Sections: Maths

Class: 4

Basic goals:

1. Form the ability to select a whole part from an irregular fraction.
2. Review the concepts of numerator and denominator, correct and incorrect fractions, mixed numbers.
3. To actualize the ability to select a whole part from an incorrect fraction.

Thinking operations required at the design stage: action by analogy, analysis, generalization.

Equipment:

Demo material:

1) Formula of division with remainder.

Handout:

1) pieces of paper with the task (to stage 2)

2) Detailed sample for self-test (to step 6)

During the classes.

1 Self-determination for learning activities.

Goals:

1. Motivate learners to learning activities by reinforcing the situation of success achieved in the previous lesson.
2. Determine the content of the lesson.

Organization educational process at stage 1.

Over the course of several lessons, we have worked with some numbers. What numbers did we work with? (With fractional numbers).

What knowledge do we have about these numbers? (We know how to read them, write them down, compare them, solve problems).

I propose to continue our fruitful work. You are ready? (Yes).

Today we will continue to work with fractional numbers. I am sure that we will succeed perfectly well. But first, let's review the material from the previous lessons.

2 Updating knowledge and fixing difficulties in individual activities.

Goals:

1. To update the ability to find right and wrong fractions, mixed numbers, definition of right and wrong fractions, mixed number.
2. Update thought operations necessary and sufficient for the perception of new material.
3. Record a situation where students are unable to select the whole part from an incorrect fraction.

Organization of the educational process at stage 2.

What numbers did we meet in the previous lesson? (With mixed numbers).
- What does the mixed number consist of? (From integer and fractional parts).

Fractions and mixed numbers are written on the board.

What groups can the presented numbers be divided into?

Regular fractions ().

What fractions are called correct? (Fraction with the numerator less denominator... The correct fraction is less than one).

Incorrect fractions. (… ..)

What fractions are called incorrect? (The fraction with the numerator greater than the denominator or the numerator equal to the denominator).

Which of the irregular fractions can be represented as a natural number?

()

What fraction can be represented as a mixed number? (Incorrect fraction, where the numerator is greater than the denominator).

Define with number beam, what mixed number is the fraction

Students have a sheet with a task (P-1), one student works at the blackboard, comments.

What is the smallest mixed number? ()

The greatest? ()

What arithmetic operation helped you? (Division. Division with remainder).

Prove it. (On the board: D-1).

12: 7 = 1 (rest 5); 15: 7 = 2 (rest 1); 25: 7 = 3 (rest 4); 31: 7 = 4 (rest 3)

Select the whole part of the fraction, write down the mixed number. Children work on the back of the leaflet. Different answer options are put on the board.

How did you proceed?

3 Identifying the causes of the difficulty and setting the goal of the activity.

Goals:

1. Organize communicative interaction to identify the distinctive property of the task to isolate a whole part from an incorrect fraction.
2. Agree on the topic and purpose of the lesson.

Organization of the educational process at stage 3.

What task did you complete? (It is necessary to select the whole part from the fraction).

How is this task different from the previous one? (The way that helped us to isolate the whole part from an improper fraction is not suitable for a fraction. It is inconvenient to show this fraction on a number ray).

What do we see? (We got different answers.)

Why? (We used different ways... We do not have an algorithm for separating the whole part from an improper fraction).

What is the purpose of our lesson? (Build an algorithm and learn how to separate the whole part from an improper fraction).

Think and formulate the topic of our lesson. ("Isolation of the whole part from an improper fraction").

Well done!

The title of the lesson topic opens on the board.

4 Building a project for getting out of the difficulty.

Target:

1. Organize communicative interaction to build a new way of action to highlight the whole part from an irregular fraction.
2. Fix new way in a sign and verbal form and with the help of a standard.

Organization of the educational process at stage 4

In what way do you propose to find how many whole units are in a fractional number? (Numerator divided by denominator).

What sign in the notation of the fraction told you how to proceed? (A slash of a fraction is a division sign).

On the desk:

Let's write the fraction as a quotient: 65: 7.

What kind of division is this? (Division with remainder. On the board: D-1).

Find the result. (65: 7 = 9) (rest 2)

What does the quotient 9 and remainder 2 mean in the resulting equality? (The quotient 9 means that 65 contains 9 times 7 and 2 remains).

What will the quotient 9 stand for in a mixed number? (9 is the integer part of the mixed number).

On the desk:

What is the remainder of 2 in the mixed number? (2 is the numerator of the mixed fraction).

On the desk:

What about the denominator? (It remains, does not change).

On the desk:

What mixed number did we get?

Have we completed the task? (Yes).

Which mathematical action did it help us? (Division with remainder. On the board: D-1).

The teacher returns to the answers on the pieces of paper, summarizes, encourages with words those who did it correctly. In a group form, students display a new method in a symbolic form on pieces of paper. The correct option is selected.

Write down, using the formula for division with remainder (D-1), what mixed number is the fraction?

On the board: D-3

How to select a whole part from an incorrect fraction?

To select the whole part from an improper fraction, you need to divide its numerator by the denominator. The quotient will be the whole part, the remainder will be the numerator, and the denominator will not change.

Well done! Thanks!

Let's check our opinion with the opinion of the textbook. Turn to page 26, Math 4 (Part 2), and read the rule silently first and then aloud.

Were we right? (Yes).

Well done!

Physical minutes (at the teacher's choice).

5 Primary reinforcement in external speech.

Target:

Fix the way of separating the whole part from an irregular fraction in external speech.

Organization of the educational process at stage 5.

Let's repeat the algorithm for extracting the whole part from an improper fraction one more time. D 2

We have compiled an algorithm for separating the whole part from an improper fraction. What is the purpose of our future activities? (Practice).

No. 4 (a, b, c) p. 26 - with commentary on the model.

No. 4 (d, e) page 26 - in pairs.

6 Self-test with self-test.

Target:

1. Organize the students' independent fulfillment of assignments to isolate an entire part from an irregular fraction.
2. Train the ability for self-control and self-esteem.
3. Test your ability to separate the whole part from an incorrect fraction.
4. Contribute to the creation of a situation of success.

Organization of the educational process at stage 6.

You have managed to deduce an algorithm for extracting an integer part from an improper fraction and have practiced solving examples. I think now you can complete the task yourself.

Do it yourself:

No. 3, page 26 - option 1 - columns 1 and 2;

Option 2 - columns 3 and 4;

Anyone who wishes can complete the task of another option.

Students perform work, at the end of which they test themselves on a sample for self-examination. Card P-2 is used.

Test yourself using the self-test pattern and record the test result using the "+" or "?" green handle.

Who made mistakes while completing the assignment? (...)

What is the reason? (...)

Who's got it right?

Well done!

You can organize work on error correction in groups or frontally. Students who have not made a mistake are appointed as counselors.

7 Incorporation and repetition.

Target:

Train the ability to isolate the whole part from an irregular fraction.

Organization of the educational process at stage 7.

Let's try to apply our knowledge when comparing fractions and mixed numbers.

Find the inequality in which you want to compare the right fraction with the wrong one.

What do we do?

Select the whole part from the improper fraction.

Means?!

An incorrect fraction is more correct. We proved this by highlighting the whole part.

Well done!

Finish the task, compare.

Let's check.

8 Reflection of educational activities in the lesson.

Goals:

1. Fix in speech the algorithm for separating the whole part from the incorrect fraction.
2. Record the remaining difficulties and ways to overcome them.
3. Assess your own activities in the lesson.
4. Agree on homework.

Organization of the educational process at stage 8.

What have you learned in the lesson? (Select the whole part from the improper fraction).

What algorithm did we build? (You can say algorithm D-2).

Who had difficulties? How will you act?

Who is pleased with themselves today? Why?

It was difficult for me in the lesson.
- I understood the lesson, but I need training.
- I understood the lesson well, but I need help.
- I'm great, I understood the lesson perfectly well.

Homework: come up with five irregular fractions and select the whole part; No. 10, No. 11 p. 28 - by choice; No. 15, page 28 (a or b) - optional.

Well done! Thanks for the work in the lesson!

Do you want to feel like a sapper? Then this tutorial is for you! Because now we will study fractions - these are such simple and harmless mathematical objects that, in their ability to “endure the brain”, surpass the rest of the algebra course.

The main danger of fractions is that they occur in real life... This is how they differ, for example, from polynomials and logarithms, which can be passed and calmly forgotten after the exam. Therefore, the material presented in this lesson can be called explosive without exaggeration.

A numeric fraction (or just a fraction) is a pair of whole numbers, separated by a forward slash or horizontal bar.

Fractions written with a horizontal bar:

The same fractions, separated by a slash:
5/7; 9/(−30); 64/11; (−1)/4; 12/1.

Usually fractions are written with a horizontal line - this makes them easier to work with, and they look better. The number written at the top is called the numerator of the fraction, and the number written at the bottom is called the denominator.

Any integer can be represented as a fraction with a denominator of 1. For example, 12 = 12/1 - this is the fraction from the above example.

In general, you can put any integer in the numerator and denominator of a fraction. The only limitation is that the denominator must be nonzero. Remember the good old rule: "You cannot divide by zero!"

If the denominator still contains zero, the fraction is called indefinite. Such a record does not make sense and cannot participate in calculations.

Basic property of a fraction

Fractions a / b and c / d are said to be equal if ad = bc.

From this definition it follows that the same fraction can be written in different ways. For example, 1/2 = 2/4, since 1 · 4 = 2 · 2. Of course, there are many fractions that are not equal to each other. For example, 1/3 ≠ 5/4 because 1 4 ≠ 3 5.

A reasonable question arises: how to find all fractions equal to a given one? We give the answer in the form of a definition:

The main property of a fraction is that the numerator and denominator can be multiplied by the same nonzero number. This will give you a fraction equal to the given one.

This is a very important property - remember it. The basic property of a fraction can be used to simplify and shorten many expressions. In the future, it will constantly "pop up" in the form various properties and theorems.

Incorrect fractions. Select whole part

If the numerator is less than the denominator, such a fraction is called correct. Otherwise (that is, when the numerator is greater than or at least equal to the denominator) the fraction is called incorrect, and the whole part can be selected in it.

The whole part is written in a large number in front of the fraction and looks like this (marked in red):

To select the whole part in an irregular fraction, you need to follow three simple steps:

1. Find how many times the denominator fits into the numerator. In other words, find the maximum integer that, when multiplied by the denominator, will still be less than the numerator (in the extreme case, equal). This number will be the whole part, so we write it down in front;
2. Multiply the denominator by the integer part found in the previous step, and subtract the result from the numerator. The resulting "stub" is called the remainder of the division, it will always be positive (in the extreme case, zero). We write it down to the numerator new fraction;
3. We rewrite the denominator without changes.

Well, is it difficult? At first glance, it can be difficult. But with a little practice, you will be doing it almost verbally. Until then, take a look at the examples:

Task. Select the whole part in the specified fractions:

In all examples, the whole part is highlighted in red, and the remainder of the division is highlighted in green.

Pay attention to the last fraction, where the remainder of the division ended up equal to zero... It turns out that the numerator is completely divided by the denominator. This is quite logical, because 24: 6 = 4 is a harsh fact from the multiplication table.

If everything is done correctly, the numerator of the new fraction will necessarily be less than the denominator, i.e. the fraction will become correct. I also note that it is better to select the whole part at the very end of the problem, before recording the answer. Otherwise, the calculations can be significantly complicated.

Going to an improper fraction

There is also a reverse operation, when we get rid of the whole part. It is called going to improper fractions and is much more common because improper fractions are much easier to work with.

Changing to an improper fraction is also done in three steps:

1. Multiply the whole part by the denominator. The result can be quite large numbers, but that shouldn't bother us;
2. Add the resulting number to the numerator of the original fraction. Write the result to the numerator of the improper fraction;
3. Rewrite the denominator - again, no changes.

Here are specific examples:

Task. Convert to an improper fraction:

For clarity, the whole part is highlighted in red again, and the numerator of the original fraction is highlighted in green.

Consider the case when the numerator or denominator of the fraction contains a negative number... For example:

In principle, there is nothing criminal in this. However, working with such fractions can be inconvenient. Therefore, in mathematics, it is customary to take out the minuses for the sign of the fraction.

This is very easy to do if you remember the rules:

1. "Plus and minus gives a minus." Therefore, if there is a negative number in the numerator, and a positive number in the denominator (or vice versa), boldly cross out the minus and put it in front of the whole fraction;
2. "Two negatives make an affirmative". When the minus is in both the numerator and the denominator, we just cross them out - no additional action is required.

Of course, these rules can also be applied in reverse direction, i.e. you can enter a minus under the fraction sign (most often in the numerator).

We deliberately do not consider the case of "plus for plus" - with him, I think, everything is clear. Let's see how these rules work in practice:

Task. Pull out the minuses of the four fractions written above.

Pay attention to the last fraction: there is already a minus sign in front of it. However, it is "burned" according to the "minus by minus gives a plus" rule.

Also, do not move minuses in fractions with a highlighted integer part. These fractions are first converted into incorrect ones - and only then the calculations begin.

Math lesson in grade 4 topic: Isolation of the whole part from an improper fraction Lesson topic: Isolation of the whole part from an improper fraction. Didactic goal: to create conditions for the formation of new educational information. Goals and objectives of the lesson: 1. To form the concept of a mixed number. 2. To form the ability to select a whole part from an incorrect fraction. 3. Develop computational skills. 4. To develop the ability to analyze and solve word problems to find a part of a number and a number in its part. 5. Develop the logical thinking of students. Planned learning outcomes, the formation of UUD: Subject: to expand the concept of a number, to form skills in translating improper fractions into mixed numbers and to apply the knowledge and skills gained when performing various tasks. Metasubject: develop the ability to see a mathematical problem in the context of a problem situation in other disciplines, in the surrounding life. Cognitive UUD: develop ideas about number; the ability to work with a textbook, additional sources of information (analyze, extract the necessary information); the ability to make generalizations, conclusions, establish causal relationships. Communicative UUD: foster respect for each other, develop the ability to enter into an educational dialogue with the teacher, with classmates, observing the norms of speech behavior, the ability to ask questions, listen and answer the questions of others, the ability to put forward a hypothesis. Regulatory UUD: determine the goal of the assignment, learn to plan the stages of work, control your actions, detect and correct mistakes, critically evaluate the results of your work and the work of everyone, based on the available criteria, form the ability to mobilize strength and energy, to overcome obstacles. Personal UUD: to form educational motivation, initiative, develop the skills of competent oral and written mathematical speech, the ability to self-assess their actions. Resources: multimedia projector, presentation. Lesson type: learning new material. Lesson stage Teacher activity Student activity Organizational moment Greeting, checking the readiness for the class, organizing the attention of children. ... They are included in the business rhythm of the lesson. Methods, techniques, forms used Verbal Formed UUD Be able to formulate your thoughts orally (Communicative UUD). Ability to listen and understand the speech of others (Communicative UUD). As you understand from what you have read, today in the lesson we will continue to work on fractions. Guys, in the lesson you should discover new knowledge, but, as you know, every new knowledge is related to what we have already learned. Therefore, we will start with repetition. Verbal counting Updating knowledge and skills Practical Answers are written in a column, we check the answers on the slides. in the lesson to pronounce Be able to sequence of actions (Regulatory UUD). Be able to convert information from one form to another (Cognitive UUD). Be able to formulate your thoughts in oral and written form (Communicative UUD). Blitz survey: What rules did you use when: 1. Found the sum of fractions. 2. Found the difference of fractions. 3. Found the number by part. 4. Found a part by number. Tell the rules. Participate in a conversation with a teacher. Be able to formulate your thoughts orally (Communicative UUD). To be able to navigate in your system of knowledge: to distinguish the new from the already known with the help of a teacher (Cognitive UUD). Ability to listen and understand the speech of others (Communicative UUD). Goal setting and motivation 3. Problem statement Verbal To be able to formulate their thoughts orally (Communicative UUD). Be able to navigate in. ... his system of knowledge: to distinguish the new from the already known with the help of (Cognitive UUD teachers). Children express their options for their decisions. 4. “Formulation of the problem and the purpose of the lesson Select the whole part of this fraction. What do you offer? What do you think, what is the purpose of the lesson we will set? The purpose of the lesson and the topic are formulated by the students. Purpose: Learn to select a whole part from an incorrect fraction Verbal, practical Be able to acquire new knowledge: find answers to questions using the textbook, your life experience and the information received at (Cognitive lesson UUD). Be able to formulate your thoughts orally; listen and understand speech (Communicative of other UUD). So, any improper fraction can be represented as a mixed number. The integer part is a natural number, and the fractional part is a regular fraction. ... ... Algorithm compilation. Verbally, a practical, reproductive analysis at work in the lesson to speak out according to the Be able to collectively draw up a plan (Regulatory UUD). Be able to sequence of actions (Regulatory UUD). Be able to formulate your thoughts verbally and in writing; listen and understand the speech of others (Communicative ECD) Be able to sequence of actions (Regulatory ECD). Be able to perform work according to the proposed plan (Regulatory UUD). to speak a lesson on Mastering new knowledge and methods of mastering 5. Opening new: Explanation on the blackboard. Write down the fraction 16/5 in the form of a quotient. What rule was used to select a whole part from an incorrect fraction To select a whole part from an incorrect fraction: divide the numerator by the denominator with the remainder; record the incomplete quotient received in Be able to make the necessary adjustments to the action after its completion on the basis of its assessment and taking into account the nature of the mistakes made (Regulatory UUD). The ability for self-assessment based on the criterion of the success of educational activities (Personal UUD). based on a whole fraction of a fraction; the remainder is written in the numerator of the fraction; the divisor is written in the denominator of the fraction. 16: 5 = 3 (rest. 1)) 3 - integer 1 - numerator 5 - denominator 16/5 = 3 1/5 Reading the rule in the textbook on page 26, No. 3 - at the blackboard 1 example with explanation. The rest are commented. No. 4 (a, b, c) - independently. Mutual verification. m is an integer, n and b are parts In a fraction, it is always an integer that is the numerator. The guys say the rule to find the whole is to multiply 6. Formulation of new knowledge. Let's confirm our statement with the rule in the textbook. 7. Primary reinforcement 8. Physical education 9. Repetition of what has been learned Writing on the board: m / n = b Select where in the fraction is the whole and the parts? How to find the whole? Applying the rule, we solve the equation. part p. 28, task 10. What additional questions can you ask? P. 27, No. 8 - at the blackboard (a, b, c) - 3 students decide. The rest are solved in pairs (d) Check Analysis of the problem. Self-recording of the decision. Answering the questions, they analyze their work in the lesson Summing up the results of the lesson Verbal, analysis 10. Lesson summary: What did you learn in the lesson? Select whole part from an improper fraction. Verbally descriptive What conclusion did you come to? it is necessary To select the integer part from an improper fraction, divide its numerator by the denominator, the quotient will be the whole part, the remainder will be the numerator, and the divisor will be the denominator of the fraction. And now let's check ourselves, how you learned this. Do it yourself. (mutual check). Homework information Reflection 11. Homework: p. 26, no. 4 (d, e, f), learn the rule on p. 26 and p. 28 №11 If you think that you have understood the topic of today's lesson, then color the leaflet with a green pencil. what not If you think you have mastered the material in yellow enough. If you think that you did not understand the topic of today's lesson in red. Self-assessment Be able to assess the correctness of the performance of an action at the level of an adequate retrospective assessment. (Regulatory UUD). based on the Ability to self-assessment criterion on the success of educational activities (Personal UUD).

Sections: Maths

Class: 4

Basic goals:

1. Form the ability to select a whole part from an irregular fraction.
2. Review the concepts of numerator and denominator, correct and incorrect fractions, mixed numbers.
3. To actualize the ability to select a whole part from an incorrect fraction.

Thinking operations required at the design stage: action by analogy, analysis, generalization.

Equipment:

Demo material:

1) Formula of division with remainder.

Handout:

1) pieces of paper with the task (to stage 2)

2) Detailed sample for self-test (to step 6)

During the classes.

1 Self-determination for learning activities.

Goals:

1. Motivate students for learning activities by reinforcing the situation of success achieved in the previous lesson.
2. Determine the content of the lesson.

Organization of the educational process at stage 1.

Over the course of several lessons, we have worked with some numbers. What numbers did we work with? (With fractional numbers).

What knowledge do we have about these numbers? (We know how to read them, write them down, compare them, solve problems).

I propose to continue our fruitful work. You are ready? (Yes).

Today we will continue to work with fractional numbers. I am sure that we will succeed perfectly well. But first, let's review the material from the previous lessons.

2 Updating knowledge and fixing difficulties in individual activities.

Goals:

1. To update the ability to find right and wrong fractions, mixed numbers, determination of right and wrong fractions, mixed numbers.
2. To actualize the mental operations necessary and sufficient for the perception of new material.
3. Record a situation where students are unable to select the whole part from an incorrect fraction.

Organization of the educational process at stage 2.

What numbers did we meet in the previous lesson? (With mixed numbers).
- What does the mixed number consist of? (From integer and fractional parts).

Fractions and mixed numbers are written on the board.

What groups can the presented numbers be divided into?

Regular fractions ().

What fractions are called correct? (The fraction with the numerator less than the denominator. The regular fraction is less than one).

Incorrect fractions. (… ..)

What fractions are called incorrect? (The fraction with the numerator greater than the denominator or the numerator equal to the denominator).

Which of the irregular fractions can be represented as a natural number?

()

What fraction can be represented as a mixed number? (Incorrect fraction, where the numerator is greater than the denominator).

Determine with the help of the number ray what mixed number the fraction is equal to

Students have a sheet with a task (P-1), one student works at the blackboard, comments.

What is the smallest mixed number? ()

The greatest? ()

What arithmetic operation helped you? (Division. Division with remainder).

Prove it. (On the board: D-1).

12: 7 = 1 (rest 5); 15: 7 = 2 (rest 1); 25: 7 = 3 (rest 4); 31: 7 = 4 (rest 3)

Select the whole part of the fraction, write down the mixed number. Children work on the back of the leaflet. Different answer options are put on the board.

How did you proceed?

3 Identifying the causes of the difficulty and setting the goal of the activity.

Goals:

1. Organize communicative interaction to identify the distinctive property of the task to isolate a whole part from an incorrect fraction.
2. Agree on the topic and purpose of the lesson.

Organization of the educational process at stage 3.

What task did you complete? (It is necessary to select the whole part from the fraction).

How is this task different from the previous one? (The way that helped us to isolate the whole part from an improper fraction is not suitable for a fraction. It is inconvenient to show this fraction on a number ray).

What do we see? (We got different answers.)

Why? (We used different methods. We do not have an algorithm for separating the whole part from an improper fraction).

What is the purpose of our lesson? (Build an algorithm and learn how to separate the whole part from an improper fraction).

Think and formulate the topic of our lesson. ("Isolation of the whole part from an improper fraction").

Well done!

The title of the lesson topic opens on the board.

4 Building a project for getting out of the difficulty.

Target:

1. Organize communicative interaction to build a new way of action to highlight the whole part from an irregular fraction.
2. To fix a new way in a sign and verbal form and with the help of a standard.

Organization of the educational process at stage 4

In what way do you propose to find how many whole units are in a fractional number? (Numerator divided by denominator).

What sign in the notation of the fraction told you how to proceed? (A slash of a fraction is a division sign).

On the desk:

Let's write the fraction as a quotient: 65: 7.

What kind of division is this? (Division with remainder. On the board: D-1).

Find the result. (65: 7 = 9) (rest 2)

What does the quotient 9 and remainder 2 mean in the resulting equality? (The quotient 9 means that 65 contains 9 times 7 and 2 remains).

What will the quotient 9 stand for in a mixed number? (9 is the integer part of the mixed number).

On the desk:

What is the remainder of 2 in the mixed number? (2 is the numerator of the mixed fraction).

On the desk:

What about the denominator? (It remains, does not change).

On the desk:

What mixed number did we get?

Have we completed the task? (Yes).

What math action helped us? (Division with remainder. On the board: D-1).

The teacher returns to the answers on the pieces of paper, summarizes, encourages with words those who did it correctly. In a group form, students display a new method in a symbolic form on pieces of paper. The correct option is selected.

Write down, using the formula for division with remainder (D-1), what mixed number is the fraction?

On the board: D-3

How to select a whole part from an incorrect fraction?

To select the whole part from an improper fraction, you need to divide its numerator by the denominator. The quotient will be the whole part, the remainder will be the numerator, and the denominator will not change.

Well done! Thanks!

Let's check our opinion with the opinion of the textbook. Turn to page 26, Math 4 (Part 2), and read the rule silently first and then aloud.

Were we right? (Yes).

Well done!

Physical minutes (at the teacher's choice).

5 Primary reinforcement in external speech.

Target:

Fix the way of separating the whole part from an irregular fraction in external speech.

Organization of the educational process at stage 5.

Let's repeat the algorithm for extracting the whole part from an improper fraction one more time. D 2

We have compiled an algorithm for separating the whole part from an improper fraction. What is the purpose of our future activities? (Practice).

No. 4 (a, b, c) p. 26 - with commentary on the model.

No. 4 (d, e) page 26 - in pairs.

6 Self-test with self-test.

Target:

1. Organize the students' independent fulfillment of assignments to isolate an entire part from an irregular fraction.
2. Train the ability for self-control and self-esteem.
3. Test your ability to separate the whole part from an incorrect fraction.
4. Contribute to the creation of a situation of success.

Organization of the educational process at stage 6.

You have managed to deduce an algorithm for extracting an integer part from an improper fraction and have practiced solving examples. I think now you can complete the task yourself.

Do it yourself:

No. 3, page 26 - option 1 - columns 1 and 2;

Option 2 - columns 3 and 4;

Anyone who wishes can complete the task of another option.

Students perform work, at the end of which they test themselves on a sample for self-examination. Card P-2 is used.

Test yourself using the self-test pattern and record the test result using the "+" or "?" green handle.

Who made mistakes while completing the assignment? (...)

What is the reason? (...)

Who's got it right?

Well done!

You can organize work on error correction in groups or frontally. Students who have not made a mistake are appointed as counselors.

7 Incorporation and repetition.

Target:

Train the ability to isolate the whole part from an irregular fraction.

Organization of the educational process at stage 7.

Let's try to apply our knowledge when comparing fractions and mixed numbers.

Find the inequality in which you want to compare the right fraction with the wrong one.

What do we do?

Select the whole part from the improper fraction.

Means?!

An incorrect fraction is more correct. We proved this by highlighting the whole part.

Well done!

Finish the task, compare.

Let's check.

8 Reflection of educational activities in the lesson.

Goals:

1. Fix in speech the algorithm for separating the whole part from the incorrect fraction.
2. Record the remaining difficulties and ways to overcome them.
3. Assess your own activities in the lesson.
4. Agree on homework.

Organization of the educational process at stage 8.

What have you learned in the lesson? (Select the whole part from the improper fraction).

What algorithm did we build? (You can say algorithm D-2).

Who had difficulties? How will you act?

Who is pleased with themselves today? Why?

It was difficult for me in the lesson.
- I understood the lesson, but I need training.
- I understood the lesson well, but I need help.
- I'm great, I understood the lesson perfectly well.

Homework: come up with five irregular fractions and select the whole part; No. 10, No. 11 p. 28 - by choice; No. 15, page 28 (a or b) - optional.

Well done! Thanks for the work in the lesson!

has a higher numerator than the denominator. Such fractions are called incorrect.

Remember!

An improper fraction has the numerator equal to or greater than the denominator. That's why improper fraction or equal to one or greater than one.

Any incorrect fraction is always more correct.

How to select a whole part

You can select the whole part of an incorrect fraction. Let's see how this can be done.

To select a whole part from an incorrect fraction, you need to:

1. divide the numerator by the denominator with the remainder;
2. the resulting incomplete quotient is written in the whole part of the fraction;
3. the remainder is written in the numerator of the fraction;
4. the divisor is written into the denominator of the fraction.

Example. Select the whole part from the improper fraction

11

2

.

Remember!

The resulting number above containing an integer and fractional part are called mixed number.

We got a mixed number from an improper fraction, but you can also do the opposite, that is represent a mixed number as an improper fraction.

To represent a mixed number as an improper fraction, you need to:

1. multiply its integer part by the denominator of the fractional part;
2. add the numerator of the fractional part to the resulting product;
3. write the resulting amount from paragraph 2 into the numerator of the fraction, and leave the denominator of the fractional part the same.

Example. Let's represent the mixed number as an improper fraction.