To find an unknown number you need

Target:

• Introduce children to solving equations based on the connection between the minuend and the subtrahend and the difference expressed as an expression.
• Improve your skills by learning to add and subtract multi-digit numbers.
• Develop the ability to competently, logically, and fully answer questions;
• Develop mental processes: memory, thinking. imagination. perception, attention, emotions.
• To cultivate perseverance, confidence in one’s abilities, accuracy in completing tasks, responsibility, curiosity, and interest in the subject.

Lesson type: Lesson of generalization and systematization of students' knowledge.

Lesson format: Lesson-travel

Methods:

• Verbal
• Practical
• Visual
• Partial search

Equipment:

• interactive whiteboard, presentation, cube layouts, cards, tickets with tasks, teaching aids.

Lesson progress

Org. moment

1. Psychological attitude

The bell rang loudly.
The lesson begins.
Stand up straight, don't make any noise,
Everything is on the desk, look.
Is everything in place, is everything in order:
Book, pen and notebook.
Every student knows
A diary will also be needed.

Hello guys. We sat down.

We will start a new topic.

Guys, do you like to travel?

Today we have an unusual lesson. We are going on a trip to Kazakhstan by plane. I will be your captain. I appoint you as my assistants. And we’ll go to the cities of Kazakhstan, where a lot of interesting things await us. When we go on a journey, we take with us knowledge, skills, abilities and friendship. These qualities will help you overcome all obstacles and achieve your desired goal.

Motivation:

Try to understand everything
Give complete answers,
To get paid for work,
Just mark five.

So, I offer an ORAL COUNT

Our task is to strengthen computing skills

Slide 2 with answers

A) reduce the number 600 by 330 =270

B) increase the number 400 by 460 = 860

B) Find the sum of the numbers 560 and 240 = 800

D) find the difference between the numbers 270 and 90 = 180

D) the product of the numbers 36 and 3 is equal to 72? no, how much is 90+18=108

E) the dividend is 75, the divisor is 25, the quotient is 3? Yes, prove 60+15=75

Find the perimeter and area of ​​a square with a side of 8 mm

Slide 3 – table

The task is to fill the table

minuend	42		60		846
subtrahend		45		537		542
difference	36	85	28	362	140	834

Answers 6,130,32,899,706,1376

In the first line - minuend

In the second line - subtrahend

In the third line - the difference

In the first column, that the unknown is subtrahendable

How to find the subtrahend?

Children - To find the subtrahend, you need to subtract the difference from the minuend.

In the second column - unknown minuend

How to find the minuend?

Children: To find the minuend you need to add the subtrahend with the difference

Answers 6,130,32, 899,706,1376

CONCLUSION: So how to find the subtrahend...

How to find a minuend...

Maybe you already guessed the topic of our lesson?

Children: Find minuend, subtrahend

Lesson topic: Finding an unknown minuend, an unknown subtrahend

Our lesson objective: Learn to solve minuend and subtrahend equations with unknowns.

Open your notebooks and write down the number

Check your posture, how your notebook is lying, place your feet on the floor

X + 274 = 1000 X = 1000 – 274 Answer: 726.

x – 274 = 326 Answer: 600.

1000 - x = 326 Answer: 674.

Children: we solved equations, found unknown minuends and subtrahends. We learned to solve equations with unknowns.

How to find the minuend? Subtrahend?

• To find the unknown term, you need to subtract the known term from the sum value
• To find the unknown minuend, you need to add the subtrahend to the difference value
• To find an unknown subtrahend, you need to subtract the difference value from the minuend

A long way to develop skills solving equations begins with the decision of the very first and relatively simple equations. By such equations we mean equations in which the left side contains the sum, difference, product or quotient of two numbers, one of which is unknown, and the right side contains a number. That is, these equations contain an unknown summand, minuend, subtrahend, multiplier, dividend or divisor. The solution of such equations will be discussed in this article.

Here we will give rules that allow you to find an unknown term, factor, etc. Moreover, we will immediately consider the application of these rules in practice, solving characteristic equations.

Page navigation.

So, we substitute the number 5 instead of x into the original equation 3+x=8, we get 3+5=8 - this equality is correct, therefore, we have correctly found the unknown term. If, when checking, we received an incorrect numerical equality, this would indicate to us that we solved the equation incorrectly. The main reasons for this could be either the application of the wrong rule or computational errors.

How to find an unknown minuend or subtrahend?

The connection between addition and subtraction of numbers, which we already mentioned in the previous paragraph, allows us to obtain a rule for finding an unknown minuend through a known subtrahend and a difference, as well as a rule for finding an unknown subtrahend through a known minuend and a difference. We will formulate them one by one and immediately present the solution to the corresponding equations.

To find the unknown minuend, you need to add the subtrahend to the difference.

For example, consider the equation x−2=5. It contains an unknown minuend. The above rule tells us that to find it we must add the known subtrahend 2 to the known difference 5, we have 5+2=7. Thus, the required minuend is equal to seven.

If we omit the explanations, the solution is written as follows:
x−2=5 ,
x=5+2 ,
x=7 .

For self-control, let's perform a check. We substitute the found minuend into the original equation, and we obtain the numerical equality 7−2=5. It is correct, therefore, we can be sure that we have correctly determined the value of the unknown minuend.

You can proceed to finding the unknown subtrahend. It is found using addition according to the following rule: to find the unknown subtrahend, you need to subtract the difference from the minuend.

Let's solve an equation of the form 9−x=4 using the written rule. In this equation, the unknown is the subtrahend. To find it, we need to subtract the known difference 4 from the known minuend 9, we have 9−4=5. Thus, the required subtrahend is equal to five.

Let's give short version solutions to this equation:
9−x=4 ,
x=9−4 ,
x=5 .

All that remains is to check the correctness of the found subtrahend. Let's do a check by substituting the found value 5 into the original equation instead of x, and we get the numerical equality 9−5=4. It is correct, so the value of the subtrahend we found is correct.

And before moving on to the next rule, we note that in grade 6 the rule for solving equations is considered, which allows you to transfer any term from one part of the equation to another with opposite sign. So, all the rules discussed above for finding an unknown summand, minuend and subtrahend are completely consistent with it.

To find an unknown factor, you need...

Let's take a look at the equations x·3=12 and 2·y=6. In them, the unknown number is the factor on the left side, and the product and the second factor are known. To find an unknown factor, you can use the following rule: to find unknown multiplier, you need to divide the product by a known factor.

The basis of this rule is that we gave the division of numbers the opposite meaning to the meaning of multiplication. That is, there is a connection between multiplication and division: from the equality a·b=c, in which a≠0 and b≠0 it follows that c:a=b and c:b=c, and vice versa.

For example, let's find the unknown factor of the equation x·3=12. According to the rule, we need to divide famous work 12 by the known factor 3. Let's carry out: 12:3=4. Thus, the unknown factor is 4.

Briefly, the solution to the equation is written as a sequence of equalities:
x·3=12 ,
x=12:3 ,
x=4 .

It is also advisable to check the result: we substitute the found value in the original equation instead of the letter, we get 4·3=12 - a correct numerical equality, so we have correctly found the value of the unknown factor.

And one more point: acting according to the learned rule, we actually divide both sides of the equation by a known factor other than zero. In 6th grade it will be said that both sides of an equation can be multiplied and divided by the same non-zero number, this does not affect the roots of the equation.

How to find an unknown dividend or divisor?

Within the framework of our topic, it remains to figure out how to find the unknown dividend with a known divisor and quotient, as well as how to find the unknown divisor with a known dividend and quotient. The connection between multiplication and division already mentioned in the previous paragraph allows us to answer these questions.

To find the unknown dividend, you need to multiply the quotient by the divisor.

Let's look at its application using an example. Let's solve the equation x:5=9. To find the unknown dividend of this equation, according to the rule, you need to multiply the known quotient 9 by the known divisor 5, that is, we perform the multiplication natural numbers: 9·5=45. Thus, the required dividend is 45.

Let's show a short version of the solution:
x:5=9 ,
x=9·5 ,
x=45 .

The check confirms that the value of the unknown dividend was found correctly. Indeed, when substituting the number 45 into the original equation instead of the variable x, it turns into the correct numerical equality 45:5=9.

Note that the analyzed rule can be interpreted as multiplying both sides of the equation by a known divisor. This transformation does not affect the roots of the equation.

Let's move on to the rule for finding an unknown divisor: to find an unknown divisor, you need to divide the dividend by the quotient.

Let's look at an example. Let's find the unknown divisor from equation 18:x=3. To do this, we need to divide the known dividend 18 by the known quotient 3, we have 18:3=6. Thus, the required divisor is six.

The solution can be written like this:
18:x=3 ,
x=18:3 ,
x=6 .

Let's check this result for reliability: 18:6=3 is a correct numerical equality, therefore, the root of the equation was found correctly.

It is clear that this rule can only be applied when the quotient is nonzero, so as not to encounter division by zero. When the quotient is equal to zero, then two cases are possible. If the dividend is equal to zero, that is, the equation has the form 0:x=0, then any non-zero value of the divisor satisfies this equation. In other words, the roots of such an equation are any numbers that are not equal to zero. If at equal to zero If the dividend is different from zero, then for no value of the divisor the original equation turns into a correct numerical equality, that is, the equation has no roots. For illustration, we present the equation 5:x=0, it has no solutions.

Sharing Rules

Consistent application of the rules for finding the unknown summand, minuend, subtrahend, multiplier, dividend and divisor allows you to solve equations with a single variable more complex type. Let's understand this with an example.

Consider the equation 3 x+1=7. First, we can find the unknown term 3 x, to do this we need to subtract the known term 1 from the sum 7, we get 3 x = 7−1 and then 3 x = 6. Now it remains to find the unknown factor by dividing the product 6 by the known factor 3, we have x=6:3, whence x=2. This is how the root of the original equation is found.

To consolidate the material, we present a brief solution to another equation (2·x−7):3−5=2.
(2 x−7):3−5=2 ,
(2 x−7):3=2+5 ,
(2 x−7):3=7 ,
2 x−7=7 3 ,
2 x−7=21 ,
2 x=21+7 ,
2 x=28 ,
x=28:2 ,
x=14 .

References.

• Mathematics.. 4th grade. Textbook for general education institutions. At 2 p.m. Part 1 / [M. I. Moro, M. A. Bantova, G. V. Beltyukova, etc.] - 8th ed. - M.: Education, 2011. - 112 p.: ill. - (School of Russia). - ISBN 978-5-09-023769-7.
• Mathematics: textbook for 5th grade. general education institutions / N. Ya. Vilenkin, V. I. Zhokhov, A. S. Chesnokov, S. I. Shvartsburd. - 21st ed., erased. - M.: Mnemosyne, 2007. - 280 pp.: ill. ISBN 5-346-00699-0.

To find an unknown term, you need ……………………………………………………….. The result of multiplying two or more factors is called………………………………… ……… To find the dividend, you need ………………………………………………………………………………… The result of subtracting numbers is called …………………… …………………………………………… The result of adding two or more terms is called ……………………………………………………… To find an unknown factor, you need to …………… ……………………………………………. The result of dividing numbers is called………………………………………………………………. To find the minuend, you need to……………………………………………………………… To find the divisor, you need to……………………………………………………… ………………………………………………………… To find the subtrahend, you need……………………………………………………………… …. To find how much one number is greater or less than another, you need………………………………………………………………………………………… ……………………………………..To find how many times one number is greater or less than another, you need to……………………….…………………………… …………………………………………………………………………………. In an expression without parentheses containing only addition and subtraction or multiplication and division, the operations are performed by ………………… ………………………………………………………………………………. In expressions containing parentheses, all actions ………………………..…………………………………………………………………… are performed first …………………………………………………………………………………………………………………………………… ………………….. The perimeter of the figure is ………………………………………………………………………………… The perimeter of the rectangle is ……… ……………………………………………………………… The perimeter of a square is ……………………………………………………… ……………………………………. The semi-perimeter of a rectangle is ………………………………………………………………………………….. To find the side of a square, you need the value of its perimeter………………………… ……………… To find the area of ​​a rectangle, you need ……………………………………………………… To find the width of a rectangle, you need its area ………………… …………………………To find the length of a rectangle, you need …………………………………………………………….

To find an unknown term, you need to subtract another term from the sum.
The result of multiplying two or more factors is called a product.
To find the dividend, you need to multiply the divisor by the quotient.

The result of subtracting numbers is called the difference
The result of adding two or more terms is called a sum.
To find an unknown factor, you need to divide the product by another factor.
The result of dividing numbers is called the quotient.
To find the minuend, you need to add the difference to the subtrahend.
To find the divisor, you need to divide the dividend by the quotient.
To find the subtrahend, you need to subtract the difference from the minuend.
To find how much one number is greater or less than another, you need to subtract the smaller number from the larger number.
……………………………………………………………………………………………………………..

To find how many times one number is greater or less than another, you need to divide the larger number by the smaller one.

………………………………………………………………………………………………………………….

In an expression without
parentheses containing only addition and subtraction or multiplication and division,
actions are performed in order.………………… ……………………………………………………………………………….

In expressions containing parentheses, all actions in the parentheses are performed first.………………………..

……………………………………………………………………………………………………………………………………………………………………………………………………………………………………..

The perimeter of a figure is the sum of the lengths of all sides.

The perimeter of the rectangle is the sum of two sides multiplied by 2. P = 2* (a + b)………………………………………………………………………

The perimeter of a square is equal to the length of the side multiplied by 4………………………………………………………………………………………………………………….

The semi-perimeter of a rectangle is the length of two sides………………………………………………………………..

To find the side of a square, you need to divide its perimeter by 4………………………………………

To find the area of ​​a rectangle, you need to multiply the length by the width.
To find the width of a rectangle, you need to divide its area by its length.

To find the length of a rectangle, you need to divide its area by its width.