Division is the inverse action of multiplication; with its help, the second factor is found from the product and one of the factors.
Divide a number A per number b- this means finding a number that, when multiplied by a number b gives a number A:
a: b = c, If c · b = a.
Number A called divisible b– divisor, With– private.
If the known and desired factors are single-digit natural numbers, then the unknown factor is found using the multiplication table.
Dividing a natural multi-digit number by a natural single-digit number is performed bitwise, starting with the most significant digit.
If the highest digit of the dividend contains a number less than the divisor, then the units of the highest digit are converted to the units of the adjacent low digit and division begins from this digit.
For example, divide 896 by 7.
- Divide 8 hundreds by 7, we get 1 hundred and one hundred remained.
- We convert the remaining hundred into tens, add 9 tens from the tens place, we get 19 tens.
- Divide 19 tens by 7, we get 2 tens, 5 tens remain.
- We convert the remaining tens into units, we get 50 units, add 6 units from the ones category, we get 56 units.
- Divide 56 units by 7, we get 8 units.
Means, 896: 7 = 128 .
Usually the division process is recorded in a “column”.
Division by a natural multi-digit number is done in a similar way. In this case, the first “intermediate” dividend includes so many high-order digits that it becomes larger than the divisor.
For example, divide 1976 by 26.
- The number 1 in the most significant digit is less than 26, so consider a number made up of the digits of the two highest digits - 19.
- The number 19 is also less than 26, so consider a number made up of the digits of the three highest digits - 197.
- The number 197 is greater than 26, divide 197 tens by 26: 197: 26 = 7 (15 tens left).
- Convert 15 tens to units, add 6 units from the units digit, we get 156.
- Divide 156 by 26 to get 6.
If at some division step the “intermediate” dividend turns out to be less than the divisor, then 0 is written in the quotient, and the number from this digit is transferred to the next, lower digit.
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Example: 3344: 16 = 209.
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Division natural numbers entirely (without remainder) is not always feasible. For example, you cannot divide 45 by 8, since there is no natural number that, when multiplied by 8, would give 45.
In such cases, division with a remainder is considered.
Division with remainder
If it is impossible to divide natural numbers completely, then divide with a remainder. With this action they are looking for greatest a natural number that, when multiplied by a divisor, produces a number less than the dividend.
a: b = c (remaining d), Where With And d such that c b + d = a, d.
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Examples: 17: 2 = 8 (remaining 1); |
Division of multi-digit natural numbers is performed in a “column”, the remainder is written after the quotient in parentheses.
284: 15 = 18 (remaining 14).
Division with decimal fraction in quotient
If a natural number is not evenly divisible by a single-digit natural number, you can continue the bitwise division and get a decimal fraction as a quotient.
For example, divide 64 by 5.
- Divide 6 tens by 5, we get 1 ten and 1 ten as a remainder.
- We convert the remaining ten into units, add 4 from the ones category, and get 14.
- We divide 14 units by 5, we get 2 units and a remainder of 4 units.
- We convert 4 units to tenths, we get 40 tenths.
- Divide 40 tenths by 5 to get 8 tenths.
Thus, if, when dividing a natural number by a natural single-digit or multi-digit number, a remainder is obtained, then you can put a comma in the quotient, convert the remainder into units of the next, smaller digit, and continue the division.
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Example: 97: 25 = 3,88
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Subject: Division of natural numbers (grade 5) teacher Tatyana Golikova
Georgievna
Target: repeat the method of solving examples by division, table
multiplication, properties of division, rules of division by digit unit,
types of angles, “what does it mean to solve an equation,” finding unknowns
elements of the equation;
develop mathematical speech, attentiveness, outlook,
cognitive activity, ability to analyze, do
assumptions, justify them, classify them;
instilling skills and abilities practical application mathematics,
drawing skills;
development logical thinking, ability to analyze dependence
between values, positive perception of Ukrainian
maintaining health, the ability to evaluate one’s knowledge, creating a situation
success, the feeling of “I CAN”, “I CAN DO EVERYTHING”,
increasing self-esteem, developing internal activity through
emotions and comprehension of the material, awareness of the importance of knowledge in life
person.
Lesson type: practicing skills and abilities
Methods: explanatory - illustrative, gaming, interactive
Forms: heuristic conversation, pair work, mutual control, work in small groups, “I myself - everyone together”, role-playing game
Equipment: interactive whiteboard, cards different types, marker,
7 sheets of A4, color-coded, tape.
Lesson Plan
1. Spiritual - aesthetic 2 min
2. Motivational 3min
3. Checking homework 5 min
5. Physical education minute 3 min
7. Homework2min
8. Reflection 4min
9.Evaluative 4min
1 Spiritual - aesthetic
All the children stood up quickly.
Good afternoon, please sit down
In order to get ready for work, I suggest repeating the multiplication table
Pick up a pencil and a card and solve the given examples in 1.5 minutes, and then read the words in ascending order of numbers.
Find which number “escaped” from the series of natural numbers?
Let's check in unison. The teacher calls the number, and the students call the word.
6:3=2 27:9=3 16:4=4
To drive ships
30:6=5 42:6=7 72:9=8 36:4=9
To fly into the sky
30:3=10 44:4=11 36:3=12
You need to know a lot
26:2=13 42:3=14 150:10=15
There's a lot to know.
Let this quatrain be the motto of today's lesson
2. Motivational
I propose to solve the puzzle in Ukrainian
LEDINE, NILDIK, KASCHAT, TOKBUDO
How many semantic groups can these concepts be divided into?
(Must receive two answer options, justify them)
Topic of today's lesson DIVISION
We opened our notebooks and wrote down the number, great job
3. Checking homework. Updating knowledge
We exchanged notebooks and check “dear colleagues”
Are there any who have not completed the work?
Who found more than two errors?
Thanks to the inspectors, return the notebooks to your neighbors.
What rule did you encounter when performing d/z?
What other properties can you name?
4.1 exercise 1
I suggest you go on a trip "In the animal world"
Take the example cards and solve them in your notebooks. Please note that not all examples are solved in writing; division by digit unit is encountered.
The work is given 4-5 minutes. After completion, the teacher accepts the answers, checking them with the corresponding group and writes with a marker on the sheets. Groups answer in any order. The teacher suggests arranging the sheets in the right order to get a story (The sheets are ordered like a RAINBOW)
Red Orange Yellow Green
1) 13000:1000; 1)120000:1000; 1) 300000:10000; 1) 35000:100;
2) 432:24; 2) 476:28; 2) 960:64; 2) 4485:23;
3) 11092:47 3) 6765:123. 3) 7956:234 3) 2790:62.
Light Blue Blue Purple
1) 43000:1000; 1) 11000:100; 1) 1400000:100000;
2) 1856:64 ; 2) 1734:34; 2) 5166:63;
3) 9126:234. 3) 3608:164. 3) 3210:214.
Gorilla sleeps 13000:1000= 13 hours a day, every day 432:24=18 hours a day, and in a state of hibernation, a hedgehog can survive without food 11092:47=236 days
Orange
The speed of the fish is the sword 120000:1000
120km/h, and the speed of the perch
476:28=17 km/h, and the speed of a shark 6765: 12355 km/h
Horses live up to 300000:10000=30 years, and dogs up to 960:64=15 years old, and the dog's life record is 7956:234=34 years
Weight polar bear reaches 35000:100=350kg, blue whale up to 4485:23=195 tons, and the weight of the East European Shepherd 2790:62=45kg
In humans normal temperature body 36.6 0 , the highest of all warm-blooded pigeons and ducks, up to 43000:1000=43 0 , and the lowest is in the anteater 1856:64=29 0 , dog body temperature 9126:234= 39 0 .
Grape snail withstands 11000:100=110 0 frost, but dies when 1734:34= 51 0 heat. Comfortable air temperature for humans 3608:164=22 0
Violet
Length of a large anaconda found in South America, can reach 1400000:100000=14m and in diameter 5166:63= 82cm. And the buildings of African termite warriors reach a height 3210:214=15m
4.2 task 2.
It's okay if we don't know the answer to a question. The main thing is to want to find the answer. We have already told you that if you are sick or miss a lesson for any reason, or something doesn’t work out for you, we have a wonderful TEXTBOOK assistant! We will now solve equations; if someone has forgotten how to find an unknown element of an equation, then do not be lazy to read page 124 of the textbook
Solve equations No. 470(3,4,6)
At the window No. 470(3)
Medium №470(4)
At the door No. 470(6)
Using the representative from the series, equations are solved. Additional task, for those who quickly mastered the equation “I AM WELL DONE! »
"I'M DONE! » (10x-4x)∙21=2268.
№470(3) №470(4) №470(6)
I'm done!
11x+6x=408; 33m- m=1024 ; 476:x=14 (10x-4x)∙21=2268.
x=24m=32 x=34 x=18
Keys to equations
X=204, P=32, M=304, !=18; Yu=302, A=34, U=24, K=3.
The correct answers are “HURRAY!”
5. Physical education minute
We're tired of sitting,
You only need a little bit of reading.
Hands up, hands down,
Marvel at the susida!
Hands up, hands on hips,
І to earn a lot of skoki.
Shvidko sat down and sat down.
The legs became dull.
Splash at the valley once.
For work. Everything is great!
They straightened their backs and put their hands on the desk.
To organize attention, the game “CORNERS”
Show sharp corner, straight, obtuse, expanded, 30 0, 70 0, 97 0, 150 0, etc., rhumb?
Problem No. 487
We read, draw up a diagram, analyze, find a solution, write down.
Let's see what's happening on the slide
Let's stage it with the students.
Making a table
| 24 km less |
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1) 58∙4=232(km) the first train traveled
2) 232+24=256(km) the second train traveled
3) 256:4=64(km/h)
Answer: the second train was traveling at a speed of 64 km/h
7. Homework
Can you handle this task at home? Let's write down the d/z.
No. 488, No. 471 (II column), repeat the rules for solving equations, creative task(rhumb)
8. Reflection
Game of Know and Dunno
Znayka asks Dunno about the properties of division, the rules for finding the elements of an equation, how the quotient will change if...
And Dunno answers!
We had some unused leaves on the table. They show dots. What type of work is this like? (graphic dictation)
How many dots are there on the piece of paper? How many questions will there be? I remind you of the answers
"Yes" ; "No" ; not sure
· · · · · · · ·
1. Numbers when divided are called dividend, divisor, quotient
2. I realized that division is not at all difficult
3. To find an unknown divisor, you need to divide the dividend by the quotient
4. To find an unknown factor, you need to divide the product by the known factor
5. Today in class I was interested.
6. I worked conscientiously in class.
7. I'm proud of myself.
The assistants collect cards in a row, and the teacher announces the marks.
| 1) 13000:1000; 2) 432:24; 3) 11092:47. | 1) 13000:1000; 2) 432:24; 3) 11092:47. | 1) 13000:1000; 2) 432:24; 3) 11092:47. | 1) 13000:1000; 2) 432:24; 3) 11092:47. |
| 1)120000:1000; 2) 476:28; 3) 6765:123. | 1)120000:1000; 2) 476:28; 3) 6765:123. | 1)120000:1000; 2) 476:28; 3) 6765:123. | 1)120000:1000; 2) 476:28; 3) 6765:123. |
| 1) 300000:10000; 2) 960:64; 3) 7956:234. | 1) 300000:10000; 2) 960:64; 3) 7956:234. | 1) 300000:10000; 2) 960:64; 3) 7956:234. | 1) 300000:10000; 2) 960:64; 3) 7956:234. |
| 1) 35000:100; 2) 4485:23; 3) 2790:62. | 1) 35000:100; 2) 4485:23; 3) 2790:62. | 1) 35000:100; 2) 4485:23; 3) 2790:62. | 1) 35000:100; 2) 4485:23; 3) 2790:62. |
| 1) 43000:1000; 2) 1856:64; 3) 9126:234. | 1) 43000:1000; 2) 1856:64; 3) 9126:234. | 1) 43000:1000; 2) 1856:64; 3) 9126:234. | 1) 43000:1000; 2) 1856:64; 3) 9126:234. |
| 1) 11000:100; 2) 1734:34; .3) 3608:164. | 1) 11000:100; 2) 1734:34; .3) 3608:164. | 1) 11000:100; 2) 1734:34; .3) 3608:164. | 1) 11000:100; 2) 1734:34; .3) 3608:164. |
| 1) 1400000:100000; 2) 5166:63; 3) 3210:214. | 1) 1400000:100000; 2) 5166:63; 3) 3210:214. | 1) 1400000:100000; 2) 5166:63; 3) 3210:214. | 1) 1400000:100000; 2) 5166:63; 3) 3210:214. |
| 1) 13000:1000; 2) 432:24; 3) 11092:47. | 1)120000:1000; 2) 476:28; 3) 6765:123. | 1) 300000:10000; 2) 960:64; 3) 7956:234. | 1) 35000:100; 2) 4485:23; 3) 2790:62. |
| 1) 1400000:100000; 2) 5166:63; 3) 3210:214. | 1) 11000:100; 2) 1734:34; .3) 3608:164. | 1) 43000:1000; 2) 1856:64; 3) 9126:234. |
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§ 1 Division of natural numbers
In this lesson you will become familiar with concepts such as dividend, divisor, quotient, and also consider some properties of division and learn how to solve equations with an unknown factor, unknown dividend and unknown divisor.
Let's solve the problem:
30 notebooks should be divided equally into 3 piles. How many notebooks will be in each stack?
Let each stack contain X notebooks, then according to the conditions of the problem
It is not difficult to guess that only one number when multiplied by 3 gives 30. This number is 10. Answer: Each stack contains 10 notebooks. Those. Using the given product 30 and one of the factors 3, we found an unknown factor. It is equal to 10.
Thus, we received a definition: the action by which another factor is found from a product and one of the factors is called division.
They write like this:
The number that is being divided is called the dividend, the number by which is being divided is called the divisor, and the result of division is called the quotient; by the way, the quotient shows how many times the dividend is greater than the divisor. In our case, the dividend is 30, the divisor is 3, and the quotient is 10.
§ 2 Properties of division of natural numbers
Now let's look at the properties of division:
Do you think any number can be a divisor? No! You can't divide by zero!
Is it possible to divide by one? Yes. When any number is divided by one, the same number is obtained, for example, 18 divided by one equals 18.
Can the dividend be equal to zero? Yes! When zero is divided by any natural number, the result is zero. For example, 0 divided by 4 equals 0.
Let's complete some tasks.
First: solve the equation 4x = 144. By the meaning of division, we have x = 144: 4, that is, x = 36. Thus, we can conclude: to find the unknown factor, you need to divide the product by the known factor.
Second task: solve the equation x: 11 = 22. In the sense of division, x is the product of factors 11 and 22. This means that x is equal to 11 times 22, that is, x = 242.
This means that to find the unknown dividend, you need to multiply the quotient by the divisor.
Task No. 3: solve the equation 108: x = 6. In the sense of division, the number 108 is the product of the factors 6 and x, that is, 6x = 108. Applying the rule for finding the unknown factor, we have x = 108: 6, that is, x = 18.
We get another rule: to find an unknown divisor, you need to divide the dividend by the quotient.
Thus, in this lesson you became acquainted with such concepts as dividend, divisor, quotient, and also examined some properties of division and received rules for solving equations with an unknown factor, unknown dividend or unknown divisor.
List of used literature:
- Mathematics 5th grade. Vilenkin N.Ya., Zhokhov V.I. and others. 31st ed., erased. - M: 2013.
- Didactic materials in mathematics 5th grade. Author - Popov M.A. – 2013
- We calculate without errors. Work with self-test in mathematics grades 5-6. Author - Minaeva S.S. – 2014
- Didactic materials for mathematics grade 5. Authors: Dorofeev G.V., Kuznetsova L.V. – 2010
- Control and independent work in mathematics 5th grade. Authors - Popov M.A. – 2012
- Mathematics. 5th grade: educational. for general education students. institutions / I. I. Zubareva, A. G. Mordkovich. - 9th ed., erased. - M.: Mnemosyne, 2009.
MATHEMATICS
5 CLASS
DIVISION OF NATURAL NUMBERS.
Plan - summary of the lesson “Division of natural numbers”.
Item: mathematics
Class: 5
Lesson topic: Division of natural numbers.
Lesson number in topic: Lesson 4 out of 7
Basic tutorial: Mathematics. 5th grade: textbook for
educational institutions / N.Ya.Vilenkin, V.I.Zhokhov, A.S.Chesnokov, S.I.Shvartsburd. – 25th edition, erased. – M.: Mnemosyne, 2009
The purpose of the lesson: create conditions for reproduction and adjustment necessary knowledge and skills, analysis of tasks and methods of their implementation; completing tasks independently; external and internal control.
As a result, students should:
be able to divide natural numbers;
be able to solve equations and word problems;
be able to draw conclusions;
be able to develop an algorithm of actions;
use mathematically literate language;
display the content of the actions performed in speech;
evaluate yourself and your comrades.
Forms of student work: frontal, steam room, individual.
Necessary Technical equipment: computer, multimedia projector, mathematics textbooks, Handout(for oral calculation, for work in class, for homework), electronic presentation made in Power program Point.
Routing lesson.
| Lesson stage | Tasks | Time | Task performance indicators |
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| teachers | student |
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| Stage 1. Organizational. | Checking class readiness. | The short duration of the moment. |
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| Stage 2. Checking homework. | The teacher collects notebooks with homework. | Students hand in their notebooks. | Before the lesson. | Homework will be checked for each student. |
| Stage 3. Updating knowledge. | introduction teachers. Verbal counting. Game "Mathematical Lotto". Historical reference. | Solve examples of mental calculation. Answer the question posed by the teacher. They work in pairs. | Development of group work skills. Students' basic knowledge was tested. |
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| Stage 4. | Together with the students, he determines the purpose of the lesson. | Determine the purpose of the lesson. | The goal of the lesson has been set. |
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| Stage 5. | Directs students' work. | Solve tasks involving calculating the values of numerical expressions, equations, and problems. Perform self-checks and draw conclusions. | Establishing the correctness and awareness of studying the topic. Identification of comprehension and correction of identified gaps. |
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| Stage 6. Physical exercise. | Manages the presentation. | The change in activity ensured emotional relief students. |
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| Stage 7. | Directs students' work. | Perform independently test tasks. | The correctness and awareness of the studied topic is established. |
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| Stage 8. | Self-assessment of activity. |
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| Stage 9. | Students write down the assignment in their diary. | Students understood the goals, content and methods of completing homework. |
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Description of the procedural part of the lesson.
| Lesson stage | Teacher activities | Student activity |
| Stage 1. Organizational. | The teacher welcomes students and checks their readiness for the lesson. | Greet the teacher and sit down. |
| Stage 2. Checking homework. | The teacher checks the availability of homework notebooks. | All students handed in their notebooks for checking. |
| Stage 3. Updating knowledge. | It is difficult to master any topic in mathematics without the ability to count quickly and accurately, therefore, as always, we begin the lesson with mental calculation. (Work in pairs). Hold hands and show that you are a couple. There are envelopes on your tables for mental calculations. Solve the examples orally and cover them with a card with the answer. Using the key (slide No. 1), replace the resulting numbers with the corresponding letters. Read the received word. | Solve one of 3 tasks. 42-d; 22nd; 10-l; 15th; 37th; 19-o; 39th; 9-t; 700 l; 20-hour; 16-a; 1-s; 36-n; 110o; 22nd. Received the words: dividend, divisor, quotient. |
| Stage 4. Setting goals, lesson objectives, motivational activities of students. | What action do all these concepts refer to? Yes, today we will continue to work on dividing natural numbers. This is not the first lesson on the topic. What goal can you set for yourself for this lesson? In the meantime, a little additional information. Students prepared reports on the topic. (Slides No. 2, No. 3, No. 4). №2 . Vladimir Ivanovich Dal - author "Explanatory Dictionary of the Living Great Russian language» in his dictionary he writes: Divide - break into parts, crush, fragment, make a section. Divide one number by another - find out how much times one is contained in a different. №3. At first there was no sign for this action. They wrote with a word, Indian mathematicians - with the first letter of the name of the action. The colon sign to indicate division came into use in late XVII century (in 1684) thanks to the famous German mathematician Gottfried Wilhelm Leibniz. №4. What other sign represents division? /(slash). This sign was first used by the 13th century Italian scientist Fibonacci. . | Answer: to division. Answer: Strengthen your knowledge on the topic. Listen to student messages. |
| Stage 5. Understanding the content and sequence of application of practical actions when performing upcoming tasks. | Open your notebooks, write down the date and topic of the lesson. (Slide No. 5) Guides students' work at this stage. Task No. 1 . Open the textbook on page 76, No. 481 (a,b,). Solve independently, 2 students complete the task on individual boards. There is an additional task on the card. Task No. 2 . Solve the equation and choose the correct solution from the 2 proposed ones. Explain the right decision and indicate the error in another .(slide No. 7) | Write down the date and topic of the lesson. a) 7585: 37 + 95 = 300 1) 7585:37=205 2) 205+95=300 b)(6738 – 834) : 123= 48 1) 6738-834=5904 2) 5904:123=48 Self-check, draw conclusions. Individual reflection. Additionally: 1440:12:24=5 1)1440:12=120 2) 120:24=5 Solve the equation (x-15)*7=70 1 solution. x-15=70:7 x=25 Answer: 25 2nd solution. x-15=70:7 |
| Stage 6. Physical exercise. | Slide number 8. | Do exercises for the hands and eyes. |
| Continuation of stage 5. | Task No. 3 . Solve a problem: One team of the plant produced 636 parts, which is 3 times more than the 2nd team and 4 times more than the 3rd team. How many parts did all the teams produce together? The student solves on the board, the rest in the notebook. Additional task: The train traveled 450 km in x hours. Find the speed of the train. Write an expression and calculate if x = 9; x=15. Task No. 4 (Slide number 10). They brought 100 kg of apples, x kg in each box, and 120 kg of pears, y kg in each box. What does the expression mean: a) 100:x b) 120:y c) 100:x+120:y d) 120:y-100:x | №3. They read the problem, make a short note, a solution algorithm, and write out the solution to the problem in a notebook. Solution. 1) 636:3=212(d) was manufactured by the 2nd brigade 2) 636:4=159(d) was manufactured by the 3rd brigade 3) 636+212+159=1007(d) were produced by 3 brigades together Answer: 1007 parts. Additional task. 450:x (km/h) - train speed. If x=9, then 450:9=50 (km/h) If x=15, then 450:15=30 (km/h) Answer : 50 (km/h), 30 (km/h) Give oral answers. a) the number of boxes of apples c) total number of boxes d) how many more boxes are there with pears than with apples? |
| Stage 7. Independent completion of tasks by students. | Directs students' work. | Perform test tasks independently. The leaves are submitted for verification. A1. What are the components of division called? 1) factors 2) quotient 3) dividend and divisor 4) terms A2. In one building there are 240 apartments, and in the second there are 2 times fewer apartments. How many apartments are there in the second building? 480 2) 138 3) 120 4) 242 A3. On day 1, tourists walked 15 km, which is 3 times more than on day 2. How many kilometers did the tourists walk on day 2? 1) 5km 2) 45km 3)12km 4)18km A4. Enter a number that is not divisible by 7. 1) 56 2) 48 3) 35 4) 21 IN 1. What number is 2 times greater than 36? Write this number down. AT 2. How many times is 890 greater than 178? Write this number down. C1. How many even three-digit numbers can be made from the numbers 4, 5, 6? (Numbers may be repeated) |
| Stage 8. Summing up the lesson. Reflection. | Summarizes students' work and gives grades. | Analyze their work in class. They answer the questions asked. |
| Stage 9. Information about homework, instructions for its implementation. | Sets differentiated homework. | Students write down the assignment in their diary. They take the task cards home. Required task: №1. Calculate: 2001:69 + 58884:84 №2. Solve the equation: a) x:17=34 b) (x – 8) *12=132 Additional task: On Sunday m people visited the museum, on Monday 4 times less than on Sunday, and on Tuesday - 33 people less than on Sunday. How many people visited the museum during these three days? Make up an expression and calculate for m =48, m = 100. |
Literature:
Mathematics. 5th grade: textbook for educational institutions / N.Ya. Vilenkin, V.I. Zhokhov, A.S. Chesnokov, S.I. Shvartsburd. – 25th edition, erased. – M.: Mnemosyne, 2009;
Testing and measuring materials. Mathematics: 5th grade / Compiled by L.V. Popova.-M.: VAKO, 2011;
Chesnokov A.S., Neshkov K.I. Didactic materials in mathematics for grade 5. M.: Classic Style, 2007.
Division of natural numbers
A lesson in the integrated application of knowledge and methods of action
based on the system-activity teaching method
5th grade
Full name Zhukova Nadezhda Nikolaevna
Place of work : MAOU secondary school No. 6 Pestovo
Job title : mathematic teacher
Topic Division of natural numbers
(training session on the integrated application of knowledge and methods of action)
Target: creating conditions for improving knowledge and skillsand skills in dividing natural numbers and methods of action in modified conditionsand non-standard situations
UDD:
Subject
They simulate a situation, illustrating the arithmetic operation and the progress of its execution, select an algorithm for solving a non-standard problem, and solve equations based on the relationship between the components and the result of the arithmetic operation.
Metasubject
Regulatory : define the goal educational activities, implement the means to achieve it.
Cognitive : Convey content in compressed or expanded form.
Communication: they know how to express their point of view, trying to substantiate it, giving arguments.
Personal:
They explain to themselves their individual immediate goals of self-development, give a positive self-assessment of the result of educational activities, understand the reasons for the success of educational activities, demonstrate cognitive interest to study the subject.
During the classes
1. Organizational moment.
In work we use addition,
Honor and honor to addition!
Let's add patience to skills,
And the amount will bring success.
Don't forget subtraction.
So that the day is not wasted,
From the sum of efforts and knowledge
We will subtract idleness and laziness!
Multiplication will help in work,
For the work to be useful,
Let's multiply hard work a hundredfold
Our deeds will increase.
Division serves in practice,
It will always help us.
Who shares the difficulties equally?
Share the successes of labor!
Any of the following will help:
They bring us good luck.
And that’s why we’re together in life
Science and labor are advancing.
II. Formulating the topic and objectives of the lesson
Did you like the poem? What did you like about it?
(students' answers)
You said it very well. The lines we read fit very well with our lesson today. Remember a poem you heard and try to determine topic of the lesson.
(Division of natural numbers) (slide 1) . Write down the date and topic of the lesson in your notebook.
Today is the first lesson on the topic “Division of numbers”? What else are you not good at and what would you like to learn? (students' answers)
So, today we will improve our division skills, learn to justify our decisions, find errors and correct them, evaluate our work and the work of our classmates.
III. Preparation for active educational and cognitive activities
- Motivation for schoolchildren's learning
Humanity has been learning division for the longest time. To this day, the saying “Division is a difficult thing” has been preserved in Italy. This is difficult both from the point of view of mathematics, and technically, and morally. Not every person is given the ability to divide and share.
In the Middle Ages, a person who mastered division received the title “doctor of the abacus”
Abacus is an abacus.
At first there was no sign for the division action. This action was written in words.
And Indian mathematicians wrote division with the first letter of the name of the action.
The colon sign for division came into use in 1684 thanks to the German mathematician Gottfried Wilhelm Leibniz.
Division is also indicated by an oblique or horizontal line. This sign was first used by the Italian scientist Fibonacci.
- How do we divide multi-digit numbers? (Corner)
Do you remember what components are called when divided?(slide 2)
- Do you know that the components of division: dividend, divisor, quotient were first introduced in Russia by Magnitsky. Who is this and what was the real name of this scientist? Prepare answers to these questions for the next lesson.
2) Update background knowledge students
- Graphic dictation
1. Division is an action by which another factor is found from a product and one of the factors.
2. Division has a commutative property.
3.To find the dividend, you need to multiply the quotient by the divisor.
4. You can divide by any number.
5.To find the divisor, you need to divide the dividend by the quotient.
6. An equality with a letter whose value must be found is called an equation
(Designation: yes; - no) (slide 3)
KEY: (slide 4)
B) Individual work of students using cards.
(simultaneously with dictation)
- Prove that the number 4 is the root of the equation 44: x + 9 = 20.
- Solution . If x=4 then 44:4+9=20
11+9=20
20=20, that's right.
2. Calculate: a) 16224: 52 = (312) d) 13725: 45 = (305)
B) 4230:18 = (235) d) 54756: 39 = (1404)
c) 9800: 28= (350)
3. Solve the equation: 124: (y – 5) = 31
Answer: y=9
4. Two students work using cards: solve 3 tasks each and ask each other theory questions
c) Collective review individual work(slide 5)
(Students ask the answering questions about theory)
- Application of knowledge and methods of action
A) Independent work with self-test(Slides 6 -7)
Select and solve only those examples in which the quotient has three digits:
Option 1 Option 2
A)2888: 76 = (38) a)2491:93= (47)
B)6539:13 = (503) b)5698: 14= (407)
B) 5712: 28 = (204) c) 9792: 32 = (306)
B) Physical education minute.
They stood up together and stretched.
Hands on the belt, turned around.
Right, left, once, twice,
They turned their heads.
We stood on our toes,
The back was held with a string
Now, sit down quietly,
We haven't done everything yet.
B) Work in pairs (slide 8)
(during work in pairs, if necessary, the teacher gives consultations)
No. 484 (textbook, page 76)
X cm is the length of one of the sides of the octagon
4x+4 4 =24
4x+16=24
4x=24-16
4x=8
X=2
2 cm is the length of one of the sides of the octagon
Solve equations:
a) 96: x = 8 b) x: 60 = 14 c) 19 * x = 76
D) Work in groups
Before you start completing tasks, read the rules for working in groups
Group I (1st row)
Rules for working in groups
Correct mistakes:
A)9100:10=91; a) 9100:10 = 910
B)5427: 27=21; b) 5427: 27 = 201
B)474747: 47=101; c) 474 747: 47 = 10101
D)42·11=442. d) 42 11 = 462
Group II (2nd row)
Rules for working in groups
- Actively participate in collaboration.
- Listen carefully to your interlocutor.
- Do not interrupt your friend until he finishes his story.
- Express your point of view on this issue, while being polite.
- Don't laugh at other people's shortcomings and mistakes, but tactfully point them out.
Check if the task was completed correctly. Suggest your solution
Find the value of the expression x:19 +95 if x =1995.
Solution.
If x=1995, then x:19 +95 = 1995:19 +95=15+95=110
(1995: 19 + 95 = 200)
Group III (3rd row)
Rules for working in groups
- Actively participate in collaboration.
- Listen carefully to your interlocutor.
- Do not interrupt your friend until he finishes his story.
- Express your point of view on this issue, while being polite.
- Don't laugh at other people's shortcomings and mistakes, but tactfully point them out.
Prove that an error was made in solving the equation.
Solve the equation.
124: (y-5) =31
U-5 = 124·31 y – 5 =124: 31
U-5 = 3844 y – 5 = 4
Y = 3844+ 5 y = 4+ 5
Y = 3849 y = 9
Answer: 3849 Answer: 9
D) Mutual check of work in pairs
Students exchange notebooks and check each other’s work, highlighting mistakes. with a simple pencil and put a mark
E) Group report on the work done
(Slides 5-7)
The slide shows the task for each group. The group leader explains the mistake made and writes the group's proposed solution on the board.
V. Monitoring student knowledge
Individual testing “Moment of Truth”
Test on the topic “Division”
Option 1
1.Find the quotient of 2876 and 1.
a) 1; b) 2876; c) 2875; d) your answer_______________
2.Find the root of equation 96: x =8
a) 88; b) 12; c) 768; d) your answer ________________
3 .Find the quotient of 3900 and 13.
a) 300; b) 3913; c) 30; d) your answer_______________
4 .One box contains 48 pencils, and the other contains 4 times less. How many pencils are there in two boxes?
a) 192; b) 60; c) 240; d) your answer________________
5. Find two numbers if one of them is 3 times larger than the other, and their
Their sum is 32.
a) 20 and 12; b) 18 and 14; c)26 and 6; d) your answer_________
Test on the topic “Division”
Last name, first name___________________________________________
Option 2
Underline the correct answer or write down your answer.
1 .Find the quotient of 2563 and 1.
a) 1; b) 2563; c) 2564; d) your answer_______________
2. Find the root of Equation 105: x = 3
a) 104; b) 35; c) 315; d) your answer ________________
3 .Find the quotient of 7800 and 13.
a)600; b) 7813; c) 60; d) your answer_______________
4 . In one tub the beekeeper had 24 kg. honey, and in the other 2 times more. How many kilograms of honey did the beekeeper have in two tubs?
a) 12; b) 72; c) 48; d) your answer_______________
5. Find two numbers if one of them is 4 times less than the other, and
Their difference is 27
A) 39 and 12; b) 32 and 8; c) 2 and 29; d) your answer_____________
Test verification key
Option 1
Job number | |||||
9; 36 |
VI. Lesson summary. Homework.
House. Exercise. P.12, No. 520,523,528 (essay).
So, our lesson has come to an end. I would like to interview you about the results of your work.
Continue the sentences:
I am...satisfied/not satisfied with my work in class
I managed …
It was difficult...
The lesson material was... useful/useless for me
What does mathematics teach?
