In mathematics, of course, it is important to be able to think and think logically, but practice is no less important. Half of the mistakes in math exams are made due to incorrect calculations of simple operations with numbers - addition, subtraction, multiplication, division. And it is important to develop these skills in primary school. In order not to miss anything, it is necessary to systematically work with the child using special exercise books. They allow you to practice mathematical skills and abilities and bring them to automaticity. There are a variety of simulators, you don’t have to download them all, just one or two you like is enough. The manuals can be used in working with primary schoolchildren, regardless of the program under which the training is conducted.
Mathematics. We solve examples with passing through tens.
A notebook for practicing addition and subtraction skills with passing through tens. Not just examples, but interesting games and tasks.
Task cards. Mathematics. Addition and subtraction. 2nd grade
Convenient cards for teachers of second graders. 2 options for addition and subtraction of the same type. Suitable for organization independent work in mathematics depending on progress in the program.
Mathematics. Addition and subtraction within 20. Grades 1-2. E.E. Kochurova
In various mathematics courses, the topic of addition and subtraction within 20 is studied either at the end of the 1st grade or at the beginning of the 2nd. In any case, the manual will help to consolidate the learned methods of manipulating numbers; in some tasks these methods are presented in the form of unique hints. During independent work with a notebook, the child is guided by the sample implementation and algorithmic instructions. The ability to use such tips in studying will allow the student not only to find and use the necessary information while completing a task, but also to carry out self-test.
The notebook begins with practicing addition and subtraction skills within 10; this part is also suitable for first-graders.
Mathematics exercise book for 2nd grade
The notebook contains not only examples of addition and subtraction, but also conversion of units into each other, and comparison of calculation results (more or less).
3000 examples in mathematics (counting within 100 part 1)
Timed counting simulator. Time it to solve one column of examples and write it down in the box below. Pay attention to the columns that the child took more than 5 minutes to solve, which means he has difficulties with this type of example. Examples are given for addition and subtraction within ten and with transition through ten, addition and subtraction of tens, manipulation within hundreds.
Counting from 0 to 100
This copybook gives many examples of addition and subtraction to strengthen mental counting skills within 100.
We think it's correct. Mathematics workbook. G.V.Belykh
The notebook is also made in the form of a simulator, full of examples and equations. It starts with counting within ten, then within a hundred (addition, subtraction, multiplication and division), and ends with comparing equations (examples with greater than, less than, equal signs).
The manuals will also be useful for teachers primary classes in their work, and for parents to study at home with their children, in particular in summer holidays. Tasks of different difficulty levels will allow for a differentiated approach to learning.
In any positional number system, the operations of adding and subtracting two numbers A B=C are carried out bit by bit, starting with the least significant bits.
When adding the overflow from the low-order bit is transferred to the high-order bit, i.e. code for the amount of each i -th category with i is obtained as a result of addition a i + b i + 1 , Where 1 corresponds to carry over from minor (i -1) -discharge in i-th, if in the least significant digit the sum code is greater than or equal to the base of the number system.
When subtracting the required loan is made from the senior rank, i.e. difference code of each i -th category with i results from subtraction a i - b i – 1 , Where 1 corresponds to the loan, if there was one, in the lower digits of a value equal to the base of the number system.
2.1. Rules for adding binary numbers.
In each digit, the addition of two digits of the terms and the carry unit from the adjacent low-order digit, if any, is performed.
Bitwise sum
0 + 0 = 0
0 + 1 = 1
1 + 0 = 1
1 + 1 = 0 – transfer is carried out 1 to senior rank
For example, addition 5 10 + 3 10 = 8 10
Summation binary numbers in computers it is carried out using devices called binary adders.
2.2. Rules for subtracting binary numbers.
In each digit, the subtracted digit is subtracted from the digit of the number; when subtracting a unit from zero, a unit is borrowed from the adjacent highest digit, which is equal to 2 units of this digit.
Bit difference is formed according to the following rules:
0 - 0 = 0
1 - 0 = 1
1 - 1 = 0
0 - 1 = 1 – after the loan 1 from the senior category
For example, subtracting 6 10 – 3 10 = 3 10
–0011 2 = 3 10
As a rule, subtraction of binary numbers in computers is carried out using binary adders: when representing the subtrahend in two's complement or inverse code, the subtraction operation can be replaced by the addition operation.
2.3. Rules for multiplying binary numbers.
Multiplication of binary numbers is carried out by forming intermediate products and their subsequent summation.
Bitwise products are formed according to the following rules:
0 x 0 = 0
0 x 1 = 0
1 x 0 = 0
1 x 1 = 1
For example, multiplying 5 10 x 3 10 = 15 10
11
2.4. Rules for dividing binary numbers.
Binary division performed according to the rules of multiplication and subtraction.
For example, division 6 10: 3 10 = 2 10
3. Shift operation along the bit grid
In computers, in addition to the operation of algebraic summation of binary numbers, which includes the operations of addition and subtraction, number shift operation along the bit grid to the left and right, which actually performs the multiplication and division of binary numbers.
In case of left shift a binary number is multiplied by 2 j, and when shifting to the right – division by 2 j, where j is the number of digits by which the binary number is shifted.
For example, shift by 2 bits
1) 000011 2 = 3 10 left
001100 2 = 12 10
i.e. 3 x 4(2 2) = 12 10
2) 001000 2 = 8 10 right
i.e. 8: 4(2 2) = 2 10
Often used in computers cyclic shift , during which the bit grid allocated for operand (the number on which the action is performed) appears to be closed in a ring. Then when shifting left the contents of the high-order bit go into the low-order bit of the operand, and when shifting to the right the contents of the low-order bit go into the high-order bit of the operand.
So, on your way young mathematicians, be careful. We are going on a trip by ship. In order for our boat to sail, who needs to be recruited. We count in rows: from 1 to 10; from 10 to 1; from 10 to 20; all together: tens up to 100.
Hooray! We managed to launch the ship. Forward!!!
And the first island we landed on was Island of Examples.
I will show you cards with examples, and you must show me the answer using the numbers that are on your tables. The game is called "Silence". You are ready?
3+2 5+2 6+1 4+2 8+1 7+1
9 -1 2-1 3-3 5-2 4-0 5- 2
Pay attention to the example: 3+2 =5
What are these numbers called when added?
The wind blows across the sea
And the boat speeds up.
He runs in the waves
With full sails.
A sea animal swims towards us and says:
Dolphin is a marine mammal belonging to the order Cetacea. They can reach speeds of up to 50 km/h and jump out of the water to a height of up to 5 m. Dolphins live in schools. They communicate with each other using whistling sounds. While hunting, they emit a variety of high-frequency sounds that stun the fish, making it easy for them to catch them. Often, sailors see how dolphins save drowning swimmers, pushing them to the surface so that they do not choke.
We're getting closer to island of "inequality"
What will we do on this island? What task should I do?
And now LET'S REMEMBER THE RULES OF WRITING.
We opened our notebooks, found a dot in the middle, and wrote down today's date and month.
Tell me guys, what should we put between these numbers?
Exchange notebooks and check each other. Evaluate your friend's work.
Well done! And we completed this task.
Tell me, guys, which expression is superfluous here? Why?
Physical education minute.
The current carried our ship to Change Island, where we will have a little rest.
Relax and hit the road again!
And now we are approaching the island of “Tasks”
-What does any task consist of?
-Our path was blocked by 4 high rocks and 2 low ones. How many rocks are there on our way?
Name the condition of the problem, question
Can you answer the question posed?
What action solves the problem?
Why addition?
How to solve the problem?
Write a summary of the problem using triangles. High cliffs - Blue colour, low – red. And solve it.
Well done!
And a swordfish appeared overboard. To get to the island "Savvy" you need to complete the task.
Read the example different ways
Swordfish- one of the largest and fastest fish. The upper jaw is elongated into the xiphoid process. Body length is up to 4-4.5 m, weighs up to 500 kilograms. It has a large semilunar fin on its tail, and its body is naked, without scales. When swimming, it can reach speeds of up to 130 km/h.
The island of “Savvy” is ahead
I see an island in the blue sea.
We need to get off now...
Here is the jungle before us
The forest is dense: vines, palm trees.
There are monkeys ahead
Can we approach them...
The monkeys are in trouble these days.
They were given a lesson at school,
But ingenuity is not enough,
And the problems are difficult. Let's help the monkeys.
There were 8 apples on the apple tree and 2 apples on the willow tree. How many apples were there in total?
Five lights were on. Two light bulbs have burned out. How many light bulbs are left?(five)
Figur Island
And interesting geometric creatures live here. Your task:
Draw a 3 cm segment.
Draw an open broken line consisting of 4 links.
So we have reached the island of “Knowledge”. And your knowledge and skills helped us get there
- Our journey has come to an end, it is time for us to return home. Thanks to the friendly and well-coordinated work of our team, we are back on our home soil.
Is quite important even in Everyday life. Subtraction can often come in handy when counting change at the store. For example, you have one thousand (1000) rubles with you, and your purchases amount to 870. Before you have paid, you will ask: “How much change will I have left?” So, 1000-870 will be 130. And there are many different such calculations, and without mastering this topic, it will be difficult in real life. Subtraction is an arithmetic operation in which the second number is subtracted from the first number, and the result will be the third.
The addition formula is expressed as follows: a - b = c
a– Vasya had apples initially.
b– the number of apples given to Petya.
c– Vasya has apples after the transfer.
Let's put it into the formula:
Subtracting numbers
Subtraction of numbers is easy for any first grader to learn. For example, you need to subtract 5 from 6. 6-5=1, 6 is greater than the number 5 by one, which means the answer will be one. To check, you can add 1+5=6. If you are not familiar with addition, you can read ours.
Big number is divided into parts, take the number 1234, and in it: 4-units, 3-tens, 2-hundreds, 1-thousands. If you subtract the units, then everything is easy and simple. But let's take an example: 14-7. In the number 14: 1 is tens, and 4 is ones. 1 ten – 10 units. Then we get 10+4-7, let’s do this: 10-7+4, 10 – 7 =3, and 3+4=7. The answer was found correctly!
Consider example 23 -16. The first number is 2 tens and 3 ones, and the second is 1 ten and 6 ones. Let's imagine the number 23 as 10+10+3, and 16 as 10+6, then imagine 23-16 as 10+10+3-10-6. Then 10-10=0, that leaves 10+3-6, 10-6=4, then 4+3=7. The answer has been found!
The same is done with hundreds and thousands.
Column subtraction
Answer: 3411.
Subtracting Fractions
Let's imagine a watermelon. A watermelon is one whole, and if we cut it in half, we get something less than one, right? Half a unit. How to write this down?
½, so we designate half of one whole watermelon, and if we divide the watermelon into 4 equal parts, then each of them will be designated ¼. And so on…
subtracting fractions, how is it?
It's simple. Subtract ¼ from 2/4. When subtracting, it is important that the denominator (4) of one fraction coincides with the denominator of the second. (1) and (2) are called numerators.
So, let's subtract. We made sure that the denominators were the same. Then we subtract the numerators (2-1)/4, so we get 1/4.
Subtracting limits
Subtracting limits is not difficult. A simple formula is enough here, which says that if the limit of the difference of functions tends to the number a, then this is equivalent to the difference of these functions, the limit of each of which tends to the number a.
Subtracting Mixed Numbers
A mixed number is a whole number with a fractional part. That is, if the numerator is less than the denominator, then the fraction is less than one, and if the numerator is greater than the denominator, then the fraction is greater than one. A mixed number is a fraction that is greater than one and has a highlighted whole part, let's illustrate with an example:
To subtract mixed numbers, you need:
Convert fractions to common denominator.
Add the whole part to the numerator
Perform calculation
Subtraction lesson
Subtraction is an arithmetic operation in which the difference between two numbers is sought and the answer is the third. The addition formula is expressed as follows: a - b = c.
You can find examples and tasks below.
At subtracting fractions it should be remembered that:
Given the fraction 7/4, we find that 7 is greater than 4, which means 7/4 is greater than 1. How to select the whole part? (4+3)/4, then we get the sum of fractions 4/4 + 3/4, 4:4 + 3/4=1 + 3/4. Result: one whole, three quarters.
Subtraction 1st grade
First grade is the beginning of the journey, the beginning of teaching and learning the basics, including subtraction. Training should be carried out in game form. Always in the first class, calculations begin with simple examples on apples, sweets, pears. This method is used not in vain, but because children are much more interested when they are played with. And this is not the only reason. Children have seen apples, candies and the like very often in their lives and have dealt with transfer and quantity, so teaching the addition of such things will not be difficult.
You can come up with a whole bunch of subtraction problems for first graders, for example:
Task 1. In the morning, while walking through the forest, the hedgehog found 4 mushrooms, and in the evening, when he came home, the hedgehog ate 2 mushrooms for dinner. How many mushrooms are left?
Task 2. Masha went to the store to buy bread. Mom gave Masha 10 rubles, and bread costs 7 rubles. How much money should Masha bring home?
Task 3. In the store in the morning there were 7 kilograms of cheese on the counter. Before lunch, visitors bought 5 kilograms. How many kilograms are left?
Task 4. Roma took the candy his dad gave him into the yard. Roma had 9 candies, and he gave his friend Nikita 4. How many candies does Roma have left?
First graders mostly solve problems in which the answer is a number from 1 to 10.
Subtraction 2nd grade
The second class is already higher than the first, and, accordingly, the examples for the solution too. So let's get started:
Numerical tasks:
Single digit numbers:
- 10 - 5 =
- 7 - 2 =
- 8 - 6 =
- 9 - 1 =
- 9 - 3 - 4 =
- 8 - 2 - 3 =
- 9 - 9 - 0 =
- 4 - 1 - 3 =
Double figures:
- 10 - 10 =
- 17 - 12 =
- 19 - 7 =
- 15 - 8 =
- 13 - 7 =
- 64 - 37 =
- 55 - 53 =
- 43 - 12 =
- 34 - 25 =
- 51 - 17 - 18 =
- 47 - 12 - 19 =
- 31 - 19 - 2 =
- 99 - 55 - 33 =
Word problems
Subtraction grade 3-4
The essence of subtraction in grades 3-4 is columnar subtraction of large numbers.
Let's look at the example 4312-901. First, let's write the numbers one below the other, so that out of the number 901, one is under 2, 0 is under 1, 9 is under 3.
Then we subtract from right to left, that is, from the number 2 the number 1. We get one:
Subtracting nine from three, you need to borrow 1 ten. That is, subtract 1 ten from 4. 10+3-9=4.
And since 4 took 1, then 4-1=3
Answer: 3411.
Subtraction 5th grade
Fifth grade is the time to work on complex fractions with different denominators. Let's repeat the rules: 1. Numerators are subtracted, not denominators.
So, let's subtract. We made sure that the denominators were the same. Then we subtract the numerators (2-1)/4, so we get 1/4. When adding fractions, only the numerators are subtracted!
2. To perform subtraction, make sure the denominators are equal.
If you come across a difference between fractions, for example, 1/2 and 1/3, then you will have to multiply not one fraction, but both, in order to bring it to a common denominator. The easiest way to do this is to multiply the first fraction by the denominator of the second, and the second fraction by the denominator of the first, we get: 3/6 and 2/6. Add (3-2)/6 and get 1/6.
3. Reducing a fraction is done by dividing the numerator and denominator by the same number.
The fraction 2/4 can be converted to the form ½. Why? What is a fraction? ½ = 1:2, and if you divide 2 by 4, then this is the same as dividing 1 by 2. Therefore, the fraction 2/4 = 1/2.
4. If the fraction is greater than one, then the whole part can be selected.
Given the fraction 7/4, we find that 7 is greater than 4, which means 7/4 is greater than 1. How to select the whole part? (4+3)/4, then we get the sum of fractions 4/4 + 3/4, 4:4 + 3/4=1 + 3/4. Result: one whole, three quarters.
Subtraction presentation
The link to the presentation is below. The presentation examines the basic questions of sixth grade subtraction: Download presentation
Presentation of addition and subtraction
Examples for addition and subtraction
Games for developing mental arithmetic
Special educational games developed with the participation of Russian scientists from Skolkovo will help improve mental arithmetic skills in an interesting game form.
Game "Quick Count"
The game "quick count" will help you improve your thinking. The essence of the game is that in the picture presented to you, you will need to choose the answer “yes” or “no” to the question “are there 5 identical fruits?” Follow your goal, and this game will help you with this.
Game "Mathematical matrices"
"Mathematical Matrices" is great brain exercise for kids, which will help you develop his mental work, mental calculation, quick search for the necessary components, attentiveness. The essence of the game is that the player has to find a pair from the proposed 16 numbers that will add up to a given number, for example in the picture below the given number is “29”, and the desired pair is “5” and “24”.
Game "Number Span"
The number span game will challenge your memory while practicing this exercise.
The essence of the game is to remember the number, which takes about three seconds to remember. Then you need to play it back. As you progress through the stages of the game, the number of numbers increases, starting with two and further.
Game "Mathematical Comparisons"
A great game with which you can relax your body and tense your brain. The screenshot shows an example of this game, in which there will be a question related to the picture, and you will need to answer. Time is limited. How much time will you have to answer?
Game "Guess the operation"
The game “Guess the Operation” develops thinking and memory. The main point game, you need to choose a mathematical sign for the equality to be true. Examples are given on the screen, look carefully and put the required “+” or “-” sign so that the equality is true. The “+” and “-” signs are located at the bottom of the picture, select the desired sign and click on the desired button. If you answered correctly, you score points and continue playing.
Game "Simplification"
The game “Simplification” develops thinking and memory. The main essence of the game is to quickly perform a mathematical operation. A student is drawn on the screen at the blackboard, and a mathematical operation is given; the student needs to calculate this example and write the answer. Below are three answers, count and click the number you need using the mouse. If you answered correctly, you score points and continue playing.
Visual Geometry Game
The game "Visual Geometry" develops thinking and memory. The main essence of the game is to quickly count the number of shaded objects and select it from the list of answers. In this game, blue squares are shown on the screen for a few seconds, you need to quickly count them, then they close. Below the table there are four numbers written, you need to select one correct number and click on it with the mouse. If you answered correctly, you score points and continue playing.
Game "Piggy Bank"
The Piggy Bank game develops thinking and memory. The main essence of the game is to choose which piggy bank has more money. In this game there are four piggy banks, you need to count which piggy bank has the most money and show this piggy bank with the mouse. If you answered correctly, then you score points and continue playing.
Development of phenomenal mental arithmetic
We have looked at only the tip of the iceberg, to understand mathematics better - sign up for our course: Accelerating mental arithmetic - NOT mental arithmetic.
From the course you will not only learn dozens of techniques for simplified and quick multiplication, addition, multiplication, division, and calculating percentages, but you will also practice them in special tasks and educational games! Mental arithmetic also requires a lot of attention and concentration, which are actively trained when solving interesting problems.
Speed reading in 30 days
Increase your reading speed by 2-3 times in 30 days. From 150-200 to 300-600 words per minute or from 400 to 800-1200 words per minute. The course uses traditional exercises for the development of speed reading, techniques that speed up brain function, methods for progressively increasing reading speed, the psychology of speed reading and questions from course participants. Suitable for children and adults reading up to 5000 words per minute.
Development of memory and attention in a child 5-10 years old
The purpose of the course: to develop the child’s memory and attention so that it is easier for him to study at school, so that he can remember better.
After completing the course, the child will be able to:
- 2-5 times better to remember texts, faces, numbers, words
Money and the Millionaire Mindset
Why are there problems with money? In this course we will answer this question in detail, look deep into the problem, and consider our relationship with money from psychological, economic and emotional points of view. From the course you will learn what you need to do to solve all your financial difficulties, start saving money and investing it in the future.
Knowledge of the psychology of money and how to work with it makes a person a millionaire. 80% of people take out more loans as their income increases, becoming even poorer. On the other hand, self-made millionaires will earn millions again in 3-5 years if they start from scratch. This course teaches you how to properly distribute income and reduce expenses, motivates you to study and achieve goals, teaches you how to invest money and recognize a scam.
“Addition and subtraction of the form +2, -2”
Lesson type: a lesson in the formation of initial subject skills and UUD, mastering new subject skills - “Adding and subtracting the number 2”.
The purpose of the lesson: Teach students how to add and subtract the number 2.
Lesson objectives:
Educational (subject):
Develop the ability to add and subtract the number 2.
Build computing skills.
Developmental (meta-subject):
Regulatory:
Create the opportunity to plan your actions together with the teacher in accordance with the task and the conditions for its implementation.
Develop skill junior school student monitor your activities as the task progresses.
Cognitive:
Develop the ability to analyze, compare, contrast and generalize.
Help to highlight and formulate a cognitive goal.
Encourage children to express their opinions and evaluate their activities in the classroom.
Communicative:
Create conditions for educational collaboration with the teacher and peers.
To facilitate the interaction of the child with his desk neighbor.
Educational (personal):
Work on self-esteem and adequate understanding of the reasons for success/failure in educational activities.
Promote independence in different types children's activities.
Work on understanding responsibility for a common cause.
During the classes
1 .Organizing time
(Checking the readiness of the workplace and getting students ready to work)
Check it out, buddy!
Are you ready to start the lesson?
Is everything in place?
Is everything all right?
Pens, books and notebooks?
Is everyone sitting correctly?
Is everyone watching carefully?
Teacher: I wish you interesting lesson, activity and vigor. And then you will succeed.
Ball game. (Whoever hits the ball is responsible).
Count from 1 to 10 in order.
Count back from 10 to 1.
What number comes after the number 5?
What is the next number after the number?
Name the neighbors of number 3.
What number is greater than 6 by 1?
What number is less than 8 by 2?
From what number must you subtract 2 to get 8?
Find the sum of numbers 1 and 2.
Guys, what are we doing now? (We repeat the material studied).
Teacher: Today we are researchers: this means that a new discovery in the science of mathematics awaits us. Who are researchers?
Any research requires curiosity, attention and consistency in your actions so that the end result pleases you. Ready to get started? Good luck to us!
Before you, researchers, is our plan of action. (An activity plan is proposed).
2 .Updating knowledge
Individual work: students solve examples at the board
4-2= 1+2= 6-2= 5+2=
Teacher: Guys, Have we resolved such issues? (No).
- What two groups can we divide these expressions into?
"Development of computing skills"
3 .Self-determination for activity
a) checking individual work at the board.
Teacher: Pay attention, young researchers, to these expressions. What do they have in common?
If you have difficulty answering, suggest a question: What number did we add and subtract? (Added and subtracted the number 2).
This is the subject of our research.
Formulate the research topic: Add and subtract 2 (adding and subtracting the number 2).
Set goals for yourself: Learn -----------
b) Working with the chain Observation of the method of action.
5 → +1 →+1 → 8 → -1 →-1 →
For example: you added 1 to 5, you got 6, you added 1 to 6, you got 7.
Subtract 1 from 8 to get 7, subtract 1 from 7 to get 6.
Teacher: How much have you added? How did we do it?
How much did you subtract? How did we act?
Draw a conclusion based on our observation (you can add and subtract the number 2 in parts).
4.Work on the topic of the lesson.
Practical work with handouts paired with illustrations on the board.
Teacher: Any research must be confirmed by practice.
Now you will work in pairs, prove that the method we have chosen is correct.
Here is the numerical expression 3 + 2.
By using geometric shapes show how you will add and show in numbers the course of your reasoning.
Teacher: How can we write an example? 3+2 = 5
3+1 +1 = 5
- Draw a conclusion : how to add the number 2?
The work with the numerical expression 5 - 2 is constructed in a similar way.
How can we write an example? Children's answers: 5-2=3
5- 1-1= 3
- Draw a conclusion : how to subtract the number 2?
5. Physical education minute. Children do exercises.
Green fir trees sway in the wind,
They sway in the wind and bend low.
Make as many bends as there are green Christmas trees.
Squat as many times as we have butterflies.
Make as many jumps as there are white circles.
6. Consolidation of the studied material
Teacher: Researchers often turn to different sources of information. What can we use in the lesson? (textbook).
Work according to the textbook. Open page 100-101.
Work "Chain". Task 3, p.100.
Children orally solve examples in a chain.
7.Reflection
Teacher: Like real researchers, let's test ourselves.
In workbooks p.86, task 1.
Solve the examples yourself.
Checking with number fans.
8. Summing up the lesson.
Teacher: So, our research took place. (Referring to the topic and objectives of the lesson.).
1.Who are researchers?
2.What did we explore today?
3.What did we do in class?
4.What did you learn?
Teacher: Look at our action plan, have we completed all the steps?
(Some results may be analyzed.)
Guys, let's now evaluate our results. If everything was clear to you in class today and you were able to complete the tasks easily, raise the green circle; if you didn’t manage to do everything in the lesson, then raise the blue circle; and if you still have questions, raise the red circle.
Teacher: The lesson is over. Thanks for the work!