Lesson objectives:
- Educational. Repeat and consolidate the principle of adding and subtracting the number 2, improve the ability to solve problems, develop mental counting skills, consolidate knowledge about geometric shapes, develop the skill of correct and beautiful writing of numbers and expressions.
- Educational. Arouse interest in the subject through didactic games, cultivate a sense of collectivism, love of mathematics, and interest in the history of one’s country.
- Developmental. Develop logical thinking skills, students’ speech, promote the development of attention and ingenuity.
Equipment: textbook “mathematics” 1st grade (author Moro), pictures depicting Winter, Santa Claus, Snow Maiden, Goblin, Kikimora, Koshchei the Immortal, Baba Yaga, Christmas trees with toys, envelopes with cards for children, notebooks, rebus, poster with geometric figures.
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During the classes
1. Organizational moment.
The bell rang loudly
Lesson begins
Our ears are on top
Eyes wide open
Listen and remember
We don't waste a minute
2. Communicating the topic and objectives of the lesson
The topic of our lesson is “Adding and subtracting the number 2. Consolidation.” We will solve examples on +-2 within 10, a mathematical chain, compose and solve problems, work with geometric material, do independent work, learn to reason and prove and at the same time be attentive and smart.
3. Oral counting
Guys, please tell me what holiday is coming up? (New Year). Yes, this is the best holiday for adults and children. How many of you know how many days are left until the New Year? (children's answers)
There are so many days left until the New Year (show card with number 22)
What number is this? (two digits)
What numbers are used to write this number? (2)
Name the neighbors of number 2 (1,3)
What are these numbers? (single digit)
Find the sum of numbers 2 and 2 (4)
Subtract two from two (0)
Remember the proverbs where the number 2 occurs
Remember the tongue twisters with the number 2
Proverbs:
- An old friend is better than two new ones.
- One mind is good, but two are even better.
- Miser pays twice.
- If you chase two hares, you won't catch either.
Tongue Twisters:
- Two puppies cheek to cheek
They pinch the brush in the corner. - Two Klavochkas were sitting on a bench,
They shared pins.
Guess the rebus 2 l each(basement)
What's happened basement? (children's answers)
How do animals prepare for winter? (children's answers)
During the autumn, some animals store food for the winter (squirrels, mice), others (bear, badger) become very fat, fat is also a kind of reserve for the winter, others (hares, wolves, foxes) do not make any reserves, they keep themselves in winter will find food.
Prepare your notebooks.
I'll open my notebook
And I'll put it on an angle
I'm friends, I won't hide it from you
I hold my pen like this.
I’ll sit straight, I won’t bend
I'll get to work.
What number is written in your notebooks? (2)
Attention to the board (I remind you how to write the number 2 correctly)
A minute of penmanship
Guys, what time of year do we celebrate New Year? (winter)
Winter sent us her portrait and a telegram in which this is what is written.
“Help, children, the forest evil spirits - Baba Yaga, Koschey the Immortal, Kikimora, Leshy stole my friends: Father Frost and the Snow Maiden, and with them the Christmas tree with toys and a bag of gifts disappeared. And without them our holiday will not take place.”
Sad news? Let's help out Santa Claus and the Snow Maiden? But to do this, we need to complete several tasks that the evil spirits have prepared for us! Do you agree?
Baba Yaga's 1st task.
Solve problems:
The hedgehog asked the hedgehog's neighbor:
“Where are you from, fidget?”
-I'm stocking up for winter,
See, the apples are on me.
He already brought 10,
Well, the neighbor took two.
How many apples does the hedgehog have left? (8 apples)
Quiet evening has fallen
Above the forest path.
The squirrel clicked upon meeting
She greeted me.
Looked into my basket
Where were 6 honey mushrooms?
-Give me a basket,
Yes, 2 mushrooms that are in it.
I shared with the squirrel,
How many mushrooms do I have now? (4 mushrooms)
3. The long-awaited December has arrived. First, 2 apple trees bloomed, and then 3 plum trees. How many trees bloomed in total? (Trees don’t bloom in winter, but 5 of them would bloom in spring)
4. Before Tsar Peter, Rus' celebrated the New Year on March 1, then on September 1, Tsar Peter ordered to celebrate the New Year on January 1. How many times has the date for the New Year been set?
5. The next task is a mathematical chain. If you solve it correctly, you will find out in which country the tradition of celebrating the New Year was born.
The first term is 6, the second is 2, find the sum, subtract one from it, add 2, decrease by 1, increase by 2, minus 1 (9)
In the lesson about the world around us, we talked about the fact that there are many countries on our land - England is one of them. It was the British who decided to celebrate the New Year, hoping for changes in life for the better and the fulfillment of all their desires.
6. What is this written down? (showing a card with the entry 1+2)
This is a numeric expression
Find its value (3)
Name numbers that are greater than 3 but less than 6 (4,5)
How can you get the number 5?
7. What is written on the board? (Inequalities) (check if these inequalities are true?)
5<7, 8>6, 10<10
(10<10 неверно, надо поставить знак =)
What happened? (equality)
8. Arrange the numbers in ascending order.
1 4 10 8 6 3 7 2
u h m a i a v d
Winter wishes you good luck. And well done, you freed Father Frost and Snow Maiden. And before we begin more complex tasks, let's rest a little.
4. Physical exercise.
We are like trees in a thicket
Branches sway in the wind in winter
In the spring we grow higher and higher
And we reach for the sun night and day
And in the fall we will shake off the leaves gradually
And the autumn wind whirls and whirls them
And again winter, again severe cold
And it became quiet in our forest, listen
5. Consolidation of what has been learned.
The following tasks are from Koshchei.
Let's remember how to add to the number 2, and how to subtract from the number 2? Open the textbook on page 82, find No. 2, what needs to be done? (solve examples)
1. Solving examples with comments (1st and 2nd article)
Solve column 3 yourself. Peer review
Guys, look carefully at how the second examples in each column were obtained? Well done!
Close your textbooks and put them on the edge of your desk.
Compose a problem and solve it. (a picture with birds is hung at the feeder)
Why do you need to feed birds in winter? What can you feed birds?
2. Open the green notebook on page 22
Let's solve the problem. (First the teacher reads the condition, then the student) There were 8 cubes in the box. Misha took 2 cubes from the box. How many cubes are left in the box?
What does the problem say? (about cubes)
What do we know?
What do you need to know in the problem?
Let's draw a diagram for it
What action will we take to solve the problem? Why?
Name the solution to the problem (8-2=6)
Let's write down the solution
What is the answer to the problem? (6 cubes)
Well done, guys, now each of you will definitely receive a New Year's gift at the holiday.
6. Now let's rest.
Fizminutka
We correct your posture
We bend our backs together
To the right, to the left we bent
We reached our socks
Shoulders up, back and down
Smile and sit down
You well? Depict a cheerful mood, sad, angry, you are sick, you are dreaming, you are happy with yourself.
7. Working with geometric material
The Leshy has prepared the next task for you. Look at the blackboard.
What do you know about the straight line?
What is shown under No. 2 (segment)
What is the difference between a segment and a straight line?
What is shown under No. 3 (broken line)
What does a broken line consist of (of links)
What are the ends of each link called? (tops)
Think about what is unnecessary here? Why? (straight, it has neither beginning nor end)
8. Independent work.
Very good, Leshy gives us the Christmas tree. But there are no toys on it. What? Come on, be quiet. Kikimora whispers something to me, telling me that the toys are here in the classroom and are in your envelopes. Some will have cones, others will have balls, others will have icicles, and others will have lanterns. Open the envelopes and take out the toys. On the other side there is a task for each of you. It is as follows: solve examples with a window. Fill in the blanks so that the equations are correct.
We check (I turn the toys over on the board to find the correct solution, the children check)
9. Lesson summary.
Well done boys! Today you worked hard, completed all the tasks, showing ingenuity and resourcefulness. We have consolidated the ability to add and subtract the number 2. So say it again as +2, -2. Amazing! And now we will be waiting for Father Frost and the Snow Maiden to visit us for the New Year's performance with big gifts.
Purpose of the service. The online calculator is designed for adding binary numbers in forward, reverse and complement codes.The following are also used with this calculator:
Converting numbers to binary, hexadecimal, decimal, octal number systems
Multiplying binary numbers
Floating point format
Example No. 1. Represent the number 133.54 in floating point form.
Solution. Let's represent the number 133.54 in normalized exponential form:
1.3354*10 2 = 1.3354*exp 10 2
The number 1.3354*exp 10 2 consists of two parts: the mantissa M=1.3354 and the exponent exp 10 =2
If the mantissa is in the range 1 ≤ M Representing a number in denormalized exponential form.
If the mantissa is in the range 0.1 ≤ M Let's represent the number in denormalized exponential form: 0.13354*exp 10 3
Example No. 2. Represent the binary number 101.10 2 in normalized form, written in the 32-bit IEEE754 standard.
Truth table
Calculation of limits
Arithmetic in binary number system
Arithmetic operations in the binary system are performed in the same way as in the decimal system. But, if in the decimal number system the transfer and borrowing are carried out by ten units, then in the binary number system - by two units. The table shows the rules for addition and subtraction in the binary number system.- When adding two units in a binary number system, this bit will be 0 and the unit will be transferred to the most significant bit.
- When subtracting one from zero, one is borrowed from the highest digit, where there is 1. A unit occupied in this digit gives two units in the digit where the action is calculated, as well as one in all intermediate digits.
Adding numbers taking into account their signs on a machine is a sequence of the following actions:
- converting the original numbers into the specified code;
- bitwise addition of codes;
- analysis of the obtained result.
When performing an operation in two's complement (modified two's complement) code, if a carry unit appears in the sign bit as a result of addition, it is discarded.
The subtraction operation in a computer is performed through addition according to the rule: X-Y=X+(-Y). Further actions are performed in the same way as for the addition operation.
Example No. 1.
Given: x=0.110001; y= -0.001001, add in reverse modified code.
Given: x=0.101001; y= -0.001101, add in additional modified code. 
Example No. 2. Solve examples on subtracting binary numbers using the 1's complement and cyclic carry method.
a) 11 - 10.
Solution.
Let's imagine the numbers 11 2 and -10 2 in reverse code.
The binary number 0000011 has a reciprocal code of 0.0000011
Let's add the numbers 00000011 and 11111101
| 7 | 6 | 5 | 4 | 3 | 2 | 1 | 0 |
| 1 | |||||||
| 0 | 0 | 0 | 0 | 0 | 0 | 1 | 1 |
| 1 | 1 | 1 | 1 | 1 | 1 | 0 | 1 |
| 0 |
| 7 | 6 | 5 | 4 | 3 | 2 | 1 | 0 |
| 1 | 1 | ||||||
| 0 | 0 | 0 | 0 | 0 | 0 | 1 | 1 |
| 1 | 1 | 1 | 1 | 1 | 1 | 0 | 1 |
| 0 | 0 |
An overflow occurred in the 2nd digit (1 + 1 = 10). Therefore, we write 0, and move 1 to the 3rd digit.
| 7 | 6 | 5 | 4 | 3 | 2 | 1 | 0 |
| 1 | 1 | 1 | |||||
| 0 | 0 | 0 | 0 | 0 | 0 | 1 | 1 |
| 1 | 1 | 1 | 1 | 1 | 1 | 0 | 1 |
| 0 | 0 | 0 |
| 7 | 6 | 5 | 4 | 3 | 2 | 1 | 0 |
| 1 | 1 | 1 | 1 | ||||
| 0 | 0 | 0 | 0 | 0 | 0 | 1 | 1 |
| 1 | 1 | 1 | 1 | 1 | 1 | 0 | 1 |
| 0 | 0 | 0 | 0 |
| 7 | 6 | 5 | 4 | 3 | 2 | 1 | 0 |
| 1 | 1 | 1 | 1 | 1 | |||
| 0 | 0 | 0 | 0 | 0 | 0 | 1 | 1 |
| 1 | 1 | 1 | 1 | 1 | 1 | 0 | 1 |
| 0 | 0 | 0 | 0 | 0 |
| 7 | 6 | 5 | 4 | 3 | 2 | 1 | 0 |
| 1 | 1 | 1 | 1 | 1 | 1 | ||
| 0 | 0 | 0 | 0 | 0 | 0 | 1 | 1 |
| 1 | 1 | 1 | 1 | 1 | 1 | 0 | 1 |
| 0 | 0 | 0 | 0 | 0 | 0 |
| 7 | 6 | 5 | 4 | 3 | 2 | 1 | 0 |
| 1 | 1 | 1 | 1 | 1 | 1 | 1 | |
| 0 | 0 | 0 | 0 | 0 | 0 | 1 | 1 |
| 1 | 1 | 1 | 1 | 1 | 1 | 0 | 1 |
| 0 | 0 | 0 | 0 | 0 | 0 | 0 |
| 7 | 6 | 5 | 4 | 3 | 2 | 1 | 0 |
| 1 | 1 | 1 | 1 | 1 | 1 | 1 | |
| 0 | 0 | 0 | 0 | 0 | 0 | 1 | 1 |
| 1 | 1 | 1 | 1 | 1 | 1 | 0 | 1 |
| 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
As a result we get:
| 7 | 6 | 5 | 4 | 3 | 2 | 1 | 0 |
| 1 | 1 | 1 | 1 | 1 | 1 | 1 | |
| 0 | 0 | 0 | 0 | 0 | 0 | 1 | 1 |
| 1 | 1 | 1 | 1 | 1 | 1 | 0 | 1 |
| 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
A carryover from the sign bit has occurred. Let's add it (i.e. 1) to the resulting number (thus carrying out the cyclic transfer procedure).
As a result we get:
| 7 | 6 | 5 | 4 | 3 | 2 | 1 | 0 |
| 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
| 0 | 0 | 0 | 0 | 0 | 0 | 0 | 1 |
| 0 | 0 | 0 | 0 | 0 | 0 | 0 | 1 |
The result of the addition: 00000001. Let's convert it to decimal representation. To translate an integer part, you need to multiply the digit of a number by the corresponding degree of digit.
00000001 = 2 7 *0 + 2 6 *0 + 2 5 *0 + 2 4 *0 + 2 3 *0 + 2 2 *0 + 2 1 *0 + 2 0 *1 = 0 + 0 + 0 + 0 + 0 + 0 + 0 + 1 = 1
Addition result (decimal notation): 1
b) 111-010 Let's imagine the numbers 111 2 and -010 2 in reverse code.
The reverse code for a positive number is the same as the forward code. For a negative number, all digits of the number are replaced by their opposites (1 by 0, 0 by 1), and a unit is entered in the sign digit.
The binary number 0000111 has a reciprocal code of 0.0000111
The binary number 0000010 has a reciprocal code of 1.1111101
Let's add the numbers 00000111 and 11111101
An overflow occurred in the 0th digit (1 + 1 = 10). Therefore, we write 0, and move 1 to the 1st digit.
| 7 | 6 | 5 | 4 | 3 | 2 | 1 | 0 |
| 1 | |||||||
| 0 | 0 | 0 | 0 | 0 | 1 | 1 | 1 |
| 1 | 1 | 1 | 1 | 1 | 1 | 0 | 1 |
| 0 |
An overflow occurred in the 1st digit (1 + 1 = 10). Therefore, we write 0, and move 1 to the 2nd digit.
| 7 | 6 | 5 | 4 | 3 | 2 | 1 | 0 |
| 1 | 1 | ||||||
| 0 | 0 | 0 | 0 | 0 | 1 | 1 | 1 |
| 1 | 1 | 1 | 1 | 1 | 1 | 0 | 1 |
| 0 | 0 |
An overflow occurred in the 2nd digit (1 + 1 + 1 = 11). Therefore, we write 1, and move 1 to the 3rd digit.
| 7 | 6 | 5 | 4 | 3 | 2 | 1 | 0 |
| 1 | 1 | 1 | |||||
| 0 | 0 | 0 | 0 | 0 | 1 | 1 | 1 |
| 1 | 1 | 1 | 1 | 1 | 1 | 0 | 1 |
| 1 | 0 | 0 |
An overflow occurred in the 3rd digit (1 + 1 = 10). Therefore, we write 0, and move 1 to the 4th digit.
| 7 | 6 | 5 | 4 | 3 | 2 | 1 | 0 |
| 1 | 1 | 1 | 1 | ||||
| 0 | 0 | 0 | 0 | 0 | 1 | 1 | 1 |
| 1 | 1 | 1 | 1 | 1 | 1 | 0 | 1 |
| 0 | 1 | 0 | 0 |
An overflow occurred in the 4th bit (1 + 1 = 10). Therefore, we write 0, and move 1 to the 5th digit.
| 7 | 6 | 5 | 4 | 3 | 2 | 1 | 0 |
| 1 | 1 | 1 | 1 | 1 | |||
| 0 | 0 | 0 | 0 | 0 | 1 | 1 | 1 |
| 1 | 1 | 1 | 1 | 1 | 1 | 0 | 1 |
| 0 | 0 | 1 | 0 | 0 |
An overflow occurred in the 5th digit (1 + 1 = 10). Therefore, we write 0, and move 1 to the 6th digit.
| 7 | 6 | 5 | 4 | 3 | 2 | 1 | 0 |
| 1 | 1 | 1 | 1 | 1 | 1 | ||
| 0 | 0 | 0 | 0 | 0 | 1 | 1 | 1 |
| 1 | 1 | 1 | 1 | 1 | 1 | 0 | 1 |
| 0 | 0 | 0 | 1 | 0 | 0 |
An overflow occurred in the 6th bit (1 + 1 = 10). Therefore, we write 0, and move 1 to the 7th digit.
| 7 | 6 | 5 | 4 | 3 | 2 | 1 | 0 |
| 1 | 1 | 1 | 1 | 1 | 1 | 1 | |
| 0 | 0 | 0 | 0 | 0 | 1 | 1 | 1 |
| 1 | 1 | 1 | 1 | 1 | 1 | 0 | 1 |
| 0 | 0 | 0 | 0 | 1 | 0 | 0 |
An overflow occurred in the 7th bit (1 + 1 = 10). Therefore, we write 0, and move 1 to the 8th digit.
| 7 | 6 | 5 | 4 | 3 | 2 | 1 | 0 |
| 1 | 1 | 1 | 1 | 1 | 1 | 1 | |
| 0 | 0 | 0 | 0 | 0 | 1 | 1 | 1 |
| 1 | 1 | 1 | 1 | 1 | 1 | 0 | 1 |
| 0 | 0 | 0 | 0 | 0 | 1 | 0 | 0 |
As a result we get:
| 7 | 6 | 5 | 4 | 3 | 2 | 1 | 0 |
| 1 | 1 | 1 | 1 | 1 | 1 | 1 | |
| 0 | 0 | 0 | 0 | 0 | 1 | 1 | 1 |
| 1 | 1 | 1 | 1 | 1 | 1 | 0 | 1 |
| 0 | 0 | 0 | 0 | 0 | 1 | 0 | 0 |
A carryover from the sign bit has occurred. Let's add it (i.e. 1) to the resulting number (thus carrying out the cyclic transfer procedure).
As a result we get:
| 7 | 6 | 5 | 4 | 3 | 2 | 1 | 0 |
| 0 | 0 | 0 | 0 | 0 | 1 | 0 | 0 |
| 0 | 0 | 0 | 0 | 0 | 0 | 0 | 1 |
| 0 | 0 | 0 | 0 | 0 | 1 | 0 | 1 |
Addition result: 00000101
We got the number 00000101. To convert the whole part, you need to multiply the digit of the number by the corresponding degree of digit.
00000101 = 2 7 *0 + 2 6 *0 + 2 5 *0 + 2 4 *0 + 2 3 *0 + 2 2 *1 + 2 1 *0 + 2 0 *1 = 0 + 0 + 0 + 0 + 0 + 4 + 0 + 1 = 5
Addition result (decimal notation): 5
Addition of binary floating point real numbers
On a computer, any number can be represented in floating point format. The floating point format is shown in the figure:
For example, the number 10101 in floating point format can be written like this:
Computers use a normalized form of writing a number in which the position of the decimal point is always given before the significant digit of the mantissa, i.e. the condition is met:
b -1 ≤|M| Normalized number - This is a number that has a significant digit after the decimal point (i.e. 1 in the binary number system). Normalization example:
0,00101*2 100 =0,101*2 10
111,1001*2 10 =0,111001*2 101
0,01101*2 -11 =0,1101*2 -100
11,1011*2 -101 =0,11011*2 -11
When adding floating-point numbers, order alignment is performed towards a higher order: 
Algorithm for adding floating point numbers:
- Alignment of orders;
- Addition of mantissas in modified additional code;
- Normalization of the result.
Example No. 4.
A=0.1011*2 10 , B=0.0001*2 11
1. Alignment of orders;
A=0.01011*2 11 , B=0.0001*2 11
2. Addition of mantissas in the additional modified code;
MA additional mod. =00.01011
MB additional mod. =00.0001
00,01011
+ 00,00010
=
00,01101
A+B=0.01101*2 11
3. Normalization of the result.
A+B=0.1101*2 10
Example No. 3. Write a decimal number in the binary number system and add two numbers in the binary number system.
The binary number system is similar to the decimal number system we are familiar with, except that instead of ten it uses base 2 and only two digits, 1 and 0. The binary system is the basis for how computers work. Binary codes use 1s and 0s to enable or disable certain processes. Just like decimals, binary numbers can be added, and although there is nothing difficult about it, adding them can seem daunting at first. Before you begin adding binary numbers, you need to thoroughly understand the concept of place value.
Steps
Part 1
Binary system- For example, you could write 1 in the eights place, 1 in the fours place, 0 in the twos place, and 1 in the ones place, resulting in the following binary number: 1101.
-
Let's look at the ones digit. If there is a 0 in this place, the bit value is 0. If there is a 1, the value is 1.
- For example, in the binary number 1101, there is a 1 in the ones place, so the place value is 1. Thus, the binary number 1 is equivalent to the decimal number 1.
-
Let's look at the twos category. If there is a 0 in this place, the place value is 0. If there is a 1 in the twos place, the place value is 2.
- For example, in the binary number 1101, there is a 0 in the twos place, so the place value is 0. Thus, the binary number 01 is equivalent to the decimal number 1, since there is a 0 in the twos place and a 1 in the ones place: 0 + 1 = 1.
-
Let's look at the rank of fours. If there is a 0 in this place, the place value is 0. If there is a 1 in the fours place, the place value is 4.
- For example, in the binary number 1101, there is a 1 in the fours place, so the place value is 4. Thus, the binary number 101 is equivalent to the decimal number 5, since it has a 1 in the fours place, a 0 in the twos place, and a 1 in the ones place: 4 + 0 + 1 = 5.
-
Let's look at the eights rank. If there is a 0 in this place, the place value is 0. If there is a 1 in the eights place, the place value is 8.
- For example, in the binary number 1101, there is a 1 in the eights place, so the place value is 8. Thus, the binary number 1101 is equivalent to the decimal number 13, since it has a 1 in the eights place, 1 in the fours place, 0 in the twos place, and 1 in the ones place : 8 + 4 + 0 + 1 = 13.
Part 2
Adding Binary Numbers Using Place Values-
Write the numbers in a column and add the corresponding numbers. Since two numbers are added, the sum of the individual digits can be 0, 1, or 2. If the sum is 0, write 0 at the bottom of the corresponding column. If the sum is 1, write 1. If the sum is 2, write 0 at the bottom of the corresponding column and move the 1 to the adjacent one. column of twos.
- For example, when adding the binary numbers 0111 and 1110 in the ones column, 1 and 0 add up to 1, so write 1 at the bottom of that column.
-
Add up the numbers in the twos column. When adding, you can get 0, 1, 2 or 3 (if you moved 1 from the units column). If the sum is 0, write a 0 under the line in the twos place. If the sum is 1, write a 1 at the bottom of the column. If the sum is 2, write a 0 under the line and move the 1 to the fours column. If the sum is 3, write 1 at the bottom and move 1 to the fours column (3 twos = 6 = 1 two and 1 four).
- For example, when adding the binary numbers 0111 and 1110, two ones in the twos column give 2 (two twos, that is, one four), so write a 0 under the line and move the 1 to the fours column.
-
Add up the numbers in a column of fours. When adding, you can get 0, 1, 2 or 3 (if you moved 1 from the column of twos). If the sum is 0, write a 0 under the line in the fours place. If the sum is 1, write a 1 at the bottom of the column. If the sum is 2, write a 0 under the line and move the 1 to the eights column. If the sum is 3, write 1 at the bottom and move 1 to the eights column (3 fours = 12 = 1 four and 1 eight).
- For example, when adding the binary numbers 0111 and 1110, three ones should be added (taking into account the twos transferred from the column). The result is 3 fours, that is 12, so write 1 in the fours column and move 1 to the eights column.
-
Continue adding the numbers in each place column until you get the final result. For convenience, you can remember that 0 = 0, 1 = 1, 2 = 10 and 3 = 11.
- For example, when adding the binary numbers 0111 and 1110 in the column of eights, you should add two ones (taking into account those transferred from the column of fours). As a result, we get 2, write 0 in the eights column and move 1 to the sixteen place. Since column sixteen has no digits, we write 1 below the line. Thus, 0111 + 1110 = 10101.
Part 3
Adding binary numbers with units carry-
Write the numbers in a column. Circle the pairs of ones (digits 1) in the ones place. Remember that the ones digit is located on the right edge.
- For example, when adding 1010 + 1111 + 1011 + 1110, circle one pair of 1's.
-
Consider the ones place. For each pair of digits 1, move the 1 to the adjacent left column, which corresponds to the digit twos. If in the units digit column there is only one digit 1 or after transferring the pairs there is one extra unit left, write 1 under the line. If all the units are included in the pairs or there are none at all, write 0 at the bottom of the column.
Draw a place value table consisting of two rows and four columns. The binary system uses base 2, so instead of the ones, tens, hundreds, and thousands in the decimal system (base 10), the digit values in the binary system are ones, twos, fours, and eights. The ones will be located in the rightmost column of the table, and the eights will be in the far left.
Write down a binary number on the bottom line of the table. In the binary system, only the following are used to write numbers: 1 (\displaystyle 1) And .
Math lesson in 1st grade. Educational and educational complex “Prospective Primary School”. Topic: “Addition of the number 2 with single-digit numbers” Purpose: to create conditions for familiarization with cases of addition in which the first term is the number 2; learn to perform addition of the form 2+a; improve knowledge of the composition of the first ten numbers; develop the ability to reason, analyze, develop mathematical speech. Planned results (meta-subject universal learning activities): Regulatory: independently set the goal of the upcoming work, plan ways to achieve the set educational task and evaluate the result of the work. Cognitive: master general techniques for solving a problem, performing calculations, performing logical mental operations (analysis, comparison) to solve a cognitive problem. Communicative: express your thoughts fully and accurately; be tolerant of the opinions of others, participate in collective discussion. Personal: establish connections between the purpose of educational activity and its motive; understand the importance of the social status of “student”, demonstrate self-organization and discipline. Equipment: game “The Best Pilot”, game “Who Will Fly into Space?”, printed notebooks, workbooks, textbook. Lesson progress: Organizational moment. 1) Greetings to guests. 2) A minute of penmanship. 128 228 328 -Look at the task. What did you notice? (The first digit in the number changes) -What entry will be next? (428, 528) -Who can read these numbers? What do they have in common? (Three digits, 3 digits per entry). Updating knowledge. 1) Oral calculations (individual and frontal). Game “Best Pilot” - 3 students are invited to the board. What is the task before you? (Find unknown numbers.) -Not only find, but also tell how you did it. 4+a=6 a-2=8 7-a=1 a+5=9 a-3=5 9-a=6 Game “Who will fly into space?” -Three astronaut candidates are preparing to fly into space. But not everyone will be able to fly. To do this, you need to read the star map and find errors in it. The first candidate claims that there are 5 errors on the map, the second one found 4 errors, and the third one found 3. Check who is right. 11-1=12 7+1>5+3 1+4=5 13-1=13 6-6=0 5+0=6 8+1=9 4<4+3 10-9=1 3+4=7 Мотивация учебной деятельности. -К какому выводу можно прийти после этого этапа урока? (Математика нужна и лётчикам, и космонавтам, и нам.) _ Чтоб водить корабли, чтобы в небо взлететь, Надо многое знать, надо много уметь. И при этом, и при этом, вы заметьте-ка, Помогает всем, ребята,…МАТЕМАТИКА! «Открытие» нового знания и определение темы урока. -Какой девиз у нас звучит на уроке математики каждый день? (Ни дня без задачи!) Прочитайте задачу: « На уроке математики Маша решила 2 примера, а Миша на 4 примера больше. Сколько примеров решил Миша?» -О чём говорится в задаче? (О примерах.) Кто решал примеры? (Маша и Миша.) Сколько решила Маша? (2) А сколько решил Миша? (На 4 больше.) А что это значит? (Столько же и ещё 4). -Каким действием решим задачу? (Сложением) -Назовите решение. (2+4=6) -Назовите ответ. (6 примеров решил Миша.) -Закройте глаза. Что изменилось в задаче? (Число 4 заменили на число 6.) Сможете решить эту задачу самостоятельно? Назовите решение и ответ.(2+6=8 Ответ: 8 примеров решил Миша.) -Внимательно посмотрите на решения задач. Чем похожи решения? (Первое слагаемое 2) -Определите тему нашего сегодняшнего урока.(Будем учиться прибавлять к числу 2 однозначные числа.) Физкультминутка. Первичное закрепление. Работа по заданиям учебника (с.29) №1.-Рассмотрите рисунки к каждой сумме. Чем похожи суммы? (Первое слагаемое 2) -Чем отличаются? (Вторые слагаемые-разные.) -Выполните сложение с помощью палочек на рисунке. -Запишите пример, которого нет в этом номере. (2+0) А какой пример получится, если мы поменяем местами слагаемые в этом примере? (0+2) Какой вывод можно сделать? (Если к числу +0, то получится это же число.) -№3. Прочитайте задание. Каким правилом нужно воспользоваться? (Правилом перестановки слагаемых) Как оно звучит? (От перестановки слагаемых сумма не меняется.) Взаимопроверка. -Поменяйтесь тетрадями, проверьте у соседа работу. -Найдите значение разностей, используя примеры на сложение: 8-2 8-6 Тренировочные упражнения и задания на повторение. Печатная тетрадь №2, стр. 41-43, №1-10. Итог урока. -Над какой темой мы работали? Чем воспользовались при изучении темы? Рефлексия. -Закончите предложения: На уроке я работал (быстро, медленно, с пользой, без пользы)… Мне было (интересно, весело, скучно, понятно)… Технологическая карта урока математики в 1 классе. УМК «Перспективная начальная школа». Тема: «Сложение числа 2 с однозначными числами». Цель: создать условия для ознакомления со случаями сложения, в которых первое слагаемое – число 2; учить выполнять сложение вида 2+а; совершенствовать знание состава чисел первого десятка; развивать умение рассуждать, анализировать, развивать математическую речь. Ход урока: Учитель Ученики Организационный момент (2-3 мин.) 1) Приветствие гостям Учащиеся находят логическое 2) Минутка чистописания обоснование и продолжают ряд чисел 128 228 328 в тетради. Актуализация знаний.(6-7 мин.) 1)Устные вычисления (индивидуальные и 3 учащихся у доски находят фронтальные). неизвестные числа в примерах с Игра «Лучший лётчик» окошечками и поясняют, как они это Игра «Кто полетит в космос?» сделали. Остальные дети определяют Мотивация учебной ошибки на карте звёздного неба(ищут выражения с неверными ответами). деятельности.(1 мин.) _ Чтоб водить корабли, Учащиеся определяют мотив для чтобы в небо взлететь, Надо многое знать, надо много изучения науки математики. уметь. И при этом, и при этом, вы заметьте-ка, Помогает всем, ребята,…МАТЕМАТИКА! «Открытие» нового знания и определение темы урока. (5-7 мин.) -Какой девиз у нас звучит на уроке Учащиеся принимают участие в математики каждый день? (Ни дня решении задачи №1. без задачи!) Прочитайте задачу: « На уроке математики Маша решила 2 примера, а Миша на 4 примера больше. Сколько примеров решил Миша?» -О чём говорится в задаче? (О примерах.) Кто решал примеры? (Маша и Миша.) Сколько решила Маша? (2) А сколько решил Миша? (На 4 больше.) А что это значит? (Столько же и ещё 4). -Каким действием решим задачу? (Сложением) -Назовите решение. (2+4=6) -Назовите ответ. (6 примеров решил Миша.) -Закройте глаза. Что изменилось в задаче? (Число 4 заменили на число 6.) Сможете решить эту задачу самостоятельно? Назовите решение и ответ.(2+6=8 Ответ: 8 примеров решил Миша.) -Внимательно посмотрите на решения задач. Чем похожи решения? (Первое слагаемое 2) -Определите тему нашего сегодняшнего урока.(Будем учиться прибавлять к числу 2 однозначные числа.) Физкультминутка.(2 мин.) Первичное закрепление.(10 мин.) Работа по заданиям учебника (с.29) №1.-Рассмотрите рисунки к каждой сумме. Чем похожи суммы? (Первое слагаемое 2) -Чем отличаются? (Вторые слагаемые-разные.) -Выполните сложение с помощью палочек на рисунке. -Запишите пример, которого нет в этом номере. (2+0) А какой пример получится, если мы поменяем местами слагаемые в этом примере? (0+2) Какой вывод можно сделать? (Если к числу +0, то получится это же Учащиеся находят разницу в условии задачи и решают новую задачу самостоятельно. Дети высказывают предположения, определяют урока. свои тему 1 ученик проводит физкультминутку. Учащиеся принимают участие разборе заданий учебника. в Дети называют правило. Работают в парах. Самостоятельно взаимопроверкой. работают с Самостоятельно работают. Вспоминают тему, над которой работали на уроке. Уточняют, достигли ли цели урока. Учащиеся анализируют деятельность на уроке. свою число.) -№3. Прочитайте задание. Каким правилом нужно воспользоваться? (Правилом перестановки слагаемых) Как оно звучит? (От перестановки слагаемых сумма не меняется.) Взаимопроверка.(2 мин.) -Поменяйтесь тетрадями, проверьте у соседа работу. -Найдите значение разностей, используя примеры на сложение: 8-2 8-6 Тренировочные упражнения и задания на повторение.(8-10 мин.) Печатная тетрадь №2, стр. 41-43, №1-10. Итог урока.(1-2 мин.) -Над какой темой мы работали? Чем воспользовались при изучении темы? Рефлексия.(2-3 мин.) -Закончите предложения: На уроке я работал (быстро, медленно, с пользой, без пользы)… Мне было (интересно, весело, скучно, понятно)…
ADDING NUMBERS 2.
Goals:1. Introduce students to ways of adding the number 2.
2.Develop computational skills, the ability to use mathematics. terms and understand them.
3. Foster love and respect for nature.
4.Develop the analytical-synthetic sphere, logical thinking.
During the classes.
1 Emotional mood.
SLIDE 2
2. Motivational and goal-oriented.
1Riddle
Both boys and girls
They are waiting for him for the New Year.
Because he's a toy
He puts it under the tree for them. (Father Frost) SLIDE 3
Today Santa Claus came to visit us.
Guys, do you love Santa Claus?
When does he come to us?
Do you make wishes?
Santa Claus did not come alone. Who will you find out when you solve the riddle?
2. Riddle.
She is dressed in silver and pearls,
Magical granddaughter, magical grandfather. (Snow Maiden) SLIDE 4
3. Setting the topic and goals of the lesson
All the animals adore the Snow Maiden and rush to meet her.
Guys, how many foxes, squirrels, bunnies, and birds are there near the Snow Maiden?
What number do you think we will need in today's lesson?
Bunnies and squirrels galloped, foxes came running, birds flew in. What mathematical action can be designated?
What will we do with the number 2?
Formulate the topic of the lesson.
Today in the lesson we will show not only our knowledge, but also how we can work together, listen carefully to our classmates and the teacher, and how to behave correctly in class.
Don't talk in class
Like a talking parrot.
If you want to answer, don’t make noise,
Just raise your hand.
A desk is not a bed
And you can't lie on it.
You sit at your desk slimly
And behave with dignity.
Let's remember the composition of the number 2 and decorate the Christmas tree. SLIDE 5
SLIDE 6
Santa Claus was hurrying to us,
I equipped my sleigh.
I prepared gifts for everyone,
I took the Snow Maiden with me...
Only someone ruined everything
And the snow and blizzard began to rise.
Everything disappeared at the same moment,
Santa Claus is now alone.
Our Grandfather Frost is crying,
Where is my granddaughter?
Where are the gifts? After all, guys
They will expect them from me.
Santa Claus's sleigh was bewitched and taken to her domain by the Snow Queen. She wants to ruin the holiday. SLIDE 7
You and I must help Santa Claus find his granddaughter and bag of gifts. You are ready? Then go ahead! A lot of interesting things await us.
3.Operational activity.
1. Palace of the Snow Queen.
Here is the Palace where the Snow Queen lives.
What geometric shapes does the Palace consist of? SLIDE 8
Count how many triangles, squares, rectangles, circles.
Finger gymnastics
A minute of penmanship.
Enter the number 2 and the + sign
(circle and shade the palace)
How many blue snowflakes fell on the Palace?
- How many lilac snowflakes fell on the Palace?
- How many snowflakes fell on the Palace?
How can this be written down?
(put the expression 1+2=3 on the magnetic board)
2.Icy river. SLIDE 9
The birds will help us cross the river, on the slippery ice. Let's call them.
SLIDE 10
Fizmin
They waved their wings,
They shook their heads,
Feathers shaken off
And they flew off the branches.
How many birds are on the left of Santa Claus, how many are on the right?
How much in total?
How can this be written down?
(put the expression 2+2=4 on the magnetic board)
Write the equality in your notebook;
3. Bunnies.
Guess who Santa Claus met on the way? SLIDE 11
1Riddle
The forests hide many troubles,
There's a wolf, a bear and a fox!
Our animal lives in anxiety,
Trouble takes you away...
Come on, quickly guess
What is the animal's name... (bunny)
The bunny will help us get to the forest if we help him count his brothers.
SLIDE 12
How many big bunnies will there be?
How many little ones?
How much in total?
How can this be written down?
(put the expression 3+2=5 on the magnetic board)
Write the equality in your notebook;
So Grandfather Frost reached the forest. SLIDE 13
What did he see in the forest? SLIDE 14
How many blue, how many lilac snowflakes? (what is 1+2)
How many big and how many small bunnies will there be? (what's 2 2)
How many decorated Christmas trees, how many ordinary ones? (what is 3+2)
5. Christmas trees.
SLIDE 15
So the Christmas trees in the forest are lined up,
What geometric shapes do they consist of?
How many triangles are there in total?
Guys, what do you know about the Christmas tree?
Do you dress up a forest beauty at home for the New Year? Where did you get it from?
What will happen to the Christmas tree after the New Year?
What will happen if everyone chops down a Christmas tree in the forest on New Year's Day?
In order for a tree to grow as tall as you, it will take 10-15 years.
Count how many dark green Christmas trees?
How many light green Christmas trees?
How much in total?
How can this be written down?
(post the expression 4+2=6 on the magnetic board)
Write the equality in your notebook;
6. Round dance of snowflakes.
SLIDE 16
Snowflakes swirled in the forest so that nothing was visible. Your eyes need a rest. SLIDE 16
Gymnastics for the eyes.
Logic problem. SLIDE 17
What color are our snowflakes?
In order for the snowstorm to stop, they need to be placed in a certain order.
In the middle is not a blue or lilac snowflake;
The first is not a lilac snowflake;
Which snowflake stands last? SLIDE 18
7.Snowmen.
SLIDE 19
Snowmen were waiting for us behind the trees. They invite us to rest.
Fizmin
SLIDE 20
How many snowmen with scarves?
How many snowmen are there without scarves?
How much in total?
How can this be written down?
(put the expression 5+2=7 on the magnetic board)
Write the equality in your notebook;
Why do you need to tie a scarf in winter?
8.Candy.
SLIDE 21
Look, here's a bag of gifts! The Snow Queen probably dropped it on the way to the castle. So we are on the right track.
SLIDE 22
Which color of candy canes are more, which are the least?
How many green candies? What number are they?
How many red candies?
How much in total?
(compare by handle size and color)
How can this be written down?
(put the expression 6+2=8 on the magnetic board)
Write the equality in your notebook;
9.Palace.
So you and I found the Palace of the Snow Queen. Now you need to get there and save the Snow Maiden.
SLIDE 23
Let's open the locks.
You need to pick up keys for the locks. SLIDE 24
Try it yourself. (connect the key and the correct door on the pieces of paper)
Let's see if you picked the right keys. SLIDE 25
SLIDE 26
How many keys are there in total?
How many keys are different from the rest?
How can this be written down?
(put the expression 7+2=9 on the magnetic board)
Write the equality in your notebook;
10. Snow Maiden.
SLIDE 27
Here is our Snow Maiden!
Now you and I can decorate the Christmas tree. SLIDE 28
To do this you need to solve examples. SLIDE 29
How many yellow balls are there on the Christmas tree?
How many red balls are there on the Christmas tree?
How many balls with numbers are there on the Christmas tree?
How many balls are there on the Christmas tree without numbers?
How much in total?
How can this be written down?
(put the expression 8+2=10 on the magnetic board)
Write the equality in your notebook;
11. New Year.
Now you can celebrate the holiday! SLIDE 30
Santa Claus and Snow Maiden give you gifts to remember our lesson.
4. Reflective-evaluative stage.
What did you learn today?
Did you like the lesson?
What do you remember most?
How do you evaluate your work in class?
What's your mood? (choose a suitable face) SLIDE 31
SLIDE 32
CHRISTMAS STORY
