One of the most difficult topics in elementary school is solving equations.
It is complicated by two facts:
First, children don't understand the meaning of the equation. Why was the number replaced by a letter and what is it all about?
Secondly, the explanation that is offered to children in the school curriculum is incomprehensible in most cases even to an adult:
In order to find the unknown term, you need to subtract the known term from the sum.
To find the unknown divisor, you need to divide the dividend by the quotient.
In order to find the unknown diminished, it is necessary to add the difference to the subtracted.
And so, having come home, the child almost cries.
Parents come to the rescue. And having looked at the textbook, they decide to teach the child to solve “easier”.
You just need to throw the numbers on one side, changing the sign to the opposite, you know?
Look, x-3 \u003d 7
We transfer minus three with plus to seven, count and get x \u003d 10
At this point, children usually experience a program failure.
Sign? Change? Transfer? What?
- Mother, father! You don't understand anything! They explained to us in a different way at school !!!
- Then decide how to explain!
And at school, meanwhile, the training of the topic continues.
1. First you need to determine which component of the action you need to find
5 + x \u003d 17 - you need to find the unknown term.
x-3 \u003d 7 - you need to find the unknown diminished.
10's \u003d 4 - you need to find the unknown subtracted.
2. Now you need to remember the rule mentioned above
In order to find the unknown term, you need ...
Do you think it is difficult for a little student to remember all this?
And you also need to add here the fact that with each class the equations get more and more complex.
As a result, it turns out that equations for children are one of the most difficult topics in math in elementary school.
And even if the child is already in fourth grade, but he has difficulty solving equations, most likely he has a problem understanding the essence of the equation. And you just have to go back to the basics.
This can be done in 2 simple steps:
Step one - Teach children to understand equations.
We need a simple mug.
Write an example 3 + 5 \u003d 8
And at the bottom there are circles "x". And, turning the mug over, close the number "5"
What's under the mug?
We are sure the child will guess right away!
Now close the number "5". What's under the mug?
So you can write examples for different actions and play. The child understands that x \u003d is not just an incomprehensible sign, but a "hidden number"
More about the technique - in the video
Step Two - Teach you to determine if the x in the equation is whole or part? The biggest or the "smallest"?
For this, the Yabloko technique is suitable for us.
Ask your child where is the largest in this equation?
The child will answer "17".
Excellent! This will be our apple!
The largest number is always a whole apple. Let's circle.
And the whole always consists of parts. Let's emphasize the parts.
5 and x are parts of an apple.
And since x is a part. Is it more or less? x large - or small? How to find it?
It is important to note that in this case the child thinks and understands why, in order to find x in this example, you need to subtract 5 from 17.
After the child understands that the key to solving the equations correctly is to determine whether x is a whole or a part, he will easily solve equations.
Because remembering the rule when you understand it is much easier than vice versa: memorize and learn to apply.
These techniques "Circle" and "Apple" allow you to teach a child to understand what he is doing and why.
When a child understands a subject, he starts to get it right.
When a child succeeds, he likes it.
When you like it, there is interest, desire and motivation.
When motivation appears, the child learns himself.
Teach your child to understand the program and then the learning process will take much less time and effort from you.
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The queen of sciences, mathematics is the foundation on which the whole surrounding world rests. It is not easy to master its basics, but it is impossible to do without them. Mothers of young children understand this perfectly, trying to instill in them a love of mathematics from an early age.
However, not every kid can learn numbers, learn to solve examples and count in his head - at least not right away. Therefore, the parents of future geniuses are trying to help them master the difficult science of counting as much as they can.
When to start?
The answer to this sensitive and burning question is given by certified psychologists and teachers.
2-3 years
At 2-3 years old, babies begin to feel not only strength, but also a desire to receive new information. Like a sponge, they try to absorb everything that happens around them, and are drawn towards the unknown. However, during this period, babies can only learn to count from 1 to 10 - and no more.
3-4 years
At the age of 3, the child counts quite deliberately, with pleasure taking away sweets from relatives and using simple counting techniques to divide them.
4-5 years old
Three whales or the basics of teaching mathematics
Very often, parents blindly believe that their child's preparation for school ends with mastering numeracy, but this is their big mistake.
Geometry to help
The kid must master the ability to recognize the shapes and sizes of objects, learn to figure out which object is shorter and which is longer, and determine where it is: to the right or to the left. A child should be able to do this (preferably) by the age of 3.
To do this, you need to repeat with him the names of figures cut out of cardboard every day, explain the direction in which the child is walking (for example, for a walk), and show which of the houses is higher and which is lower.
To gnaw the granite of science was not a burden, my mother should conduct lessons in a playful way: easy and interesting. Mathematical games such as dominoes or bingo and pictures with numbers come to the aid of parents.
Visibility and simplicity are the keys to success
You need to start with the simplest lessons: add one to one by illustrative example. Any kid will understand that if you add one more to three pears, there will be not three, but four pears. In this case, the complex terms "plus" and "minus" should be introduced a little later - as soon as the child understands the essence of the process.
Important account rules
Dispensing information feed
Teach 3 lessons a day, allotting 10 minutes for each lesson. So the kid will not get tired of the abundance of information and will not lose interest in learning.
Lack of daily repetition
The mother of learning is repetition, but if we talk about it in the context of mathematics, then repeating the material covered daily is not worth it. Return to what you have learned only when you need it to solve more difficult problems.
Feasible complexity
Do not yell or scold your baby if the learning process is difficult. Maybe some example is really difficult for him? Think of yourself as a child and just find an easier task for your child.
Consolidation of material in everyday life
Not all toddlers find math part of their lives - even with their daily activities. To consolidate the achieved results, consider with your child everything that "comes to hand": cars, leaves on the asphalt, apples in a plate, cats on the roof, trams on the street.
Compliance with the steps
Psychologists say that while learning the material, the child goes through three stages at once:
- addiction (for example, to terms);
- understanding the essence of what is being studied;
- memorization of information.
Don't rush it in the process! Talk to your baby, compare objects, mention numbers in conversation, help memorize numbers.
For example, when setting the dining table, talk about how many plates you put on it. You will see that in a couple of weeks, the child, with the air of a professional accountant, will talk about how many appliances are on the table.
Teaching your kid to count to 10
When the first "five" is mastered, it will be possible to increase the counting range to 10.
Ways to speed up the learning process
To master counting much faster and more successfully, you can use some tips and game ways of learning.
Including, you can diversify the process:
- using your fingers;
- including developmental programs;
- using educational toys and abacus;
- telling rhymes to the child;
- counting everything with the baby and every day.
Introducing the child to household chores
Ask the child to wash two or three cups and have him count them. You can also invite your child to memorize 5 items in the grocery list that you create before each trip to the store.
Enabling cards
The flashcard activities are very useful while learning numbers. Show them to the baby first sequentially, then alternating, so that the baby learns to count the objects in the pictures, and not just automatically memorize them.
Good games are a great tradition
On the way to mastering counting, the game form of classes will help you: the games themselves, directly, funny poems and counting rhymes.
"Count with me!"
“I count to five,
I can't until ten
One, two, three, four, five -
I'm going to look!
Ready or not, here I come!"
Shop game
One of the favorite games of children is the store, which will help you quickly and correctly teach your baby to count. Lay out “goods” on the table: books, toys, fruits and shower gels, and set a certain price for each of them.
Let your child be a cashier in this store, and you will come to visit him as a customer. Businesslikely ask how much and what it costs, regardless of the price tags (for the convenience of the child, it would be better to attach them to each "lot").
"Guess!"
Take plastic numbers on magnets and, showing them to your child, ask them to name their numerical values. Reward each correct answer with either candy or watching a cartoon.
We sculpt from plasticine
You can include plasticine in your work: when making figures of animals, ask the child to mold two ears of a hare or make 4 paws for a bear.
We teach how to write numbers
As soon as the 10-digit milestone is overcome, start teaching your baby how to write numbers, devoting each of them to a separate day.
You can do it like this:
- depict a figure on a sheet and fix it in a conspicuous place;
- mold it from plasticine;
- include a program that tells about the number;
- to give illustrative examples: "On the 1st, a trip to the circus will take place!";
- use the dial on the watch: “What time is it? One p.m!".
Learning to count to 20
A prerequisite for learning should be the fact that the baby knows all the numbers from 1 to 9, as well as the number 10.
The concept of tens and units
Explain to your child that any number after 10 is made up of two numbers, the first being tens and the second being ones. To make him understand this, take two boxes and put ten cubes in one of them, and ten balls in the other.
A sequence of numbers in numbers
The kid should remember that two-digit numbers have a certain sequence and go one after the other - 11, then 12, then 13. As soon as the kid learns this, ask him to put 16 cubes in an empty box and let him recount them aloud when adding them.
Learn to count to 100
At 4-5 years old, a child counting from 1 to 20, gets acquainted with a new frontier: numbers up to 100. The process is long, laborious, requiring patience from both you and the baby.
Expanding the number of tens
Explain to your child that there are as many as 9 similar dozens (in a number of up to a hundred) and name these numbers. Warn that there are ones in between and the numbers do not go one after the other. Show him examples within 20: books on the shelf, trees in the garden, cars in the parking lot.
New day - new numbers!
Learn 10 new numbers with your baby every day. Let him tell you exactly what he remembered. When the kid learns at least three dozen, start a game: skip one number in a row up to one hundred and let him find the necessary "element" on his own.
Teaching your child to count examples
Addition and subtraction are basic skills that will come in handy for your baby both at school and before starting school.
"Beloved" guide
A visual aid can help the study: apples, cubes or candy. In general, everything that is interesting to look at, and eat, and count.
Start simple
Start your debriefing "flights" with something simple: for example, with the number three. How can you get it? Putting 1 and 2 candies together.
Follow the order
Continue adding until the baby understands the principle of addition, and only then smoothly move on to subtraction.
Speak out loud
Say everything that you do: "I will take two pears from you, now there will be one left." Any kid will remember well how exactly he was deprived of one fruit.
Use tutorials
Take for help notebooks, books and other manuals containing examples of addition and subtraction, since there are a great many of them on sale today.
No boredom!
If you come up with examples, don't make them boring. Let the proposed problem be funny so that the kid is interested in its solution.
Learn the composition of the number
The child must remember the composition of the number. Explain to the kid that the number 10 can consist of 6 and 4, 5 and 5, 7 and 3, and so on.
How to teach a kid to count in the mind?
Mental counting has a beneficial effect on your baby's mental abilities. But, thinking about how to teach a child to count in his head, you need to understand that you should not start such activities earlier than 4 years, otherwise you will not succeed.
The bigger, the better
Remember: the more the baby counts in his head, the better for him.
More less
Help your little one learn the concept of "more and less." When reading books, ask your child which color is more present and which is less.
What is equal?
The kid should know what is "equally". Ask him a question: "Here are 3 cucumbers, and here are 3. Where are the more cucumbers?"
From changing the places of the terms
Explain to the kid that when the places of the terms are changed, the amount does not change. This is the foundation of mathematics that only the lazy cannot remember.
Educational games
Tables with numbers or learning cubes can help you. Use them to memorize the count.
Counting everything in a row
Summing up
How to teach a child to count quickly? Quite difficult, especially for him to do it easily and without thinking. Only everyday practice and personal experience, only exciting activities and your perseverance will help your child to master such a difficult science as mathematics.
And if you doubt your abilities and do not feel “harsh” pedagogical inclinations, just ask the kindergarten staff or grandmothers for help. They will help you teach your child to count mentally and out loud, so that in the future a real genius will grow out of him!
Parents often ask how to teach a child to count up to 20. Sometimes a small student successfully calculates up to 10, but does not fully understand how to add / subtract large values.
The material contains examples of exercises, an analysis of the main mistakes that parents often make during classes.
general information
Calculations are often more difficult for young learners than reading. For a child to fall in love with mathematics, it is important for parents to know the basic rules and teaching methods. "But what about the school, teachers?" - many will ask.
Of course, the main burden falls on teachers, but when doing homework, parents must correctly explain certain rules and find mistakes. When adults understand how to instill a love of mathematics, classes are much easier.
You still have to pay attention to learning counting. This is parental work, there is no escape from joint activities with the child. Even when visiting a tutor (children's development center), homework must be completed. If parents know the basic techniques, modern teaching methods, it will be much easier for an adult and a child.
How to teach to count within 20
Teachers, parents give recommendations, offer proven algorithms, thanks to which a small student will understand what dozens are, how to learn more complex concepts. Always check whether the "young mathematician" has memorized the material he has passed, do not skip, even if the study takes not 2-3 days, but a week.
Where to begin
Algorithm:
- learn the names of the numbers in the second ten;
- you need two sets of cubes. The items must be the same;
- the child must put 10 things in a row, always from left to right;
- say that 10 is ten, it is called “dtsat”;
- put another one on the first row of cubes. It turned out - 11 or one plus "twelve" \u003d eleven;
- put two, then three, four cubes on the dc's. It turned out: three - for - twenty, four - for - twenty and so on;
- let the little student put the cubes on his own, add a familiar figure to ten;
- the child clearly remembered the scheme for constructing numbers from 11 to 19? Move on to the next step.
How a hundred is formed
Algorithm:
- most children who have mastered the education of numbers up to 20 quickly understand how to make two, three, four tens to a hundred;
- the beginning of the exercise is the same: lay out 10 cubes, say that it is a ten or "twelve";
- put the same row of ten cubes next to it, you get two rows. Name: two plus “dtsat” \u003d twenty, three plus “dtsat” \u003d thirty;
- 40 (forty) and 90 (ninety) leave for later, say: these round numbers have a different name. Show that ten always has a "0" at the end, therefore the number is round, the numbers 1, 5, 8 are added to it, and so on;
- 50, 60, 70, 80 are even easier to remember. Ask how many tens are in the number 50. That's right, five. Let the children name the first number, add the word "ten" - it will be FIFTY. When the student understands the principle, ask: "How many tens did you find in 60, 70 and 80?" Of course six, seven, eight. So the new names will be obtained: SIXTY, SEVENTY, EIGHTY.
Counting up to 20 without going over ten
Algorithm:
- remove the same cubes again;
- have the child build a row of ten;
- put on top (necessarily from left to right) two more cubes. It turned out 12;
- next on the same principle build the number 15;
- explain to a young student how to quickly add 12 and 15. Add 1 + 1 ten, it turns out 2 tens or TWENTY;
- add units: 2 + 5 \u003d 7. Now there are TWENTY and SEVEN, together - TWENTY SEVEN;
- support the explanation with cubes. Have the child count whether the 27 cubes are really on the table;
- consolidate the lesson, let them try different options until the "young mathematician" understands the principle;
- addition mastered? Start subtracting: the principle is the same;
- go after a dozen only after fully understanding the material with any numbers from 10 to 100.
Advice! By the beginning of training, the child must clearly understand where are tens, and where are units in two-digit numbers, clearly know the concept of "left - right".
Account rules with the transition over ten
Use the table that shows the composition of the number. Kids need to understand how to get numbers in different ways. For example, 8 \u003d 3 + 5, 4 + 4, 6 + 2, 7 + 1, 8+ 0. Without the skills of quick counting, addition / subtraction from 0 to 10, you cannot proceed to more complex exercises.
Parents' task: explain that one of the numbers needs to be decomposed into two to get 10, then add the remainder. The rule is easy to understand with an example.
See:
- task: find how much 18 + 6 will be;
- 18 is 10 and 8;
- write in a new way (10 + 8) + 6;
- ask how much from 6 to 10 is not enough to add to 8;
- correctly, 2 (the table "Composition of numbers is useful);
- now write 6 as 2 and 4. It turned out: 10 + 8 + 2 + 4 or 10 + 10 + 4. Two tens plus four units equals TWENTY FOUR;
- when the child remembers addition, also explain the subtraction;
- always keep the Number Composition chart handy. Children will be less lost, easier to navigate.
Constantly carry out "training in between cases" to better remember the composition of the number. Speak more often, connect the child, let him finish the phrase: “There are 3 plates on the table on the left, I put 3 more plates on the right. How many items are there? That's right, 6 ". Show another way: “I will put 2 plates on the left, 4 plates on the right, again 6 plates turned out” and so on (1 + 5).
At the address read the instructions for the use of Vibrocil nose drops for children.
- conduct classes in a playful way. Preschoolers and junior schoolchildren react sharply to boring tasks, "gray", inexpressive pictures;
- give simple examples, look for characters to count, understandable by age. A small student should easily recognize objects, animals that need to be counted. For example, a cat is suitable, a porcupine is not (many kids think that this is a hedgehog with long thorns, they do not immediately recognize and name the animal). Orange - suitable, kiwi - no (exotic fruit is somewhat reminiscent of potatoes, you can make a mistake) and so on;
- math games are a great option for educational activities. Dominoes, loto, a labyrinth where you can travel with the help of chips, cubes with a large image will do. Buy games, make cardboard cards yourself;
- get the child interested, tell us how important the counting is in everyday affairs. Count the stairs in the stairwell, chairs by the table, windows in a store, blue or white cars on the road. When shopping at the supermarket, ask your child to serve 1 carton of milk, 2 bagels, 3 cartons of cottage cheese from the shelf, and so on. Say, "There are 4 bananas in the basket, I will put 1 more, it will make 5 bananas." Pronounce all the numbers clearly. Such conversations often "strain" parents, often seem boring, empty, but it is difficult to overestimate the benefits of classes for children;
- training in between. This technique clearly demonstrates what numbers and calculations mean to people. Unobtrusively teach your toddler to the world of mathematics. When setting the table for dinner or lunch, say: "I put 5 plates, I put 5 forks." Gradually, the little man will understand that each time the number of cutlery and dishes is different. Put on one plate, sound it, add another - name the number again, and so on;
- regularity, persistence is one of the main rules. Conduct training in between, come up with fairy tales with a mathematical bias about surrounding objects (animate / inanimate).
- ask the "young mathematician" for help, let him tell you how many cats are sitting near the entrance. Crumble the bread, ask them to count the pigeons arriving for food. Often 10, 20 or more birds flock. Here is a good reason to show that “you counted to 10, and there are more numbers, for example, 11, 15, 20 and so on, to count all the birds”;
- game in a cafe / shop. Many parents and experienced educators advise a simple trick for teaching counting, especially for adding, subtracting numbers after ten. Adding another 1, 2 or 5 rubles to 10 rubles, the child will understand what the number 15 \u003d 10 + 5, 20 \u003d 10 + 10. Make paper money from dense material. You will need "coins" and "bills" of all denominations, even those that are not in real circulation. Draw 3,4,7,8 rubles: you get any number when added to 10. What size of "money" should I choose? To clearly see the denomination;
- school. Another useful game. Children love to be teachers. Give them this opportunity, solve examples, sometimes with mistakes, so that the "teacher" can correct you, test your knowledge. If the little teacher himself made a mistake, tell me gently, do not laugh. Check the correctness of the solution on cubes, apples, counting sticks, think together who is right. Praise your knowledge, promise to correct your grade, improve your math;
- to add numbers within 20, use visual aids, counting sticks, cubes. An ordinary soft meter, which is used when sewing, will help to study the numbers from 0 to 100. The "young mathematician" will see all the numbers, understand which one is to the left, which one is to the right. It is convenient to explain that 12 is less than 17 because it is to the left. You can measure 12 and 17 cm of fabric, cut it off, compare pieces, confirm the correctness;
- enter the concepts of "plus" and "minus" later, when the rules of addition / subtraction up to 10 have been mastered;
- always explain every word in a problem. Until the student understands what the condition means, he is unlikely to solve the problem. At first, come up with examples yourself, look for good textbooks with interesting, understandable tasks;
- in case of difficulties, do not hesitate to ask for advice from a tutor, child center teacher or teacher. The main thing is to find a person who understands not only mathematics, but also child psychology. The task is quite difficult, but solvable;
- psychological contact with a young student is a prerequisite for successful learning. Shouts, humiliation, a constant reminder of failures discourage learning, provoke lack of confidence in their abilities, severe complexes.
Arm yourself with the advice of teachers, parents, try to teach children to count correctly up to 20. In some cases, the material is easy to learn, in others persistence, patience, long explanations are required. Do not despair, do not scold the "young mathematician", consult with teachers, psychologists. Only regular exercises, encouraging the slightest achievements will bring results.
This lesson describes in detail the order of performing arithmetic operations in expressions without and with brackets. Students are given the opportunity, in the course of completing the tasks, to determine whether the value of expressions depends on the order of performing arithmetic operations, to find out whether the order of arithmetic operations in expressions without brackets and with brackets is different, to practice applying the learned rule, to find and correct mistakes made in determining the order of actions.
In life, we constantly perform any actions: we walk, study, read, write, count, smile, quarrel and make peace. We perform these actions in a different order. Sometimes they can be swapped and sometimes not. For example, getting ready for school in the morning, you can first do exercises, then make the bed, or vice versa. But you can't go to school first and then put on your clothes.
And in mathematics, is it necessary to perform arithmetic operations in a certain order?
Let's check
Let's compare expressions:
8-3 + 4 and 8-3 + 4
We see that both expressions are exactly the same.
Let's perform actions in one expression from left to right, and in another from right to left. The numbers can be used to indicate the order of actions (Fig. 1).
Figure: 1. Procedure
In the first expression, we first perform a subtraction action, and then add the number 4 to the result.
In the second expression, we first find the value of the sum, and then subtract the resulting result 7 from 8.
We see that the values \u200b\u200bof the expressions are different.
Let's conclude: the order of performing arithmetic operations cannot be changed.
Let's learn the rule of performing arithmetic operations in expressions without brackets.
If the expression without parentheses includes only addition and subtraction or only multiplication and division, then the actions are performed in the order in which they are written.
Let's practice.
Consider the expression
This expression contains only addition and subtraction actions. These actions are called first step actions.
We perform actions from left to right in order (Fig. 2).
Figure: 2. Procedure
Consider the second expression
In this expression, there are only multiplication and division actions - these are the actions of the second stage.
We perform actions from left to right in order (Fig. 3).
Figure: 3. Procedure
In what order are arithmetic operations performed if the expression contains not only addition and subtraction, but also multiplication and division?
If an expression without brackets includes not only addition and subtraction, but also multiplication and division, or both of these actions, then first multiply and divide in order (from left to right), and then add and subtract.
Consider the expression.
We reason like this. This expression contains the operations of addition and subtraction, multiplication and division. We act according to the rule. First, we perform multiplication and division in order (from left to right), and then addition and subtraction. Let's arrange the order of actions.
Let's calculate the value of the expression.
18:2-2*3+12:3=9-6+4=3+4=7
In what order are arithmetic operations performed if the expression contains parentheses?
If the expression contains parentheses, then the value of the expressions in parentheses is calculated first.
Consider the expression.
30 + 6 * (13 - 9)
We see that this expression contains an action in brackets, which means that we will perform this action first, then multiply and add in order. Let's arrange the order of actions.
30 + 6 * (13 - 9)
Let's calculate the value of the expression.
30+6*(13-9)=30+6*4=30+24=54
How should one reason in order to correctly establish the order of arithmetic operations in a numeric expression?
Before proceeding with the calculations, you need to consider the expression (find out if it contains brackets, what actions it contains) and only after that perform the actions in the following order:
1. actions written in brackets;
2. multiplication and division;
3. addition and subtraction.
The diagram will help you remember this simple rule (Fig. 4).
Figure: 4. Procedure
Let's practice.
Let's look at the expressions, set the order, and perform the calculations.
43 - (20 - 7) +15
32 + 9 * (19 - 16)
We will act according to the rule. Expression 43 - (20 - 7) +15 contains operations in parentheses, as well as addition and subtraction operations. Let's establish the order of actions. The first step is to perform the action in parentheses, and then, in order from left to right, subtraction and addition.
43 - (20 - 7) +15 =43 - 13 +15 = 30 + 15 = 45
The expression 32 + 9 * (19 - 16) contains actions in parentheses, as well as multiplication and addition actions. According to the rule, we first perform the action in parentheses, then multiply (the number 9 is multiplied by the result obtained by subtraction) and addition.
32 + 9 * (19 - 16) =32 + 9 * 3 = 32 + 27 = 59
There are no parentheses in the expression 2 * 9-18: 3, but there are operations of multiplication, division and subtraction. We act according to the rule. First, we perform multiplication and division from left to right, and then subtract the result obtained from division from the result obtained by multiplying. That is, the first action is multiplication, the second is division, and the third is subtraction.
2*9-18:3=18-6=12
Let's find out if the order of actions is defined correctly in the following expressions.
37 + 9 - 6: 2 * 3 =
18: (11 - 5) + 47=
7 * 3 - (16 + 4)=
We reason like this.
37 + 9 - 6: 2 * 3 =
There are no parentheses in this expression, which means that we first perform multiplication or division from left to right, then addition or subtraction. In this expression, the first action is division, the second is multiplication. The third action should be addition, the fourth is subtraction. Conclusion: the order of actions is defined correctly.
Let's find the value of this expression.
37+9-6:2*3 =37+9-3*3=37+9-9=46-9=37
We continue to argue.
The second expression contains parentheses, which means that we first perform the action in parentheses, then from left to right, multiplication or division, addition or subtraction. Check: the first action is in brackets, the second is division, and the third is addition. Conclusion: the order of actions is defined incorrectly. Let's fix the errors, find the value of the expression.
18:(11-5)+47=18:6+47=3+47=50
This expression also contains parentheses, which means that we first perform the action in parentheses, then from left to right, multiplication or division, addition or subtraction. Check: the first action is in brackets, the second is multiplication, and the third is subtraction. Conclusion: the order of actions is defined incorrectly. Let's fix the errors, find the value of the expression.
7*3-(16+4)=7*3-20=21-20=1
Let's complete the task.
Let's arrange the order of actions in the expression using the learned rule (Fig. 5).
Figure: 5. Procedure
We do not see numerical values, so we cannot find the meaning of expressions, but we will practice applying the learned rule.
We act according to the algorithm.
The first expression contains parentheses, so the first action is in parentheses. Then from left to right multiplication and division, then from left to right subtraction and addition.
The second expression also contains parentheses, which means that the first action is performed in parentheses. After that, from left to right, multiplication and division, after that - subtraction.
Let's check ourselves (fig. 6).
Figure: 6. Procedure
Today in the lesson we got acquainted with the rule of the order of actions in expressions without brackets and with brackets.
List of references
- M.I. Moreau, M.A. Bantova and others. Mathematics: Textbook. Grade 3: in 2 parts, part 1. - M .: "Education", 2012.
- M.I. Moreau, M.A. Bantova and others. Mathematics: Textbook. Grade 3: in 2 parts, part 2. - M .: "Education", 2012.
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Homework
1. Determine the order of actions in these expressions. Find the meaning of expressions.
2. Determine in what expression this order of performing actions:
1. multiplication; 2.division; 3. addition; 4. subtraction; 5.addition. Find the meaning of this expression.
3. Make three expressions in which the following order of actions is performed:
1. multiplication; 2. addition; 3. subtraction
1.addition; 2. subtraction; 3.addition
1. multiplication; 2. division; 3.addition
Find the meaning of these expressions.
Visual-figurative thinking prevails in children. The problem is that most mathematical concepts are abstract and poorly understood or memorized by younger students. Therefore, any mathematical operations must be based on practical actions with objects.
Teachers use three main ways to teach a child to count in the head:
- based on knowledge of the composition of numbers;
- memorizing tables of mathematical actions by heart;
- using special techniques for performing mathematical operations.
Let's consider each of them.
Preparation for learning oral counting
Preparation for oral counting should begin with the first steps in learning mathematics. Introducing the child to numbers, it is imperative to teach him that each number represents a group with a certain number of objects. It is not enough, for example, to count to three and show the child the number 3. Be sure to ask him to show three fingers, put three candies in front of him, or draw three circles. If possible, connect the number with fairy-tale characters known to the child or other concepts:
- 3 - three pigs;
- 4 - ninja turtles;
- 5 - fingers on the hand;
- 6 - heroes of the "Turnip" fairy tale;
- 7 - gnomes, etc.
The child should form clear images attached to each number. At this stage, it is very useful to play math dominoes with the children. Gradually, pictures with dots that correspond to the corresponding numbers are imprinted in their memory.
You can also practice learning numbers with a box of cubes. Such a box should be divided into 10 cells, which are arranged in two rows. Getting acquainted with each number, the child will fill in the required number of cells and memorize the appropriate combinations. The benefit of these dice games is that the child will subconsciously notice and remember how many more dice are needed to complete the number to 10. This is a very important skill for verbal counting!
Alternatively, you can use Lego details for such an exercise or apply the principle of pyramids from Zaitsev's technique. The main result of all the described methods of acquaintance with numbers should be their recognition. It is necessary to ensure that the child, when looking at a combination of objects, immediately (without recounting) can name their number and the corresponding number.
Verbal counting based on the composition of the number
Based on the knowledge of the composition of the number, the child can perform addition and subtraction. For example, to say how much “five plus two,” he must remember that 5 and 2 are 7. And “nine minus three” is six, because 9 is 3 and 6.
Without knowledge of the corresponding tables, a child is unlikely to be able to learn how to divide numbers in his head. Constant exercise in the use of tables greatly improves the speed of obtaining results when doing calculations in your head.
Using computational techniques for oral counting
The highest degree of proficiency in oral counting skills is the ability to find the fastest and most convenient way to calculate the result. Such techniques should begin to be explained to children immediately after familiarizing them with the actions of addition and subtraction.
So, for example, one of the first ways to teach a child to count in the mind in the 1st grade is the technique of counting and "jumping over". Children quickly learn that adding 1 is the next number, and subtracting 1 is the previous one. Then you need to offer to meet the best friend of number 2 - a frog who can jump over a number and immediately name the result of adding or subtracting 2.
The explanation of the principle of performing these mathematical actions with the number 3. The example of a bunny who knows how to jump farther - immediately through two numbers will help in this.
Also, children need to demonstrate techniques:
- permutations of terms (for example, to count 3 + 68, it is easier to swap numbers and add);
- counting in parts (28 + 16 \u003d 28 + 2 + 14);
- reduction to a round number (74 - 15 \u003d 74 - 4 - 10 - 1).
The counting process facilitates the ability to apply combination and distribution laws. For example, 11 + 53 + 39 \u003d (11 + 39) + 53. In this case, children should be able to see the easiest way to count.
How to learn to count quickly in the mind of an adult
An adult can use more complex algorithms for oral counting. The most convenient way to quickly calculate in your head is to round and complete the numbers. For example, example 456 + 297 can be calculated like this:
- 456 + 300 = 756
- 756 - 3 = 753
Subtraction is performed similarly.
To perform multiplication and division, special rules have been developed for dealing with individual numbers. For example, such:
- to multiply a number by 5, it's easier to multiply it by 10, and then divide it in half;
- multiplying by 6 involves performing the previous steps and then adding the first multiplier to the result;
- to multiply a two-digit number by 11, you need to write the first digit in place of hundreds, and the second in place of units. In place of tens, the sum of these two digits is written;
- you can divide by 5 by multiplying the dividend by 2, and then divide by 10.
There are rules for calculating decimal fractions, calculating percentages, and exponentiation.
You can get acquainted with these techniques at school or find material on the Internet, but in order to learn how to quickly calculate in your head on their basis, you need to train and train again! In the process of training, many results will be remembered by heart, and the child will name them automatically. He will also learn to operate with large numbers, decomposing them into simpler and more convenient terms.
