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Target. Introduce the method of multiplication three-digit number to single digit; promote the development of mental activity techniques: analysis, synthesis, comparison, generalization; memory, attention; cultivate interest in the subject, love for your country.
Lesson type: combined
During the classes
1. Organizational moment.
Teacher. Today in mathematics lesson we have to do a lot of work. Here is our lesson plan: (write on the board)
math warm-up,
meeting with works,
excursion to the streets of Moscow,
Don't break your head!
– And remember that the motto of our work is the words: (read in unison):
A little luck is the path to a big victory.
– Write down the number, great job. (Please mark your mood in the margins.) (I give cards to 3 students.)
2. Mathematical warm-up(a minute of penmanship, oral counting).
1) Teacher. Let's start with a math warm-up. Let's practice writing numbers beautifully and correctly, and count orally.
Teacher. What can you say about writing on the board?
On the board: 472, 454, 728, 436
Children. The numbers are written down, there are four of them.
– All these numbers are natural, three-digit.
– Almost all numbers have 4 hundreds.
Teacher. Find the “extra” number among these numbers and explain the choice.
Children. The “extra” number is 728, because it has 7 hundreds, and the rest all have 4 hundreds.
(I emphasize the number 728.)
Teacher. Write down the remaining numbers in your notebook. Please note that we write the numbers on the right side of the cell, and the left is free, each number is in one cell!
Teacher. Compare them. Is there any pattern in their series?
Children. They are arranged in decreasing order.
– Each next number has 2 tens less than the previous one.
– But in each next number there are 2 more units than in the previous one.
– they decrease by 18, because first they decrease by 20, and then increase by 2.
- How interesting it turned out! Instead of subtracting 18, you can subtract 20 and add 2!
Teacher. Yes, this is very interesting, I didn’t think of it myself! What great fellows you are!
2) Sound dictation. Independent work.
Teacher. Attention! And now the sound mathematical dictation. You need to be very careful, the announcer's voice will not wait for you and will not repeat it. Let's check how you know the multiplication table.
Write down the values:
product of numbers 7 and 9,
the first factor is 4, the second is 6,
8 multiplied by 7,
5 multiplied by the sum of numbers 4 and 6,
seven nine,
2 multiplied by 3 and multiplied by 5,
8 multiplied by the product of numbers 2 and 4,
nine nine.
(I check my work on cards.)
1) >,<,=
0 x 26…1 x 26
49 x 0 … 49 + 0
9: 1…9 x 1
36 + 1 … 36 x 1
(51 – 9) x 0 … (51 + 9) x 0
9 – 9 …. 9 + 9
2) >, <, =
1kg…1000g
1kg400g…2kg
4kg…4000g
200g…240g
5kg…5000g
500g…501g
3) Blitz tournament (write down expressions for problems).
The tourists walked a km, they still have a km to go. What is the entire journey of tourists?
Petya bought books for rubles and one for rubles. How much money did Petya pay?
There are many times more girls than boys in the circle. How many children are in the circle?
4) Let's check the math. dictation.
Teacher. Examination. (Orally, one student reads a series of numbers, the rest check themselves.)
Teacher. Bottom line.
3. Health-saving moment.“Collect expressions.”
Teacher. There are cards with expressions in different places in the classroom. Find the card with your eyes and, when the teacher calls, put it on the board. Teacher.
4. Activation of supporting knowledge.
Teacher. Look at the expressions and determine what we will do?
459 x 2
41 x 8
327 x 3
36 x 2
385 x 2
347x 2
18 x 4
Target.
Children.– We will perform extra-table multiplication, multiplying 2- and 3-digit numbers by a single-digit number.
Teacher.– Formulate a task for these expressions.
Children.– Distribute into groups.
Teacher.– What groups can expressions be divided into?
Children.– Multiplication of a two-digit number by a single-digit number and group 2 – multiplication of a three-digit number by a single-digit number.
Children arrange examples into 2 groups:
| 41 x 8 36 x 2 18 x 4 32 x 6 |
459 x 2 327 x 3 347 x 2 385 x 2 |
Teacher. Can we multiply a two-digit number by a single-digit number? (Yes)
Teacher. Okay, then write down the products with the value 72
Teacher. What expressions did you write down?
36 x 2
18 x 4
Teacher. Well done, you completed the task.
5. Assimilation of new knowledge
Teacher. Look at the remaining works. What did you notice?
– How to multiply a 3-digit number by a 1-digit number?
Children. The units of each digit are multiplied by the number.
Teacher. What will help in solving these examples?
Children. Algorithm. (We have already compiled it for a two-digit number.)
Teacher. Name it. (I put out the cards.)
Teacher. Does everything in this algorithm suit us?
Children. No, we have an algorithm for a 2-digit number. We need to change it - indicate that we are expanding a 3-digit number.
Change the line of the algorithm:
I will decompose a 3-digit number into the sum of its digit terms.
Teacher. We will do 1 example with an explanation at the board. (Strong student.)
Solve the 2nd example in pairs. (One pair decides on the board.)
– Let’s check: who has this?
– Solve example 3 yourself.
Teacher. Let's check what answer we got. Who disagrees?
Teacher. Algorithm.
Teacher. What knowledge did you use to do this?
Children. Knowledge of the multiplication table, the ability to represent a number as a sum of digit terms, the distributive law of multiplication.
Teacher. At home you will also practice multiplying a three-digit number by a single-digit number, the task is written on cards (the remaining examples from No. 212 (4)).
6. Physical education minute.
Teacher. Let `s have some rest.
I’m playing Yu. Antonov’s song “I’ll walk along Apricotovaya.”
Movements to music.
7. Working on the task.
Teacher. I included this song not by chance, now we will solve an interesting problem about streets, about Moscow streets.
– P. 12 No. 213. Read the problem. (1 student reads aloud.)
– What streets are mentioned in the problem?
Children. Garden Ring, Tverskaya street, Mozhaiskoe highway.
Teacher. STREET (from Ushakov’s explanatory dictionary) is the space between two rows of houses in populated areas for travel and passage. Highway 1. A compacted road paved with crushed stone. 2. In general - a road with an improved road surface (highway, asphalt, etc.). Street, highway, ring - these are types (types) of streets.
– Types (types) of Moscow streets: alleys, boulevards, blocks, lines, microdistricts, embankments, alleys, squares, passages, clearings, avenues, dead ends, highways, etc.
– The children, on my instructions, prepared mini projects “Streets of Moscow”.
Performances by children (very briefly about the history of the streets of Tverskaya, Garden Ring, Mozhaiskoye Highway)
Tverskaya street.
Tverskaya Street begins its history back in the 14th century, when a road was built here that connected Moscow with the city of Tver.
Foreign ambassadors and trade guests came to Moscow along Tverskaya. Russian tsars drove through this street and were crowned in the Assumption Cathedral. This was the grand entrance to Moscow. However, despite this, Tverskaya Street was poorly paved at that time, and miserable shacks were sometimes adjacent to the palaces. Moreover, like most Moscow streets, Tverskaya at that time was not distinguished by straightness. Tverskaya Street took on a completely new look in the late 30s during the reconstruction of Moscow. The main highway of Moscow has become straight and wide.
The entire length of the highway within Moscow has four lanes in each direction, as well as one lane in the middle, intended for the movement of government motorcades.
Mozhaiskoe highway.
The Mozhaisk Highway is an old, well-trodden road from the 14th to 15th centuries to Mozhaisk and led further to the west of Moscow - to Smolensk. Mozhaiskoe Highway is the ancient Smolensk Highway, which has always played an important role in the history of Moscow.
The Old Smolensk Road is the road along which Emperor Napoleon retreated during the Patriotic War of 1812.
Garden Ring road.
The Garden Ring is a circular transport route in the center of Moscow. Historically, Moscow was surrounded by an earthen rampart, which was a closed ring about 16 km long.
By the end of the 18th century, the shaft gradually collapsed, in some places the shaft was torn down, resulting in the formation of spacious squares and passages.
According to the project of the Commission for the construction of Moscow, it was proposed to demolish the remains of the rampart and create a wide ring street paved with cobblestones. Homeowners were obliged to arrange front gardens from plantings to their liking. This was the beginning of the Garden Ring.
Teacher. Let's read the problem again.
– Convenient formulation of the problem? Let's create a more convenient one.
– Write down a short condition. What is the best main word to start with? What else is known? What do you need to find?
– Is it possible to immediately answer the question of the problem? Why not?
– What do you need to know first? After?
– Solve for yourself (1 student decides from the back of the board.)
- Let's check. (Check with the solution on the board, if there are errors, correct them.)
-Which street is the widest? (Mozhaiskoe highway.)
– How many inverse problems can you create? (3)
Write down the solution to the problem as an expression immediately. On one's own .
Teacher. Guys, at home you will solve the problem about our Kotovsky streets. Whoever has the card with an asterisk will change the question to the problem so that it becomes a compound one.
8. Puzzle.
Teacher. I suggest you solve the puzzle.
Draw one segment on the drawing so that you get 3 different rectangles.
Independent work in notebooks (or give sheets of paper with drawings in advance).
(I walk around and see how they are coping. Put different ways on the board and discuss.)
9. Summary. Lesson reflection.
The lesson ends. What did you learn in the lesson?
Did you like the lesson or not? Explain why.
Mark your mood with an icon.
Who's in this mood right now? (The picture shows the faces.)
Summary of a math lesson in 6th grade
Lesson topic: “Multiplying a three-digit number by a one-digit number.”
Purpose of the lesson: To create conditions for mastering the algorithm for multiplying a two- and three-digit number by a single-digit number through various types of student activities.
Lesson objectives.
Educational:
Expanding the conceptual base by including new elements into it; mastering the algorithm for multiplying a two- or three-digit number by a single-digit number; skill
Calculate the product; improving computational skills and mental calculation skills; improving the ability to work in a team, in
For couples and independently.
Educational:
Development of observation, attention, memory, logical thinking; activation of mental activity; development of communication skills.
Educational:
Developing the ability to listen, communicate, and the desire to consciously observe discipline; fostering responsibility and conscientious attitude towards
Work, respectful and friendly relations with comrades; promotion of healthy lifestyles
Formed UUD:
Regulatory UUD:
Work according to the proposed plan, instructions; put forward your hypotheses based on educational material; exercise self-control.
Cognitive UUD:
Reveal the meaning of the concepts “multiplier”, “product”, “sum”, “difference” and use them in an active dictionary;
Determine the conditions for the written multiplication of a three-digit number by a single-digit number without going through the digit and justify your opinion;
Determine the correctness of multiplying a two-digit number by a one-digit number and justify your opinion;
Determine the order of written multiplication of a three-digit number by a single-digit number and justify your opinion;
Use the acquired knowledge to determine the amount of braid for edging the potholder.
Communication UUD:
Formulate a statement using mathematical terms as part of an educational dialogue;
Coordinate positions and find a common solution;
Adequately use verbal means to present the result of the activity.
Personal UUD: establish a connection between the goal of an activity and its result; determine common rules of behavior for everyone; be able to read assignments consciously and carefully; express the ability to self-assess based on the criterion of success in educational activities.
During the classes:
Org. moment. Organization of the workplace, correct posture, mood for the lesson.
Motivation for educational activities:
Guess the riddle:
It's much easier to walk with her
And a little more fun
It doesn't put a burden on your shoulders
And there are plenty of friends around. (Smile) Guys, let's cheer each other up with a smile and start the lesson in a good mood.
Goal: creating favorable conditions for children’s cooperation with the teacher and among themselves, activating thinking and attention through solving riddles
Checking homework.
What is the answer to 1 example, (50)?
Read the example where it turned out to be 480.
Is there a number 1000 among your answers?
4. Oral counting.
Solve the examples orally and you can guess what we will do in class?
And 5 x 10 = 50 N 3x7 = 21 O 8x3 = 24
E 4x8 = 32 N 6x8 = 48
E 9x7 = 63 U 9x1 = 9
M 2x8 = 16 F 5x6 = 30
List the answers in ascending order
9 16 21 24 30 32 48 50 63
Replace the numbers with the corresponding letters, what word do you get? What will we do in class? (multiply). Name the components and the result of multiplication.
Updating knowledge.
Open your notebooks, write down the number, class work and topic of the lesson: Multiplying two-digit and three-digit numbers by one-digit numbers.
Tell me again, what date is today? What day of the week? State the number of days in a week. What is Monday? What month is it? What can you say about him? (first day of autumn), what month is this? What is the year now? Which year starts in January? What is the last digit of the year that begins in January? What did we get?
Learning new material.
Name any single-digit number (for example 3), let's multiply it by 26 columns.
First, the number that is larger is written down; there is one digit in each cell, this is the first factor.
Under the first factor, the second factor is written so that the units are under the units.
We start multiplying with units: 6 units multiplied by 3, we get 18; then we sign 8 ones under the ones, and remember one ten and sign them above the tens of the first factor.
We multiply tens: we multiply 2 tens by 3, we get 6 tens; to 6 tens we add 1 ten, which we memorized. We get 7 tens, sign under the tens.
The product is 78.
The multiplication of a three-digit number by a one-digit number is explained by analogy.
Do you understand how such examples are solved?
PHYSICAL MOMENT Exercise for the eyes “Horizontal figure eight”. Extend your right hand in front of you at eye level, clench your fingers into a fist, leaving the middle and index fingers extended. Draw a horizontal figure eight in the air as large as possible. Start drawing from the center and follow your fingertips with your eyes without turning your head.
Where might we need such multiplication? When solving problems. Write down the word: Task. There are 238 apple trees in the garden, and 3 times more cherries. How many trees are there in the garden?
What does the problem say?
What is known? What do you need to find?
Will we be able to immediately answer the problem question? Why? What will be the short summary? A student goes to the blackboard
vish - ? der, 3 rubles total - ? der
solution: 238 * 3 = 714 + 238 = 952
Primary consolidation of the studied material
Work at the board:
315*3=945 23*4=92 142*3=426
408*2=816 226*3=678 96*4=384
Independent work of children. Textbook page 17 No. 71 first 4 examples
772 624 580 1581
Ind. Work: Vanya, Vasya using cards:
240* 3=720 201 *4=804 23 * 3=69 413*2=826
Checking work:
What is the smallest answer? (580)
Vanya, Vasya 69
The biggest answer? (1581)
Vanya, Vasya (826)
How much did you get in 1 example? 772 and 720, and in 2? 624 and 804
Rate it in pencil. Result of the work
Home assignment: page 17 No. 71 3, 4 column
Vanya, Vasya No. 67 1 column
Reflection, summary. What did you learn in the lesson? (how to multiply 2-3-digit numbers by a single digit. What is the most convenient way to multiply? (column). Where can we apply the acquired knowledge? (when solving examples, problems). Rate your work on a 5-point scale: raise your hand, whoever counts who earned a “5” rating today, and who earned a “3”?
Our lesson has come to an end, I liked how they worked today...
Teacher activities
Greeting from the teacher.
Checking readiness for the lesson.
- Check how your “workplace”, textbook, pencil case is organized.
Why is it important? Have your say.
Look at each other, smile, wish each other good luck, good mood.
Let's do finger exercises. (Children touch their finger to their neighbor on the desk and say:
I wish (thumb)
Large (medium)
Success (index)
In everything (nameless)
And everywhere (little finger)
Good luck! (whole palm)
Motivation for learning activities.
- I also want to wish you success. You are talented children. Someday you will be pleasantly surprised at how smart you are, how much you know and can do. But for this you need to constantly work on yourself, set new goals and strive to achieve them. And that's all we have...
You will mark all your results on a score sheet (each child has a score sheet)
Where do we start our work?
Why do we need this?
Write down the last digit of today's date (4).
In the next cell, write down a number showing the serial number of the current day (3).
Next, write down the last digit of the current year (2).
What number did you get?
What can you say about him?
Write other three-digit numbers yourself using these numbers. The numbers in the number record should not be repeated.
We check it using the example on the interactive whiteboard. If the task is completed correctly, give 3 points on the evaluation sheet, with one error - 2 points, more than two - 1 point.
What does the number 4 in the underlined numbers mean?
Why does this depend?
How are all these numbers similar?
What kind of work can we do with three-digit numbers?
Present verbally 432 and 342 as a sum of digit terms.
Write down the number 234. Present it as a sum of digit terms.
Swap notebooks with your deskmate and check each other's work. If your neighbor completed the task, give him 1 point on the score sheet. Failed - 0 points.
What skills did we use to complete this task?
Where can we use these skills?
Look at the blackboard.
800*3 200*4
234*2 432*3
324*4 400*2
What two groups can these expressions be divided into?
Which column example can we solve easily and quickly? Why?
Write down the answers to the examples in the first column in your notebook.
Whoever wrote it down, stand up. Check the sample.
On the evaluation sheet, put 3 points if you completed the task without errors, 2 points - one error, 1 point - more than two.
Read the expressions in the second column in different ways.
Try 324*4.
Who did the job? Who found it difficult? Why?
State the topic of today's lesson.
What do you want to learn by studying this topic? Think, take a colored magnet and, attaching it to the board, say about it.
Why do we need to know how to multiply a three-digit number by a one-digit number? Where can we use this in life?
So, let's start discovering something new. Let's work in a group (groups are given a task on a separate sheet)
Answer all questions asked. Write the answer to the 10th question on a large piece of paper (see Appendix No. 1)
The results of the groups' work appeared on the board.
What method of multiplication does this expression give us?
What property of multiplication is written on the board? Choose the correct answer. (combinative, distributive, commutative).
We need 576*9. Not everyone can do this yet.
- Who and what can help us?
Today we have neither instructions nor a reference book; we will not turn to adults. Where can we find the answer to our question?
Open the textbook part 2, page 1 number 2a
What did we do with the number 576?
Now we multiply the sum by the number. How to do it?
What to do with the received works?
Do the addition in a column in the textbook.
What result did you get?
Is this recording convenient?
Let's look at the task page 1, number 2b
Again a large rectangle, as in group work.
What is its length?
Width?
Let's find S 1, S 2, S 3. A new entry has appeared in the second column. Is this entry convenient?
Why are the zeros crossed out in the column?
Let's look at the entry for this example in the third column. What is she like?
Can anyone explain this entry?
Let's try to explain this notation together and create an algorithm for multiplying a three-digit number by a single-digit number, arranging the sentences in the right order (deformed text). We are working in groups again. (see Appendix No. 2).
What word did you come up with?
What have we discovered?
Will it be different if it is not a three-digit number, but a four- or five-digit number?
Write numbers from 1 to 9 with your chin (the numbers are as tall and wide as possible).
Is it time to evaluate your work in the group? If you were active, put 1 point on the score sheet; if you were inactive, give about 0 points.
324*5
906*4
1241*3
Using the algorithm, solve the examples at the board, writing down the actions in a column.
Option 1 Option 2
132*4 144*6
342*5 234*5
Testing using a sample (interactive whiteboard). Enter on the score sheet: 2 points - everything is correct,
1 point – 1 example correct,
0 points no correct answers.
Let's try to apply new knowledge in solving problems. (from 2 No. 4 – student).
1. Reading the problem
2. What is the problem about?
3. Condition
4. Question
5. How to graphically represent the condition of the problem?
6. How to answer the problem question?
7. Is there another way to solve this problem?
What is the topic of today's lesson?
What did you learn today?
Remember what goals we set for ourselves? Have we achieved them?
What did they open?
At the end of the lesson we wanted to give the title "Scholar on the topic", can I do that today? Why?
Calculate your points on the score sheet. Who got 10 points?
This is the highest number of points that the guys could score during the lesson.
What can we tell them?
What do we wish for those who had fewer points?
And that's all we have...
