyevich Suvorov said: "Mathematics is the gymnastics of the mind." We will also do this fascinating gymnastics.
II. Knowledge update
Target: repetition of the studied material necessary for the "discovery of new knowledge".
Students work on computers, perform exercises on tthe Fraction Division simulator - http://www.download.ru, which contains a series of examples for practicing the skills of division and multiplication of ordinary fractions and mixed numbers. The student solves the example and enters the answer from the keyboard. If the solution is correct, then the transition to the next example is automatically carried out. If there is an error in the solution, then the computer returns the child to the same example. Examples are randomly generated, and students studying on neighboring computers work on different assignments. The program tracks the mistakes that the child made and writes its conclusion. Then a grade is given. All work takes 3 minutes.
- What topic are we studying?
- What do you think is the work ahead in the lesson?
- What will you have to do for this?(Themselves to understand that we do not know, and then to discover something new.)Ready?
- Where did we start the lesson?(With repetition.)
- What did we repeat?(What we need to learn new things.)
Homework check.
During this time, two students write the solution on the chalkboard of the numbers from the homework that caused the most difficulty. The teacher finds out the gaps, organizes their elimination.
Guys, the task is completed, that's right, the sun on the screen smiles at us cheerfully. May we have the same good mood during the lesson.
One student works on a computer with an educational electronic edition for grades 5-11. "New opportunities for mastering the course of mathematics" (fills in the answers to home examples.)
The rest check the solution of the problem, after that they check the solution of the examples that the student wrote down on the computer screen (mutual check).
Dictation "Right - Wrong"(Students clap their hands if they are incorrect.)
1. To find the fraction of a number, you need to multiply this number by this fraction (correct)
2. To divide one fraction by another, you need to multiply the divisor by the reciprocal of the dividend (not correct)
3. Two numbers, the product of which is equal to zero, are called mutually inverse (not correct).
4.8/9: 0 = 0 (not correct). (Which rule is used in this example?)
5.0: 5/6 = 0 (correct)
O! You are doing great. And in the old days, ordinary fractions were very difficult to assimilate. They were considered the most difficult section of arithmetic. This can be judged by the following facts. We have a proverb: "I got into a dead end", the Germans still use a saying similar to ours: "I got into fractions." Both of these sayings mean the same thing: a person is in a very difficult situation.
Mathematicians developed rules for dealing with fractions, forcing students to mechanically memorize these rules without realizing their meaning. This was the reason for those sometimes insurmountable difficulties that students encountered. In our time, rules that children could not understand have long disappeared from mathematics. These rules are rediscovered by children themselves. So, in the field of fractions, we have to make a discovery for ourselves today.
Fixing the difficulty in trial action.
Analyze all the proposed tasks and tell me which one is “superfluous”? Why?
1. In class, 34 students 6/17 went on an excursion. How many students have gone on the field trip?
2. There are 12 boys in the class. This amounts toall students in the class. How many students are there in the class?
3.Zina read a book with 120 pages. How many pages did she read?
4.A family of hedgehogs collected 50 mushrooms. The smallest hedgehog has collected 6% of all mushrooms. How many mushrooms did the rest of the hedgehogs collect?
5. Mom bought 6 kg of sweets. Vitya immediately ateall the sweets, and he felt bad. After how many sweets did Viti have a stomach ache?
Students choose an extra problem (2) and justify their choice. So the topic of the lesson is the solution of this type of problem. Various ways of solving this problem are presented. Work in pairs.
The solution of the problem:
Let's compose the expression: 12: 3 × 8 = 32 (academic) in the class.
How else can we denote the division sign? (slash) So 12 needs to be multiplied by... Fraction reciprocal of a given fraction. Or split into .
Let's make an equation, denoting by x the number of students in the class.
× x = 12 and solve it,
X = 12:
Despite the different ways of reasoning, we solved the problem and came to the conclusion that ... The conclusion is formulated by the students themselves.
To find a number for a given value of its fraction, you need to divide its value by this fraction.
We compose an algorithm.
Algorithm for finding a number by its part b , expressed as a fraction m / n
Divide the number b by the fraction m / n.
Supporting synopsis
Number - ?
m / n of it (number) is b, then number = b:
Independent work with self-test against the standard.
- Have you learned how to solve problems of finding a number by its part? How can I check this?(Do independent work.)
Find a number if: a) it is 45, b)it is 24,
) it is 18, d) it is made up , e) 6% of it is 48 For weak students, a hint is given at will: the percentage is one hundredth of the number. This means 6% = 0.06.
Checking against a standard.
Physical education.
Solving problems.
Repetition of the rule, algorithm.
- How to find a number by its fraction?
Training exercise.
- Solve the problems, write down the solution in a notebook:
1) There are 24 students in the class. 3/8 of them are boys. How many boys are there in the class?
2) How many people were in the cinema, if 1/9 of all viewers are 10 people?
- Who did everything right away without mistakes? Well done!
- Who found their mistakes? What do you need to repeat?
- Have all the bugs been fixed? Well done!
Knowledge inclusion and repetition.
- Let's complete the task number 647, 648, 652.
Independent work on cards
Students are offered a choice of sets of cards with problems of varying degrees of difficulty. If the student is quite successful at low-level tasks, he can take cards with more difficult problems.
On "3":
Card 1
The tourists walked 18 km to the halt. From the map, they determined that it was 2/5 of the entire route. How long is the entire route? (45 km)
Card 2
The game was attended by 15 students. Which was 5/6 of all students in the class. How many students are there in the class? (18 people)
Card 3
After covering 36 km, the runner ran 3/4 of the distance. Determine the length of the distance. (48 km)
On “4”:
Card 1
Ivan planted 2/5 of all apple tree saplings, Peter - a third, and Anton - the last 8 apple trees. How many apple trees have you planted? (30 apple trees).
Card 2
In the school garden, 40% of all trees are apple trees, 25% are cherries, 28% are plums. The other 14 trees are pears. How many trees are there in the school garden? (200 trees)
Card 3
On the first day, 40% of all notebooks were sold at the kiosk, on the second day 3/5 of what was sold on the first, on the third - the remaining 864 notebooks. How many notebooks did the kiosk sell in three days?
On "5":
Card 1 - No. 662 (300 t)
Card 2 - No. 664 (576 ha)
Card 3 - No. 665 (360 km)
(Students who are doing well can then complete the supplementary assignment in their workbooks)
- Checking against a standard. Who could not complete the task correctly? Where can you once again practice performing such tasks?(When doing homework)
- Who has no mistakes? Well done! Give yourself an A.
Reflection of activity(lesson summary).
- How do we end the lesson?(We analyze our activities.)
- What was the purpose of the lesson? Have we reached our goal? Prove it.
- What difficulties do you still face? Where can you work on them?
- Draw a “ladder of success” in your notebook and evaluate your performance.
Homework. No. 680, 681, 691 (a)
Creative task.
To solve the task:
A mother for her three sons left plums on a plate in the morning, and she went to work. The eldest son woke up first. Seeing plums on the table, he ate a third of them and left. The second to wake up the middle one. Thinking that his brothers had not yet eaten the plum, he ate a third of what was on the plate and left. The youngest got up later than everyone else. Seeing the plums, he decided that his brothers had not yet eaten them, and therefore ate only a third of the plums on the plate, after which there were 8 plums on the plate. How many plums were there in the beginning?
Compose a task yourself on the topic of this lesson.
Thank you for the lesson!
Class: 6
Lesson presentations
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Epigraph to the lesson:
“The one who studies independently, succeeds seven times more than the one to whom everything is explained” (Arthur Giterman, German poet)
Lesson type: lesson in learning new material.
Methods: partial search.
Forms: individual, collective, group, individual.
(Place - 1 lesson on the topic)
Lesson type: explanatory and illustrative
The purpose of the lesson: to come up with a new way of solving problems in fractions, to consolidate the skills and abilities of solving problems.
- to systematize the solution of problems into parts, to deduce a new method of solving problems for finding a number according to its part.
- to help the development of students' interest not only in the content, but also in the process of mastering knowledge, to expand the mental horizons of students. Development of students' thinking, mathematical speech, motivational sphere of personality, research skills.
- to instill in students a sense of satisfaction from the opportunity to show their knowledge in the lesson. To create positive motivation among schoolchildren to perform mental and practical actions. Education of responsibility, organization, perseverance in solving tasks.
Equipment: illustrative material, presentation for the lesson. Sheets with an assignment for reflection, a textbook on mathematics Mathematics. Grade 6 / N. Ya. Vilenkin, V.I. Zhokhov, A.S. Chesnokov, S.I.Shvartsburd. M .: Mnemosina, 2011.
Lesson plan:
- Organizing time.
During the classes
1. Organizational moment.
(Didactic task - psychological attitude of students)
Hello, sit down. We communicate the topic, the purpose of the lesson and the practical meaning of the topic.
The goal of our lesson is to come up with a new way of solving problems using fractions.
2. Actualization of basic knowledge and their correction
(The didactic task is to prepare students for work in the classroom. Providing motivation and acceptance by students of the goal, educational and cognitive activities, updating basic knowledge and skills).
15; ; 3 6; ; (2;; 19; c)
Questions for the class:
- How to multiply a fraction by a natural number?
- How to find the product of fractions?
- How to find the product of a mixed number and a number? (using the distribution property of multiplication or convert a mixed number to an improper fraction)
- How to multiply mixed numbers?
2): 2; v:; :; :; (; ; ; X)
Questions for the class:
- How to divide a fraction by a natural number?
- How to divide one fraction by another?
- How to divide a mixed number by a mixed number?
Tables on the slide and supports on desks for the weak group:
Repeat the algorithms for solving problems to find a number by its part.
1) Cleared of snow from the skating rink, which is 800 m 2. Find the area of the entire ice rink.
(800: 2 5 = 2000 m 2)
2) Winnie collected x kg of honey from the hives, which is 30% of the amount he dreamed of. How much honey have you dreamed of, Winnie the Pooh? (x: 30 100)
3) The boa constrictor gave the monkey "v" bananas, which is the amount that he always gave. How much did he always give? (a)
Question to the class:
- What rule should be remembered here?
(To find a number based on its fractional part, you can divide this part by the numerator and multiply by the denominator)3. Learning new material. “Discovery” of new knowledge by children.
(The didactic task is to organize and direct the cognitive activity of students towards the goal)
Today in the lesson we will try to find an easier way to solve problems of finding a number by its fraction. The learned rules for multiplying and dividing fractions will help us with this.
- Write down the rule (a = b: m n) in a notebook.
- Replace the division sign with a slash and try to write it down as one action with the number "a" and a fraction.
N = = in = in:
- Translate the resulting rule into mathematical language.
(To find a number by its part, you can divide this part by a fraction) Opening. We repeated this rule to ourselves.Now work in pairs:
Option 1 tells the rule to option 2, and option 2 tells the first option.- Why is this rule more convenient than the previous one? (The problem is solved with one action instead of
two)4. Physical education.
(The task is to relieve tension)
Find all the colors of the rainbow (every hunter wants to know where the pheasant is sitting). Colored squares are posted in different places in the classroom. To find the desired color, you need to twist. Then charge for the eyes.
Annex 1.
5. Primary anchoring.
(The didactic task is to achieve from students the reproduction, awareness, primary generalization and systematization of new knowledge. Consolidation of the methodology of the student's forthcoming answer during the next survey)
Primary reinforcement takes place in the form of frontal work and work in pairs.
(with commentary in loud speech)1) Find the number if it is 10.
2) Find the number if 1% is 4.
In writing
(with commentary and writing on the board and in notebooks)1) Masha skied 500 m, which was the entire distance. How long is the distance? (500: = 800m)
2) The mass of dried fish is 55% of the mass of fresh fish. How much fresh fish to take. To get 231 kg of jerky? (231: = 420kg)
3) The mass of strawberries in the first box is equal to the mass of strawberries in the second box. How many kg of strawberries were there in two boxes if there were 24 kg of strawberries in the first box?
Working in pairs
(teamwork) Make up an expression for the tasks.1) On a beautiful summer morning, a kitten named Woof ate x sausages, which made up his daily diet. How many sausages does a Woof kitten eat in a day? (x: = sausages)
2) Dunno read 117 pages, which was 9% of the magic book. How many pages are there in a magic book? (117: = 1300str)
6. Initial check of understanding of what has been learned
(in the form of independent work with verification in the classroom).(Didactic task- knowledge control and elimination of gaps on this topic)
One person from each call option, they will silently work on the wings of the board. Then we check the solution.
Option 1
1) find the number if it is 21. (49)
2) find a number if 15% of it is x. ()
3) find the number if 0.88 is 211.2. (240)
Option 2
1) find the number if it is 24. (64)
2) find a number if x is 20% of it. (5x)
3) find the number if 0.25 is 6.25. (25)
Assess yourself: not a single mistake - “5”; 1 error - “4”; who has more mistakes - to do the work on the mistakes.
7. Summing up the lesson.
(Didactic task- to analyze and evaluate the success of achieving the goal and outline the prospect of further work). You made a discovery in class today
have come up with a new way of solving problems in fractions, which means they have succeeded seven times more than if I had told you everything myself (we look again at the epigraph to our lesson)
Reflection.
(Didactic task - mobilizing students to reflect on their behavior, motivation, methods of activity, communication).And now the guys continue the sentence: Today in the lesson I learned ... Today in the lesson I liked it ... Today in the lesson I repeated ... Today in the lesson I reinforced ... Today in the lesson I gave myself an assessment ... What types of work caused difficulties and require repetition ... In what knowledge I'm sure ... Did the lesson help to advance in knowledge, skills, skills in the subject ... Who, on, what else should be worked on ...
How effective was the lesson today ... smiling little man, if you liked the lesson and everything worked out and a sad little man, if still, something doesn't work out (everyone has pictures with little people on their desks).
6
. Homework(Comment, it is differentiated) (Didactic task - ensuring an understanding of the purpose, content and ways of doing homework).
P. 104-105. Clause 18. # 680; # 683; No. 783 (a, b)
Additional task No. 656. (for strong students).
For the creative group - come up with tasks on a new topic.
7. Grades for the lesson.
Everyone worked well, absorbed knowledge with appetite. Children! Thank you for the lesson.
Finding a number by its fraction
Remark 1
To find a number for a given value of its fraction, you need to divide this value by a fraction.
Example 1
Anton earned in a week of study three quarters excellent marks. How many marks did Anton get if there were excellent marks? 6 .
Solution.
By the problem statement, $ 6 $ marks are $ \ frac (3) (4) $.
Let's find the number of all marks:
$ 6 \ div \ frac (3) (4) = 6 \ cdot \ frac (4) (3) = \ frac (6 \ cdot 4) (3) = \ frac (2 \ cdot 3 \ cdot 4) (3) = 2 \ cdot 4 = $ 8.
Answer: only $ 8 $ marks.
Example 2
Mowed $ \ frac (4) (9) $ wheat in the field. Find the area of the field if it was cut $ 36 $ ha.
Solution.
By the hypothesis of the problem, $ 36 $ ga is $ \ frac (4) (9) $.
Find the area of the entire field:
$ 36 \ div \ frac (4) (9) = 36 \ cdot \ frac (9) (4) = \ frac (36 \ cdot 9) (4) = \ frac (4 \ cdot 9 \ cdot 9) (4) = $ 81.
Answer: the area of the entire field is $ 81 $ ha.
Example 3
In one day, the bus passed the $ \ frac (2) (3) $ route. Find the duration of the planned route, if the bus traveled $ 350 $ km per day?
Solution.
By the problem statement, $ 350 $ km is $ \ frac (2) (3) $.
Let's find the duration of the entire bus route:
$ 350 \ div \ frac (2) (3) = 350 \ cdot \ frac (3) (2) = \ frac (350 \ cdot 3) (2) = 175 \ cdot 3 = 525 $.
Answer: duration of the planned route $ 525 km.
Example 4
The worker raised his labor productivity by $% \ $ and made $ 24 more parts in the same period than it was planned. Find the number of parts scheduled to be completed by the worker.
Solution.
By the condition of the problem, $ 24 $ parts = $ 8 \% $, and $ 8 \% = $ 0.08.
Let's find the number of parts planned for execution by the worker:
$ 24 \ div 0.08 = 24 \ div \ frac (8) (100) = 24 \ cdot \ frac (100) (8) = \ frac (24 \ cdot 100) (8) = \ frac (3 \ cdot 8 \ cdot 100) (8) = 300 $.
Answer: planned $ 300 of parts for the worker.
Example 5
In the workshop, $ 9 $ machines were repaired, which is $ 18 \% $ of all machines in the workshop. How many machines are there in the workshop?
Solution.
By the condition of the problem, $ 9 $ machines = $ 18 \% $, and $ 18 \% = 0.18. $
Let's find the number of machines in the workshop:
$ 9 \ div 0.18 = 9 \ div \ frac (18) (100) = 9 \ cdot \ frac (100) (18) = \ frac (9 \ cdot 100) (18) = \ frac (9 \ cdot 100 ) (2 \ cdot 9) = \ frac (100) (2) = 50 $.
Answer: in the workshop $ 50 $ machines.
Fractional expressions
Consider the fraction $ \ frac (a) (b) $, which is equal to the quotient $ a \ div b $. In this case, it is convenient to write the quotient from dividing one expression by another using a line.
Example 6
for instance, the expression $ (13.5–8.1) \ div (20.2 + 29.8) $ can be written as follows:
$ \ frac (13.5-8.1) (20.2 + 29.8) $.
After performing the calculations, we get the value of this expression:
$ \ frac (13.5-8.1) (20.2 + 29.8) = \ frac (5.4) (50) = \ frac (10.8) (100) = $ 0.108.
Definition 1
Fractional expression is the quotient of two numbers or numerical expressions in which the $ ":" $ sign is replaced with a fractional bar.
Example 7
$ \ frac (2,4) (1,3 \ cdot 7,5) $, $ \ frac (\ frac (5) (8) + \ frac (3) (11)) (2.7-1.5 ) $, $ \ frac (2a-3b) (3a + 2b) $, $ \ frac (5,7) (ab) $ are fractional expressions.
Definition 2
A numeric expression that is written above the slash is called numerator, and the numerical expression, which is written below the fractional bar, is denominator fractional expression.
The numerator and denominator of a fractional expression can contain numbers, numeric or literal expressions.
For fractional expressions, the same rules apply as for ordinary fractions.
Example 8
Find the value of the expression $ \ frac (5 \ frac (3) (11)) (3 \ frac (2) (7)) $.
Solution.
Multiply the numerator and denominator of this fractional expression by $ 77 $:
$ \ frac (5 \ frac (3) (11)) (3 \ frac (2) (7)) = \ frac (5 \ frac (3) (11) \ cdot 77) (3 \ frac (2) ( 7) \ cdot 77) = \ frac (406) (253) = 1.6047 ... $
Answer: $ \ frac (5 \ frac (3) (11)) (3 \ frac (2) (7)) = 1.6047 ... $
Example 9
Find the product of two fractional numbers $ \ frac (16,4) (1,4) $ and $ 1 \ frac (3) (4) $.
Solution.
$ \ frac (16,4) (1,4) \ cdot 1 \ frac (3) (4) = \ frac (16,4) (1,4) \ cdot \ frac (7) (4) = \ frac (4.1) (0.2) = \ frac (41) (2) = $ 20.5.
Answer: $ \ frac (16.4) (1.4) \ cdot 1 \ frac (3) (4) = 20.5 $.
The rule for finding a number by its fraction:
To find a number for a given value of its fraction, you need to divide this value by a fraction.
Let's consider how to find a number by its fraction, with specific examples.
Examples.
1) Find the number 3/4 of which is 12.
To find a number by its fraction, divide this number by this fraction. To, you need to multiply the given number by the inverse of the fraction (that is, by the inverted fraction). To, it is necessary to multiply the numerator by this number, and leave the denominator unchanged. 12 and 3 by 3. Since the denominator is one, the answer is an integer.
2) Find a number if 9/10 is 3/5.
To find a number for a given value of its fraction, divide this value by this fraction. To divide a fraction into a fraction, multiply the first fraction by the reciprocal of the second (inverted). To multiply a fraction by a fraction, multiply the numerator by the numerator, and the denominator by the denominator. Reduce 10 and 5 by 5, 3 and 9 - by 3. As a result, we got the correct irreducible fraction, which means this is the final result.
3) Find a number whose 9/7 are equal
To find a number based on the value of its fraction, divide this value by this fraction. Mixed number and multiply it by the inverse of the second (inverted fraction). Reduce 99 and 9 by 9, 7 and 14 - by 7. Since we received an incorrect fraction, it is necessary to select the whole part from it.
Math lesson.
Class: 6
Topic: "Finding, numbers by its fraction."
Lesson objectives:
Educational:
Developing:
Educational:
fostering interest in a subject based on the use of multimedia capabilities of a computer;
Lesson type: combined lesson.
Equipment: screen, PC, projector, presentation, cards, textbook.
Plan:
Organizing time
Homework check.
Verbal counting
Learning new material
Test
Lesson summary
Homework
Reflection
During the classes
1. Organizational moment
–Hello guys! Today we have guests at the lesson, let's greet them and say hello! Have a seat. I am very glad to see you today. My name is Tatiana Mikhailovna.
2. Checking homework
- Please tell me what was asked at home?
(No. 635 (d, e), No. 641)
- Please look at the slide on it the home problem is solved compare with your solution
In total - 156 notebooks
I-? notebooks
II-? notebooks are from
Solution:
Let x notebooks in 1 pack, then x notebooks in 2 pack
x = 156;
x = 156:;
x = 156: 
;
x = 156 * 
;
x = 84. (tet.) - in 1 pack
Answer: 84 notebooks, 72 notebooks.
- Well done!
- Today I would like to start my lesson with the following statement: “Consider that day or that hour unhappy when you did not learn anything new and did not add anything to your education”. (J.-A. Kamen sky)
- These words will be the motto of our lesson. And this day will not be unhappy, because we will learn something new again, we will consolidate the skills of finding a fraction of a number, multiplying and dividing ordinary fractions, converting% to decimal fractions and vice versa.
- Guys, tell me, what month began?
(December)
- And what time of year is December?
(winter)
- And what is the most long-awaited holiday in winter?
(New Year)
We always prepare for this friendly and cheerful holiday, buy gifts, decorate the place where we live and spend a lot of time, and also decorate the Christmas tree.
And today in the lesson I invite you to participate in a small project "Our New Year tree". This will not be a project itself, but preparation for it, because the tree is part of the New Year's holiday.
2. Verbal counting
First, I suggest you light a garland for our Christmas tree!
Let's start the “New Year's Oral Counting”! Before you is a New Year's garland, if you count correctly or answer, then its lights will become multi-colored.
Next task:
How to multiply two fractions?
How to divide by a fraction?
What numbers are called mutually inverse?
Guys, how do you convert% to a number?
(% divided by 100)
How do you convert a number to a percentage?
(multiply the number by 100)
And so the next task (Slide)
0,65 65%
0,3 30%
48% 0,48
150% 1,5
Who's to say how to find a fraction of a number?
(To find the fraction of a number, you need to multiply this number by this fraction)
from 36; 28
0.4 from 60; 24
1.2 from 0.5; 0.6
Next task:
There are 60 balls on the tree. of them are red. How many balls are red?
(10)
Well done guys, we have decorated our New Year tree with a garland.
Explanation of the new material
Guys. And what is the decoration of the Christmas tree after the garland?
(star)
And so the next task "New Year's Star"
Please read the problem on the slide
« The ice rink was cleared of the snow, which is 800 m 2 ... Find the area of the entire ice rink.
- What is known in the problem?
(cleared, and this is 800 m 2 )
- A 800 m 2 is it part of the ice rink or the entire ice rink?
(Part)
_ What do you need to find in the problem?
(The area of the entire skating rink)
- Let x m 2 whole skating rink
Cleared of snow how to find a fraction of a number?
(You need to multiply this number by this fraction)
THOSE. X *
- and we know what it is equal to?
(800)
- Let's make an equation
X * = 800
What is the main action
(Multiplication)
- name the components
(1 factor, 2 factor, product)
- what is unknown?
(1 multiplier)
- how can we find it?
(1 factor = product: by 2 factor)
X = 800:
X = 800 *
X = 1600 m 2
And so the area of the entire skating rink is 1600 m 2
The guys in the problem did not know the number itself, but we knew what the cocoa was equal to those part of it, that is, by its fraction, we found the number itself.
So let's conclude,to find a number by its fraction, you need to divide this number by this fraction.
Children, everything is elementary!
I explain popularly:
You don't have to be a genius here
And the number given to us
Let's start dividing into a fraction.
And so guys, we were able to decorate our Christmas tree with a New Year's star.
Fizminutka
The music sounds, the child comes out and spends a physical minute
We counted with you and talked about numbers,
And now we stood up together, kneaded our bones.
On the count of one we will clench the fist, on the count of two in the elbows we will clench.
On the count of three - press to the shoulders, on 4 - to heaven
They bowed well and smiled at each other
Let's not forget about the five - we will always be kind.
On the count of six, I ask everyone to sit down.
Numbers, me, and you, friends, together friendly 7th.
4. Consolidation of the learned knowledge.
Well, you coped with all my previous tasks, so I propose to move on to the next stage of decorating the Christmas tree "New Year's ball". - At this stage, we will solve the problem of finding a number by its fraction and decorate the Christmas tree with New Year's toys.
Guys, please look at the board on the board there are written examples that we must solve
(for each example, 1 student after solving the student hang balls)
Find a number if:
these numbers are equal to 24 = 56
0.6 of this number equals 6 = 10
0.3 of this number is equal to 33 = 110
Guys please look at the slide
3) Guys, you have worksheets on your tables, with the help of which we will solve more than one problem today. So, we read carefully the condition of problem No. 1 and pay attention to what we know in the problem and what needs to be found.
Total - ? km
By car - 30 km is
Solution:
Answer: 50 km
Total - ? games.
Grade 6 - 15 games. - it
The rest of the classes are? games.
Solution:
Answer: 30 toys
After solving two problems, 3 students solve the test on the computer, and the rest continue to solve problems.
Independent work
K) 49; L) 64; M) 56.
G) 90; G) 10; H) 20.
B) 30; D) 4; E) 25.
Answers:
1
Total - ? gir.
Grade 6 - 3 weights. - it
The rest of the students -? gir.
Solution:
1)3: = 11 (weight) - total
2) 11-3 = 8 (gir.) - other classes
Answer: 8 garlands
Total - ? windows
I - 30 windows are
II-? windows
Solution:
30: 0,6 = 50 (windows) - total at school
50 - 30 = 20 (windows) - on day 2
Answer: 20 windows
Lesson summary
– Our lesson is coming to an end, let's summarize it.
What rules have WE REPEATED IN TODAY'S LESSON?
What rule did we meet today?
And so if you look, then for the new year we started to prepare the Christmas tree and brought it and decorated it, and in all this we were helped by our favorite mathematics and our topic "Finding, numbers by its fraction"
As a homework assignment, I suggest you the assignments SUBMITTED IN YOUR WORK SHEETS.
Homework.
3. Mom asked her son to water 0.2 of all the flower beds in the country. My son quickly calculated and said that it would not be difficult for me to water one flower bed well. How many flower beds are there in the country?
4. Five friends bought candy and immediately ate three of them, which amounted to
At the end of our lesson, we must do the most enjoyable task is to dress up our green beauty colorful balloons! These SMILEY balls are on your tables, choose the one that suits your mood and, leaving, attach it to our Christmas tree!
Those guys who received gifts can submit diaries for grading.
ALL THANK YOU VERY MUCH FOR THE LESSON! I wish you the best in your next lessons.
The red card means: "I am satisfied with the lesson, the lesson was useful for me, I worked a lot, usefully and well in the lesson, I understood everything that was said and what was done in the lesson."
The yellow card means: "The lesson was interesting, I took an active part in it, the lesson was to a certain extent useful for me, I answered from the spot, I managed to complete a number of tasks, I was quite comfortable in the lesson."
The blue card means: “I got little benefit from the lesson, I didn’t really understand what was being said, I don’t really need it, I won’t do my homework, I’m not interested, I was not ready for answers in the lesson” ...
WORK SHEET
to systematize the knowledge of students about the division of ordinary fractions;
to work out the skills of performing actions with ordinary fractions;
contribute to the formation of the ability to solve problems of finding a number by its part, expressed as a fraction, by dividing by a fraction;
create organizational conditions for the development of students' skills to analyze and compare;
create positive motivation for students to perform mental and practical actions, promote the development of the ability to cooperate.
Schoolchildren decorated the school windows for two days. On the first day of Ukrainian
We took 0.6 of all windows, which is 30 windows. How many windows were decorated on the second day?
Homework.
1. Find the value of the quantity if:
a) 0.8 it is equal to 576 g; b) 2/9 of it are equal to 36 liters;
c) 24% of it is equal to 57.6 km; d) 2.3% of it is equal to 2.07 rubles.
2. For a present for the boy, friends collected one fourth of the cost of a bicycle, which amounted to 120 rubles. What amount is not enough for the guys to buy a gift?
1. Mom asked her son to water 0.2 of all the flower beds in the country. My son quickly calculated and said that it would not be difficult for me to water one flower bed well. How many flower beds are there in the country?2. Five friends bought sweets and immediately ate three of them, which made up the total. How many candies were purchased in total?Introspection.
Topic: " Finding a number by its part ».
Lesson objectives:
Educational:
Developing:
promote the development of logical thinking, memory;
develop the ability to analyze the situation and evaluate the results of activities;
develop independence and attention.
Educational:
fostering interest in the subject through the use of the multimedia capabilities of the computer, as well as interest in the traditions of the New Year.
education of accuracy in the design of work.
Lesson objectives are aimed at knowledge and skills:
Understand the educational task, carry out the solution of the educational task both under the guidance of a teacher and independently, control one's actions in the process of its implementation, detect and correct mistakes, both others' and one's own, evaluate one's own achievements.
To cultivate a love for mathematics, interest in it, respect for each other, the ability to listen, discipline, independence.
F To form the skills of division and multiplication of ordinary fractions, to correctly read and write expressions containing ordinary fractions, to form the ability to solve problems on the topic "Finding a number by its fraction".
Lesson type: learning new material.
Equipment: screen, PC, projector, presentation, worksheets.
Forms lesson organization:
Frontal
individual
Teaching methods:
Visual
Problem-search
Reproductive
Description of the lesson
The topic of the lesson reflects in thematic planning and presents 1 lesson out of 5 in the topic "Finding a number by its part" and is based on the content of three topics: "Reciprocal numbers", "Multiplication of fractions" and "Division of fractions". I wanted the students in this lesson to see the connection of this topic with the previously studied one and realize(which is especially important in mathematics) that all topics are closely interrelated, and they cannot be studied in isolation from each other. In the course of the lesson, the children apply the knowledge gained not only in this lesson, but also in the previous lessons.
The structure of the lesson consisted of 9 main stages
Organizing time
Homework check.
Verbal counting
Learning new material
Consolidation of the studied material
Test
Lesson summary
Homework
Reflection
At the beginning of the lesson org. moment let me tune in to the lesson. Allowed to give a positive attitude towards fruitful cooperation.
On thestage oral counting the goal was to include students in the work, to define the scope of work in the classroom, to set a goal for the students: creating a playful situation about the project “Our Christmas tree.” Oral work in a playful way allowed to create a situation of success and responded to the psychological characteristics of age. Mathematical dictation contributed the formation of the ability to correctly read expressions containing ordinary fractions, as well as perform actions on their own, evaluate their achievements.
At the stage learning new materialthe guys were asked to come to the conclusion themselves thatto find a number by its fraction, you need this number pa divided by this fraction.
At the stage of consolidationthe material studied frontal and individual work was used, the skills of division and multiplication of ordinary fractions were formed. Self-examination (test) contributed to the formation of the ability to see their mistakes, evaluate their achievements.
Explaining homework stage helped to generate interest among students. The assignments are practice-oriented and help to convince children that mathematics is a science closely related to life.
Reflection stage became the logical conclusion of the lesson and helped students express their attitude to the lesson, and for me, as a teacher, to see the assessment of my lesson.
Thus, in my opinion, the goals set for the lesson have been achieved.
