Mark the indicated part on the segment with a colored pencil.

>> Lesson 19. Measurements and fractions

Man needs measurements at every step. Without measurements, he would not be able to sew clothes, build a house, or launch a spaceship. Man has learned to measure many quantities, such as length, area, volume, mass, time, temperature.

To measure a quantity, you need to find out how many times it contains the selected unit of measurement. However, the measure does not always fit into the measured value an integer number of times. For example, the measure e is contained in the segment AB more than 5, but less than 6 times:

The area of ​​the figure in the figure is greater than 4, but less than 5 square units:

5 apples were divided equally between three children. Everyone got one apple and some other part of the apple:

1 < n < 2

In all such cases, natural numbers allow you to indicate only an approximate value of a quantity. To find its exact value, you need to learn to express in numbers parts of units of counting or measurement (apple, segment, square, etc.). Such numbers are called in fractions.

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Lesson objectives. During the lesson, students will be able to:

• formulate a question using a key;
• find the answer to the question during the research;
• gain an understanding of fractions as numbers expressing parts of units of counting or measurement;
• work in a group, improving communication skills.

Materials:“how?” key, paper questions, worksheets, shape models (rectangle, circle); for each group 4 circles, scissors; a card with the definition of the concept of “fractions”, models of figures for the “Application” stage, cards with fractions written on them.

During the classes

I. Review.

Remember the topic we worked on in math class. (Values. Area estimate.)

What is magnitude? (This is something that can be measured and the result of the measurement is expressed as a number.)

Today in class we will learn something new.

Practical work.

You have figures on the tables. Take a rectangle. Divide it into 2 parts without using a ruler or pencil. (Students find a way out: divide by bending.)

How many parts is the rectangle divided into? (Into 2 parts)

Shade 1 part.

How many parts are not painted?

Take a circle. Divide it into 4 parts without using a ruler or pencil. (The students do the same.)

How many parts did you get? (4 parts)

Paint over 1 part. What part of the circle is this? (fourth)

How many parts are not painted? (3 parts)

II. Motivation.

One student, whose name was Petya, was solving the problem. But I found it difficult to decide.

Let's help him.

Task. Divide 4 apples equally between three children.

You have object models on your tables. (circles instead of apples)

Using scissors, try dividing 4 circles equally. (Students work in groups).

Conclusion: Each child will receive 1 whole apple and a third part.

How can Petya write down the answer to this problem in numbers?

What's the difficulty? Can we write a part as a number? (No)

With a key "How?" formulate a question for the lesson.

(The lesson question is written on a question paper and posted on the board).

III. Study.

To answer the question, let's work in groups.

Read the plan on the board.

1. Work according to plan.

1. Mark the indicated part on the segment with a marker.
2. Write your own way of representing this part using a number.

2. Work in groups.

The groups are given worksheets with the task.

IV. Information exchange.

1. Each group reports according to the proposed plan. Children offer their own way of designating a part using a number. (Pay attention to the correct entry) The teacher summarizes all the answers.

What do all the proposed tasks have in common? (The segment had to be divided into parts and one such part should be selected).

2. Formulating a conclusion.

Conclusion: in mathematics there are numbers that express parts of units of counting (measurement). They're called - fractions.

(The number below the line shows how many equal parts the segment is divided into.

The number above the line shows how many such pieces were taken.)

How to write down the highlighted parts correctly? ()

The teacher returns to the task from the “Motivation” stage.

How can Petya write down the answer to the problem? (One whole apple and one third of an apple is).

V. Application.

Children are offered various models of figures that are divided into parts.

Determine which part is shaded.

How to write as a number?

VI. Reflection.

Did we manage to answer the lesson question?

What are fractions? (These are numbers expressing parts of units of counting or measurement).

Measurements and fractions. Mathematics 4th grade

5. Divide the rectangles into 3 equal parts in different ways. Color the third part of each of them with a colored pencil. Are these parts equal in area? Prove it.

6. Mark the indicated part on the segment with a colored pencil and come up with your own way of designating these parts using numbers.

7. Solve the equations:

32 x - 59 = 453 y: 23 + 312 = 390 7035: (120 - z) = 67

8. In the school garden, 900 flowers were planted in the flower beds, 630 of them were tulips, and the rest were roses. In the flowerbeds with tulips, 35 flowers were planted per flowerbed, and in the flowerbeds with roses - 30 flowers. How many flower beds did you get?

9. a) 306 24: 72 - (35 280: 7 - 63 80): 97;

b) (2005 8 - 704 21 + 6400: 800): (702 860 - 603 704).

10. Literary quiz “In the animal world.”

a) Decipher the name of the handsome and courageous black fox from the story by E. Seton-Thompson?

b) Which writer told the story about chanterelle bread? Check your answer by arranging the example answers in descending order and matching them with the corresponding letters. What other stories by this writer do you know?

11. How many minutes in one hour? How many seconds are in one minute? Express: a) in hours and minutes: 142 minutes, 256 minutes, 1032 minutes; b) in minutes and seconds: 68 s, 608 s, 6008 s.

12*. There are 5 chain links in front of the master. They must be connected into one chain without using additional rings. What is the smallest number of rings that a master needs to unforge for this, and then forge them again?