Instruction

1

The most important thing in solving problems is the ability to identify the condition (the circumstance of Affairs at the moment) and the question (what happens when the situation changes). The more you need to find, the more manipulations are necessary.

2

Need to teach

**the child**to identify the main words: given-took, buy-sell, has taken put. To reveal the meaning of the words: if the boy was treated, something gave – he has added, if the girl was taken away, claimed she became paralyzed.3

Visibility – compulsory methodically the correct condition of the learning

**child**. Abstract concepts the child is not able to operate, so the first step was to explain on concrete examples. For example, my mom has seven cubes, four she gives to her son and asks to know what she left. Thus, it is important that all manipulations were carried out by the child, be sure to muttering aloud that what he is doing. Thus, use all types of memory: visual, motor, auditory.4

When training the tasks you need to tell the kid how to distinguish between part and whole. The meaning of these words can be explained on a concrete example: take an orange and divide it into slices. The fruit itself is the whole and slices – it's part of the whole. A child considers how many parts is orange. Clean half and ask the kid to find out how much is left. He counts, I ask, how else can you find a solution to this

*task*? Correctly, by subtraction. How to know how much would be slices, if to the first part add the second? Right, I need to lay down, get an orange.5

The final stage of training the tasks must be the repetition, the analysis of the performed operations. Baby items says, what was the condition, what is the question, what did he do to get the answer. Once the algorithm learned, should be given the same task for independent work.

Useful advice

Start with simple tasks, it is not necessary to require all at once. Child, one way or another, learn to solve problems, most importantly, what attitude will give him such exercises.

# Advice 2: How to solve mathematics problems

To learn solving problems on

**mathematics**for the students is often difficult. Work on training of the decision task begins with the first class, with the most simple tasks. Types of there are many tasks, each requiring specific techniques. But first it is advisable to know a specific algorithm that we can rely on when solving particular**tasks**. The skill of solving problems in elementary school will help pupils to cope with them during further studies.Instruction

1

The perception of the content of

Read the problem and highlight the main idea, as stated in the problem.

Define the group to which this task applies. This can be

**tasks**Read the problem and highlight the main idea, as stated in the problem.

Define the group to which this task applies. This can be

**tasks**to interest, the motion for unit time**tasks**with proportional values, etc.2

Finding a solution plan

Depending on the group to which the task belongs, determined action to address it. The key to the solution is for each group of tasks. The key is a unique formula, which solved the problem. Not knowing this, we will not be able to cope with the task.

In the primary grades also have formulas, for example, speed = distance : time.

For clarity, make a picture or drawing. An unknown number is taken for x (X). So clearly you can see the condition and question

Analyze the condition

Think we can immediately give the answer to the question

How will find the value of X? Why?

Can now answer the question?

Depending on the group to which the task belongs, determined action to address it. The key to the solution is for each group of tasks. The key is a unique formula, which solved the problem. Not knowing this, we will not be able to cope with the task.

In the primary grades also have formulas, for example, speed = distance : time.

For clarity, make a picture or drawing. An unknown number is taken for x (X). So clearly you can see the condition and question

**tasks**. Unknowns in the illustration, denoted by "?".Analyze the condition

**of the tasks**, logical thinking according to plan.Think we can immediately give the answer to the question

**task**? Why?How will find the value of X? Why?

Can now answer the question?

3

The solution to

To solve you can make an equation with X, if the task is simple, i.e. it is necessary to find only one unknown.

When solving the equation X Express in the left part of the expression, the rest of the data move to the right.

If the problem is somewhat unknown, then decide, in accordance with the plan outlined in the analytical analysis, finding one number after the other to reach the answer to the question

Shall describe each action, explaining that finding.

Logical

**the problem**.To solve you can make an equation with X, if the task is simple, i.e. it is necessary to find only one unknown.

When solving the equation X Express in the left part of the expression, the rest of the data move to the right.

If the problem is somewhat unknown, then decide, in accordance with the plan outlined in the analytical analysis, finding one number after the other to reach the answer to the question

**task**.Shall describe each action, explaining that finding.

Logical

**tasks**can be solved by brute force, which remains one correct answer.4

Check solved

To verify the result found we can solve the problem another way if possible.

You should also relate the obtained result with the condition

The correct solution is to identify, making the task of selling this. Reframe the task so that only what was found the number was in the condition and the value of the known values we find. If the solution of unknown number was the same as in the initial task, then, its solution was correct.

Another way to verify the correctness of the decision of

**the problem**To verify the result found we can solve the problem another way if possible.

You should also relate the obtained result with the condition

**task**. To do this, insert this number in the text.The correct solution is to identify, making the task of selling this. Reframe the task so that only what was found the number was in the condition and the value of the known values we find. If the solution of unknown number was the same as in the initial task, then, its solution was correct.

Another way to verify the correctness of the decision of

**tasks**– estimation. "Think you could the answer to get a number if the action took place in practice.Note

Do not proceed with solving the problem, if you do not fully understand its meaning and the essence of the job, because the selected actions for response can be incorrect. When defining the plan objectives should be used all the data. How many unknowns in the problem, so "?" should be on your artwork.

Useful advice

Write down the formula for solving the problem to make it easier to navigate the solution. For the reliability of the decision task, use multiple means of verification.

# Advice 3: How to teach a child math

At the age of 4-5 years, and in some cases even before, you can start to teach

**baby**to master basics of math. If you do it in the form of games, using objects familiar to the baby since childhood, the result of a wait will make, believe me.Instruction

1

So delve into the essence of the process, how to teach

**child****math**. Start with the basics. Teach your toddler to count to five – just learn the sequence of numbers, but to let the child know that this is the account, and the numbers follow one another. Take, for example, apples. Put them in a row and count out loud. For a start, there should be no more than four or five, not peretrudites**child**long math next. Several times the count, pointing fingers at them and calling numbers. Then take 1 Apple, explaining aloud, "I'm holding an Apple". Then the second, third, and so on. Do that kind of manipulation about three to four days until you become clear that your child has grasped the essence of what you wanted to convey.2

A week later you can try to begin to explain to a child how to add numbers. First let it be basic examples: 1+1, 1+2. "I take one Apple and add it to another, it turns out two apples".

3

In principle, you can take any items, but it is very desirable that they were identical and small in size. For example, the pins or the same sticks for the account. To teach

**child****math**, especially the basics of this simple method is very easy. Most importantly, patience, to carry out such simple classes regularly, preferably daily in these for some time.4

A couple of weeks already you can move on to learning to count to ten and try to explain to the kid how to solve more complex examples. If you do a little – no more than 10-15 minutes a day, each time repeating previously learned, just three months you can teach

**the child**everything he needs to know before school in mathematics.# Advice 4: How to teach a child to solve mathematics problems

Solving problems in the study of mathematics in elementary school paid much attention. Need to teach

**the child**to find a solution to correctly draw it in your notebook, explain what was found in a particular action. Most problems arise when searching for solutions. Main duties thus imposed on teachers, but the responsibility of parents to reinforce skills at home and work for the development**of the child**. And it should be done well before school.Instruction

1

Teach

**the child**to establish the logical connection between objects and phenomena. For example, why one standing next to multi-storey buildings above and the other below? For an adult it is obvious that its height depends on the number of floors. This relationship, maybe with your help, needs to set and child. Why wolf got to grandma's house faster than Red Hat? Establish communication between path length and time (in this case, the concept of "speed" can not be considered). Why to move some items have the strength of a man, and for others you have to call a crane? Encourage your**child**to answer the questions "how?" "why?" "why?" "where?" and the like, develop the ability to establish logical connections.2

Broadens the mind

Broaden their horizons and increase their knowledge about the world tour, playing in various clubs and sections.

**of the child**. Read various fiction and children's non-fiction will help to do it. Getting answers to "why?" the little man learns. In the future, when solving mathematical problems, he is using his horizons, and realizing how there are those or other processes, it is easy to find the solution.Broaden their horizons and increase their knowledge about the world tour, playing in various clubs and sections.

3

Work on speed of reading the child of the printed text. It is impossible to solve the problem, reading it syllable by syllable and by the end of the reading forgetting about what was discussed in the beginning! After reading

**task**, ask the child a few questions on its content. Check to see if he understood what it was.4

Achieve durable learning child relationships between units of measurement quantities. Know that 1 meter contains 100 centimeters, and 1 quintal 100 kilos, a must!

5

Form a

**child's**ability to solve simple**tasks**in a single action. Examples can be found in textbooks of mathematics.6

Solving the compound task (in several steps), break it into simple

**tasks**that the child already knows how to solve it.7

Automate your mental calculation skills. Addition and subtraction within 100 (all cases) and mild cases of calculations in the range of 1000 and times tables a child needs to know well.

8

For some tasks (driving, e.g.) must know formula. Check out their knowledge with the

**child**.9

Lead the work on formation of skills to solve

**tasks**regularly and not from time to time. The results will be visible only when the daily hard work.Useful advice

Use in the classroom are numerous literature on the development of children's logical thinking, attention, memory.

# Advice 5: How to solve problems with math homework

According to many sources, resolving problems, developing logical and intellectual thinking. Tasks "on the job" are some of the most interesting. In order to learn how to solve such problems, you should be able to present the process of work, as they say.

Instruction

1

Tasks "on the job". For their solution it is necessary to know the definition and formula. Remember the following:

A=R*t formula works;

P=A/t – formula performance.

t=A/P – time formula, where A is work, f - labor productivity, and t is time.

If the problem statement does not specify the work, then it take 1.

A=R*t formula works;

P=A/t – formula performance.

t=A/P – time formula, where A is work, f - labor productivity, and t is time.

If the problem statement does not specify the work, then it take 1.

2

The examples will examine how one can solve such problems.

Condition. Two workers, working at the same time, dug up the garden for 6 h. First, a worker might perform the same work in 10 hours how many hours the second worker can dig up the garden?

Solution: Take all the work for 1. Then, in accordance with the formula for productivity is P=A/t , 1/10 of the work is done the first working for 1hour. 6/10 he does for 6 hours. Therefore, the second work in 6 hours makes 4/10 ( 1 – 6/10). We determined that productivity of the second worker is equal to 4/10. In a joint operation, according to the problem is 6 hours. For X take what you need to find, i.e. the work of the second worker. Knowing that t=6, P=4/10, then write and solve the equation:

0.4 x=6,

x=6/0,4,

x=15.

Response: the Second worker can plant a garden in 15 hours.

Condition. Two workers, working at the same time, dug up the garden for 6 h. First, a worker might perform the same work in 10 hours how many hours the second worker can dig up the garden?

Solution: Take all the work for 1. Then, in accordance with the formula for productivity is P=A/t , 1/10 of the work is done the first working for 1hour. 6/10 he does for 6 hours. Therefore, the second work in 6 hours makes 4/10 ( 1 – 6/10). We determined that productivity of the second worker is equal to 4/10. In a joint operation, according to the problem is 6 hours. For X take what you need to find, i.e. the work of the second worker. Knowing that t=6, P=4/10, then write and solve the equation:

0.4 x=6,

x=6/0,4,

x=15.

Response: the Second worker can plant a garden in 15 hours.

3

Let us consider another example: For filling the container with water, there are three pipes. The first tube for filling the container must time three times less than the second, and 2 hours more than a third. Three pipes operating simultaneously, fill the container for 3h, but the conditions simultaneously can work only two tubes. Determine the minimum cost of filling the container, if the value of 1H of one of the tubes is 230 rubles.

Solution: This problem is convenient to solve using the table.

1). Take all of the work for 1. For X we take the time required for the third pipe. The condition of the first tube need 2 hours more than the third. Then the first tube need (X+2) hours. And the third pipe need 3 times more time than the first, i.e. 3(X+2). Based on the performance formula, we get: 1/(X+2) – the performance of the first trumpet, 1/3(X+2) – a second tube, 1\X – third of the pipe. Put all the data in the table.

Work time,the hour performance

1 tube A=1 t=(X+2) P=1/X+2

2 pipe A=1 t=3(X+2) P=1/3(X+2)

3 pipe A=1 t=X P=1/X

Along A=1 t=3 P=1/3

Knowing that the joint performance is equal to 1/3, we set up and solve the equation:

1/(X+2)+1/3(X+2)+1/X=1/3

1/(X+2)+1/3(X+3)+1/X-1/3=0

3X+X+3X+6-x2-2X=0

5X+6-x2=0

X2-5X-6=0

When solving quadratic equations find the roots. It turns out

X=6(hours) – time to need a third pipe for filling the container.

From this it follows that the time should the first pipe is equal to (6+2)=8 (hours) and the second = 24(hours).

2). From these data we conclude that the minimum time is for the 1 and 3 pipes ,i.e., 14h.

3). Determine the minimum cost of filling the container with two pipes.

230*14=3220(RUB)

Response: 3220 RUB.

Solution: This problem is convenient to solve using the table.

1). Take all of the work for 1. For X we take the time required for the third pipe. The condition of the first tube need 2 hours more than the third. Then the first tube need (X+2) hours. And the third pipe need 3 times more time than the first, i.e. 3(X+2). Based on the performance formula, we get: 1/(X+2) – the performance of the first trumpet, 1/3(X+2) – a second tube, 1\X – third of the pipe. Put all the data in the table.

Work time,the hour performance

1 tube A=1 t=(X+2) P=1/X+2

2 pipe A=1 t=3(X+2) P=1/3(X+2)

3 pipe A=1 t=X P=1/X

Along A=1 t=3 P=1/3

Knowing that the joint performance is equal to 1/3, we set up and solve the equation:

1/(X+2)+1/3(X+2)+1/X=1/3

1/(X+2)+1/3(X+3)+1/X-1/3=0

3X+X+3X+6-x2-2X=0

5X+6-x2=0

X2-5X-6=0

When solving quadratic equations find the roots. It turns out

X=6(hours) – time to need a third pipe for filling the container.

From this it follows that the time should the first pipe is equal to (6+2)=8 (hours) and the second = 24(hours).

2). From these data we conclude that the minimum time is for the 1 and 3 pipes ,i.e., 14h.

3). Determine the minimum cost of filling the container with two pipes.

230*14=3220(RUB)

Response: 3220 RUB.

4

There are tasks the most difficult, where you must enter several variables.

Condition: the expert and the trainee, working together, have done a certain work in 12 days. If the first specialist performed one half and then the second half finished one Intern, all would have gone to 25 days.

a) Find the time that could spend a specialist to complete all of the work, provided that it will work faster and one Intern.

b) How to divide the workers received for work sharing of 15000 rubles?

1).Let all the work specialist can perform in X days, and Intern for Y days.

Get 1 day specialist performs 1/X operation, and the trainee for 1/Raboty.

2). Knowing that, working together, for all the work it took them 12 days will get:

(1/X+1/Y)=1/12 – ‘this is the first equation.

The condition, working by turns, alone, had spent 25 days will get:

X/2+Y/2=25

X+Y=50

Y=50-X is the second equation.

3) Substitute the second equation into the first gives: (50 - x +x) / (x(x-50)) = 1/12

X2-50X + 600 = 0,x1= 20,x2=30 (then Y=20) that satisfies the condition.

Answer: X=20,Y=30.

The money should be divided inversely proportional to the elapsed job time. Because the expert has worked faster and, consequently, can make more. To split the money should be in the ratio 3:2. Specialist 15000/5*3 = 9000 RUB.

Intern 15000/5*2 = 6000 RUB.

Useful tips: If you do not understand the problem, it is not necessary to proceed to its solution. First carefully read the problem, highlight all that is known, and that it is necessary to find. If possible, draw a picture – diagram. You can also use the tables. The use of tables and charts can facilitate the understanding and solution of the problem.

Condition: the expert and the trainee, working together, have done a certain work in 12 days. If the first specialist performed one half and then the second half finished one Intern, all would have gone to 25 days.

a) Find the time that could spend a specialist to complete all of the work, provided that it will work faster and one Intern.

b) How to divide the workers received for work sharing of 15000 rubles?

1).Let all the work specialist can perform in X days, and Intern for Y days.

Get 1 day specialist performs 1/X operation, and the trainee for 1/Raboty.

2). Knowing that, working together, for all the work it took them 12 days will get:

(1/X+1/Y)=1/12 – ‘this is the first equation.

The condition, working by turns, alone, had spent 25 days will get:

X/2+Y/2=25

X+Y=50

Y=50-X is the second equation.

3) Substitute the second equation into the first gives: (50 - x +x) / (x(x-50)) = 1/12

X2-50X + 600 = 0,x1= 20,x2=30 (then Y=20) that satisfies the condition.

Answer: X=20,Y=30.

The money should be divided inversely proportional to the elapsed job time. Because the expert has worked faster and, consequently, can make more. To split the money should be in the ratio 3:2. Specialist 15000/5*3 = 9000 RUB.

Intern 15000/5*2 = 6000 RUB.

Useful tips: If you do not understand the problem, it is not necessary to proceed to its solution. First carefully read the problem, highlight all that is known, and that it is necessary to find. If possible, draw a picture – diagram. You can also use the tables. The use of tables and charts can facilitate the understanding and solution of the problem.

Note

The overall performance is equal to the sum of capacities.