Separate the whole part from a fraction. Mixed fractions. Adding two mixed numbers

§ 1 Isolation of an entire part from improper fraction

In this lesson you will learn how to convert an improper fraction into a mixed number by highlighting the whole part, and also vice versa to obtain an improper fraction from a mixed number.

First, let's remember what a mixed number and an improper fraction are.

A mixed number is a special form of writing a number that contains an integer and a fractional part.

An improper fraction is a fraction whose numerator is greater than or equal to its denominator.

Let's consider the problem:

We will divide 8 candies among three children. How much will each person get?

To find out how many candies each child will receive, you need to

But it is not customary to write an improper fraction in the answer. It is first replaced by either one equal to it natural number(when the numerator is divisible by the denominator), or the so-called separation of the whole part from the improper fraction is carried out (when the numerator is not divisible by the denominator).

Isolating an integer part from an improper fraction is replacing the fraction with an equal mixed number.

To separate the whole part from an improper fraction, you need to divide the numerator by the denominator with a remainder. In this case, the incomplete quotient will be the whole part, the remainder will be the numerator, and the divisor will be the denominator.

Let's return to the task.

So, we divide 8 by 3 with a remainder, we get 2 in the incomplete quotient and 2 in the remainder.

§ 2 Representation of a mixed number as an improper fraction

Let's do the following task:

Divide 49 by 13, we get 3 in the incomplete quotient (this will be the integer part) and the remainder 10 (we will write this in the numerator of the fractional part).

Representation skills are useful for performing various operations with mixed numbers. mixed numbers in the form of improper fractions. It's time to figure out how such a translation is carried out.

To represent a mixed number as an improper fraction, you need to multiply the denominator of the fraction by the whole part and add the numerator to the resulting product. As a result, we get a number that will be the numerator of the new fraction, and the denominator remains unchanged.

The first step is to multiply the whole part of 5 by the denominator 7, we get 35.

The second step is to add the numerator 4 to the resulting product 35, it will be 39.

Now let's write 39 in the numerator and leave 7 in the denominator.

Thus, in this lesson you learned how to convert an improper fraction into a mixed number; to do this, you need to divide the numerator by the denominator with a remainder. Then the incomplete quotient will be the integer part, the remainder will be the numerator, and the divisor will be the denominator of the fractional part of the mixed number.

You also learned about representing a mixed number as an improper fraction. In order to represent a mixed number as an improper fraction, you need to multiply the denominator of the fractional part of the mixed number by the whole part and add the numerator to the resulting product.

List of used literature:

1. Mathematics 5th grade. Vilenkin N.Ya., Zhokhov V.I. and others. 31st ed., erased. - M: 2013.
2. Didactic materials in mathematics 5th grade. Author - Popov M.A. - year 2013
3. We calculate without errors. Work with self-test in mathematics grades 5-6. Author - Minaeva S.S. - year 2014
4. Didactic materials for mathematics grade 5. Authors: Dorofeev G.V., Kuznetsova L.V. - 2010
5. Tests and independent work in mathematics grade 5. Authors - Popov M.A. - year 2012
6. Mathematics. 5th grade: educational. for general education students. institutions / I. I. Zubareva, A. G. Mordkovich. - 9th ed., erased. - M.: Mnemosyne, 2009

Sections: Mathematics

Class: 4

Basic goals:

1. Develop the ability to isolate the whole part from an improper fraction.
2. Review the concepts of numerator and denominator, proper and improper fractions, mixed numbers.
3. Update the ability to isolate the whole part from an improper fraction.

Mental operations necessary at the design stage: action by analogy, analysis, generalization.

Equipment:

Demo material:

1) Division formula with remainder.

Handout:

1) leaflets with the task (for stage 2)

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

During the classes.

1 Self-determination for educational activities.

Goals:

1. Motivate students to educational activities by securing success situations, achieved at previous lesson.
2. Determine the content of the lesson.

Organization educational process at stage 1.

Over the course of several lessons we 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, write, compare, solve problems).

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

Today we will continue working with fractions. I am sure that everything will work out great for you and me. But first, let's review the material from previous lessons.

2 Updating knowledge and recording difficulties in individual activities.

Goals:

1. Update the ability to find proper and improper fractions, mixed numbers, determine proper and improper fractions, mixed numbers.
2. Update mental operations, necessary and sufficient for the perception of new material.
3. Fix a situation when students cannot isolate the whole part from an improper fraction.

Organization of the educational process at stage 2.

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

Fractions and mixed numbers are written on the board.

What groups can the presented numbers be divided into?

Proper fractions ().

What fractions are called proper? (A fraction whose numerator is less than its denominator. A proper fraction is less than one).

Improper fractions. (…..)

What fractions are called improper? (A fraction in which the numerator is greater than the denominator or the numerator is equal to the denominator).

Which improper fractions can be represented as a natural number?

()

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

Using the number line, determine which mixed number the fraction is equal to

Students have a sheet with a task (P-1), one student works at the board and 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 and write down the mixed number. Children work for back side leaf. Different answer options are put on the board.

How did you act?

3 Identifying the causes of difficulties and setting goals for the activity.

Goals:

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

Organization of the educational process at stage 3.

What task were you doing? (You need to select the whole part from the fraction).

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

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

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

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

Think and formulate the topic of our lesson. (“Isolating the whole part from an improper fraction”).

Well done!

The name of the lesson topic appears on the board.

4 Construction of a project for getting out of the difficulty.

Target:

1. Organize communicative interaction to build a new method of action to isolate a whole part from an improper fraction.
2. Fix the new method in symbolic and verbal form and using a standard.

Organization of the educational process at stage 4

How do you propose to find how many whole units are in a fraction? (Numerator divided by denominator).

What sign in the fraction notation told you how to act? (The fraction line is a division sign).

On the desk:

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

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

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

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

What does the quotient 9 mean in a mixed number? (9 is the integer part of a mixed number).

On the desk:

What does the remainder 2 mean in a mixed number? (2 is the numerator of the mixed number 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 mathematical activity helped us? (Division with remainder. On the board: D-1).

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

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

On the board: D-3

How to separate the whole part from an improper fraction?

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

Well done! Thank you!

Let's check our opinion with the opinion of the textbook. Turn to page 26, Mathematics 4 (Part 2), read the rule first to yourself, and then out loud.

Were we right? (Yes).

Well done!

Physical exercise (at the teacher's choice).

5 Primary consolidation in external speech.

Target:

Fix a method for isolating the whole part from an improper 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 once again. D 2

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

No. 4 (a,b,c) page 26 – with commentary according to the sample.

No. 4 (d, e) p. 26 – in pairs.

6 Self-control with self-test.

Target:

1. Organize self-execution Students will complete tasks on isolating the whole part from an improper fraction.
2. Train the ability to self-control and self-esteem.
3. Test your ability to isolate the whole part from an improper fraction.
4. Contribute to creating a situation of success.

Organization of the educational process at stage 6.

You were able to derive an algorithm for separating the whole part from an improper fraction and practiced solving examples. I think now you can complete the task yourself.

Do it yourself:

No. 3 p. 26 – 1st option – 1st and 2nd column;

Option 2 – 3rd and 4th column;

Anyone who wishes can complete the task in another way.

Students perform work, after which they test themselves using a sample for self-test. Card R-2 is used.

Test yourself using the self-test sample and record the test result using the “+” or “?” green pen.

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

What is the reason? (...)

Who has everything right?

Well done!

You can organize error correction work in groups or frontally. Students who have not made mistakes are appointed as consultants.

7 Inclusion in the knowledge system and repetition.

Target:

Train your ability to isolate the whole part from an improper fraction.

Organization of the educational process at stage 7.

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

Find an inequality in which you need to compare a proper fraction with an improper fraction.

What do we do?

Let's select the whole part from the improper fraction.

Means?!

An improper fraction is larger than a proper fraction. We proved this by highlighting the whole part.

Well done!

Finish the task, compare.

Let's check.

8 Reflection on learning activities in the lesson.

Goals:

1. Fix in speech an algorithm for separating the whole part from an improper fraction.
2. Record the difficulties that remain and ways to overcome them.
3. Evaluate your own activities in the lesson.
4. Agree on homework.

Organization of the educational process at stage 8.

What did you learn in the lesson? (Isolate the whole part from an improper fraction).

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

Who had difficulties? How will you act?

Who is happy with themselves today? Why?

I had a hard time in class.
- 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.

Homework: come up with five improper fractions and highlight the whole part; No. 10, No. 11 p. 28 – optional; No. 15 p. 28 (a or b) – optional.

Well done! Thanks for your work in class!

In this article we will talk about mixed numbers. First, let's define mixed numbers and give examples. Next, let's look at the connection between mixed numbers and improper fractions. After that, we'll show you how to convert a mixed number to an improper fraction. Finally, let's study the reverse process, which is called separating the whole part from an improper fraction.

Page navigation.

Mixed numbers, definition, examples

Mathematicians agreed that the sum n+a/b, where n is a natural number, a/b is a proper fraction, can be written without the addition sign in the form. For example, the sum 28+5/7 can be briefly written as . Such a record was called mixed, and the number that corresponds to this mixed record was called a mixed number.

This is how we come to the definition of a mixed number.

Definition.

Mixed number- this is the number equal to the sum natural number n and the correct common fraction a/b , and written as . In this case, the number n is called whole part of the number, and the number a/b is called fractional part of a number.

By definition, a mixed number is equal to the sum of its integer and fractional parts, that is, the equality is valid, which can be written like this: .

Let's give examples of mixed numbers. A number is a mixed number, the natural number 5 is the integer part of the number, and the fractional part of the number. Other examples of mixed numbers are .

Sometimes you can find numbers in mixed notation, but having an improper fraction as a fraction, for example, or. These numbers are understood as the sum of their integer and fractional parts, for example, And . But such numbers do not fit the definition of a mixed number, since the fractional part of mixed numbers must be a proper fraction.

The number is also not a mixed number, since 0 is not a natural number.

The relationship between mixed numbers and improper fractions

Follow connection between mixed numbers and improper fractions best with examples.

Let there be a cake and another 3/4 of the same cake on the tray. That is, according to the meaning of addition, there are 1+3/4 cakes on the tray. Having written down the last amount as a mixed number, we state that there is a cake on the tray. Now cut the whole cake into 4 equal parts. As a result, there will be 7/4 of the cake on the tray. It is clear that the “quantity” of the cake has not changed, so .

From the example considered, the following connection is clearly visible: Any mixed number can be represented as an improper fraction.

Now let there be 7/4 of the cake on the tray. Having folded a whole cake from four parts, there will be 1 + 3/4 on the tray, that is, a cake. From this it is clear that .

From this example it is clear that An improper fraction can be represented as a mixed number. (In the special case, when the numerator of an improper fraction is divided evenly by the denominator, the improper fraction can be represented as a natural number, for example, since 8:4 = 2).

Converting a mixed number to an improper fraction

To perform various operations with mixed numbers, the skill of representing mixed numbers as improper fractions is useful. In the previous paragraph, we found out that any mixed number can be converted into an improper fraction. It's time to figure out how such a translation is carried out.

Let us write an algorithm showing how to convert a mixed number to an improper fraction:

Let's look at an example of converting a mixed number to an improper fraction.

Example.

Express a mixed number as an improper fraction.

Solution.

Let's perform all the necessary steps of the algorithm.

A mixed number is equal to the sum of its integer and fractional parts: .

Having written the number 5 as 5/1, the last sum will take the form .

To finish converting the original mixed number into an improper fraction, all that remains is to add fractions with different denominators: .

A short summary of the entire solution is: .

Answer:

So, to convert a mixed number to an improper fraction, you need to perform the following chain of actions: . Finally received , which we will use further.

Example.

Write the mixed number as an improper fraction.

Solution.

Let's use the formula to convert a mixed number to an improper fraction. In this example n=15 , a=2 , b=5 . Thus, .

Answer:

Separating the whole part from an improper fraction

It is not customary to write an improper fraction in the answer. The improper fraction is first replaced either by an equal natural number (when the numerator is divisible by the denominator), or the so-called separation of the whole part from the improper fraction is carried out (when the numerator is not divisible by the denominator).

Definition.

Separating the whole part from an improper fraction- This is the replacement of a fraction with an equal mixed number.

It remains to find out how you can isolate the whole part from an improper fraction.

It's very simple: the improper fraction a/b is equal to a mixed number of the form, where q is the partial quotient, and r is the remainder of a divided by b. That is, the integer part is equal to the incomplete quotient of dividing a by b, and the remainder is equal to the numerator of the fractional part.

Let's prove this statement.

To do this, it is enough to show that . Let's convert the mixed into an improper fraction as we did in the previous paragraph: . Since q is an incomplete quotient, and r is the remainder of dividing a by b, then the equality a=b·q+r is true (if necessary, see

Lesson summary in 5th grade

“Mixed numbers. Isolating the whole part from an improper fraction"

During the classes

Organizing time. Greetings.

We will conduct an oral count and break all the records.

Verbal counting.

Find the mistakes

Proper fractions.

b)

Let's write down on the board what we can't compare yet.

2. Perform division:

45: 9=5 ; 0: 67=0; 234: 1=234;

567: 567=1; 34:17=2; a:a=1;

3. Perform division with remainder:

6 = 2 (remaining 2)

3 = 8 (remaining 1)

48: 9 = 5 (remaining 3)

Follow these steps:

We can't solve the last example, so let's write it down.

Explanation of new material

What is shown in the picture? How many parts was the cake divided into? How many parts did you take? Express it as a fraction.

What's in this picture? You can see that the cake is on different trays. How many pieces are on the first tray? Second?

Can be expressed as a number like this:

1 – integer part, - fractional part.

The sum of the integer and fractional parts is calledmixed number .

Determine from the picture which mixed number is equal to the fraction?

That is, we saw the connection between an improper fraction and a mixed number.

Let's draw conclusions: we can turn an improper fraction into a mixed number, i.e. as they say in mathematics, to separate the whole part from an improper fraction.

The rule for separating the whole part from an improper fraction:

Divide the numerator by the denominator with the remainder

The incomplete quotient will be the whole part

The remainder is the numerator, and the divisor is the denominator of the fraction.

Work on the topic of the lesson.

Select the whole part from an improper fraction (along with class):

Select the whole part from an improper fraction (at the board)

Compare

Historical information.

In the old days, coins in denominations of less than one kopeck were used in Rus':

penny - k. Andhalf - k.

Other coins also had names:

3 k. - altyn, 5 k. - nickel, 15 k. - five altyn,

10 kopecks - ten kopecks, 20 kopecks - two kopecks,

25 k. - a quarter, 50 k. - fifty kopecks.

Independent work

How can you imagine

1 hryvnia, 1 altyn, three half rubles .

Reflection

What's your mood?

Write the fraction that best matches your knowledge:

2 (can not understand anything)

2 (it was interesting, but not clear)

3 (difficult, the topic is not interesting)

3 (it was difficult, but I will definitely make an effort to study the topic)

4 (some examples caused difficulties)

4 (everything is clear, but I can’t help)

5 (everything is clear, I can help others)

I hope your grade will only increase with each lesson! And to get a grade of 5, you need to work not only in class, but also at home.

Homework.

Sections: Mathematics

Class: 4

Basic goals:

1. Develop the ability to isolate the whole part from an improper fraction.
2. Review the concepts of numerator and denominator, proper and improper fractions, mixed numbers.
3. Update the ability to isolate the whole part from an improper fraction.

Mental operations necessary at the design stage: action by analogy, analysis, generalization.

Equipment:

Demo material:

1) Division formula with remainder.

Handout:

1) leaflets with the task (for stage 2)

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

During the classes.

1 Self-determination for educational activities.

Goals:

1. Motivate students for learning activities by consolidating 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 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, write, compare, solve problems).

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

Today we will continue working with fractions. I am sure that everything will work out great for you and me. But first, let's review the material from previous lessons.

2 Updating knowledge and recording difficulties in individual activities.

Goals:

1. Update the ability to find proper and improper fractions, mixed numbers, determine proper and improper fractions, mixed numbers.
2. Update mental operations necessary and sufficient for the perception of new material.
3. Fix a situation when students cannot isolate the whole part from an improper fraction.

Organization of the educational process at stage 2.

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

Fractions and mixed numbers are written on the board.

What groups can the presented numbers be divided into?

Proper fractions ().

What fractions are called proper? (A fraction whose numerator is less than its denominator. A proper fraction is less than one).

Improper fractions. (…..)

What fractions are called improper? (A fraction in which the numerator is greater than the denominator or the numerator is equal to the denominator).

Which improper fractions can be represented as a natural number?

()

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

Using the number line, determine which mixed number the fraction is equal to

Students have a sheet with a task (P-1), one student works at the board and 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 and write down the mixed number. Children work on the back of the piece of paper. Different answer options are put on the board.

How did you act?

3 Identifying the causes of difficulties and setting goals for the activity.

Goals:

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

Organization of the educational process at stage 3.

What task were you doing? (You need to select the whole part from the fraction).

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

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

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

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

Think and formulate the topic of our lesson. (“Isolating the whole part from an improper fraction”).

Well done!

The name of the lesson topic appears on the board.

4 Construction of a project for getting out of the difficulty.

Target:

1. Organize communicative interaction to build a new method of action to isolate a whole part from an improper fraction.
2. Fix the new method in symbolic and verbal form and using a standard.

Organization of the educational process at stage 4

How do you propose to find how many whole units are in a fraction? (Numerator divided by denominator).

What sign in the fraction notation told you how to act? (The fraction line is a division sign).

On the desk:

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

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

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

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

What does the quotient 9 mean in a mixed number? (9 is the integer part of a mixed number).

On the desk:

What does the remainder 2 mean in a mixed number? (2 is the numerator of the mixed number 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 mathematical activity helped us? (Division with remainder. On the board: D-1).

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

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

On the board: D-3

How to separate the whole part from an improper fraction?

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

Well done! Thank you!

Let's check our opinion with the opinion of the textbook. Turn to page 26, Mathematics 4 (Part 2), read the rule first to yourself, and then out loud.

Were we right? (Yes).

Well done!

Physical exercise (at the teacher's choice).

5 Primary consolidation in external speech.

Target:

Fix a method for isolating the whole part from an improper 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 once again. D 2

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

No. 4 (a,b,c) page 26 – with commentary according to the sample.

No. 4 (d, e) p. 26 – in pairs.

6 Self-control with self-test.

Target:

1. Organize students’ independent completion of the task of isolating the whole part from an improper fraction.
2. Train the ability to self-control and self-esteem.
3. Test your ability to isolate the whole part from an improper fraction.
4. Contribute to creating a situation of success.

Organization of the educational process at stage 6.

You were able to derive an algorithm for separating the whole part from an improper fraction and practiced solving examples. I think now you can complete the task yourself.

Do it yourself:

No. 3 p. 26 – 1st option – 1st and 2nd column;

Option 2 – 3rd and 4th column;

Anyone who wishes can complete the task in another way.

Students perform work, after which they test themselves using a sample for self-test. Card R-2 is used.

Test yourself using the self-test sample and record the test result using the “+” or “?” green pen.

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

What is the reason? (...)

Who has everything right?

Well done!

You can organize error correction work in groups or frontally. Students who have not made mistakes are appointed as consultants.

7 Inclusion in the knowledge system and repetition.

Target:

Train your ability to isolate the whole part from an improper fraction.

Organization of the educational process at stage 7.

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

Find an inequality in which you need to compare a proper fraction with an improper fraction.

What do we do?

Let's select the whole part from the improper fraction.

Means?!

An improper fraction is larger than a proper fraction. We proved this by highlighting the whole part.

Well done!

Finish the task, compare.

Let's check.

8 Reflection on learning activities in the lesson.

Goals:

1. Fix in speech an algorithm for separating the whole part from an improper fraction.
2. Record the difficulties that remain and ways to overcome them.
3. Evaluate your own activities in the lesson.
4. Agree on homework.

Organization of the educational process at stage 8.

What did you learn in the lesson? (Isolate the whole part from an improper fraction).

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

Who had difficulties? How will you act?

Who is happy with themselves today? Why?

I had a hard time in class.
- 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.

Homework: come up with five improper fractions and highlight the whole part; No. 10, No. 11 p. 28 – optional; No. 15 p. 28 (a or b) – optional.

Well done! Thanks for your work in class!