How many equal edges does a cube have? Independent work check
A cube is a geometric figure with 8 vertices. In addition, the cube is characterized by many geometric parameters that make it a special representative of the family of polyhedra.
Cube as a polyhedron
From the point of view of geometry, the cube belongs to the class of polyhedra, representing a special case of a regular geometric figure. In turn, within the framework of this science, regular polyhedra are recognized as those that consist of identical polygons, each of which has correct form: This means that all its sides and angles are equal to each other.In the case of a cube, each face of this figure is indeed a regular polygon, since it is a square. It certainly satisfies the condition that all its angles and sides are equal to each other. Moreover, each cube consists of 6 faces, that is, 6 regular squares.
Each face of the cube, that is, included in its composition, is limited by four equal sides, which are called edges. Moreover, adjacent faces have adjacent edges, so the total number of edges of a cube is not equal to the simple product of the number of faces and the number of edges surrounding them. In particular, each cube has 12 edges.
The point where three edges of a cube meet is called the vertex. In this case, any edges that intersect each other converge at an angle of 90°, that is, they are perpendicular to each other. Each cube has 8 vertices.
Cube properties
Since all the faces of the cube are equal to each other, this provides ample opportunities to use this information to calculate various parameters of a given polygon. Moreover, most formulas are based on the simplest geometric characteristics cubes, including those listed above.So, for example, let the length of one face of a cube be taken as a value equal to a. In this case, you can easily understand that the area of each face can be found by finding the product of its sides: thus, the area of the face of the cube will be a^2. In this case, the total surface area of this polygon will be equal to 6a^2, since each cube has 6 faces.
Based on this information, you can also find the volume of the cube, which, according to geometric formula, will essentially be the product of its three sides - height, length and width. And since the lengths of all these sides, according to the conditions of the problem, are the same, therefore, to find the volume of a cube, it is enough to cube the length of its side: thus, the volume of the cube will be a^3.
Sections: Primary School
Goals.
- Introduce the cube, its elements, development, and application in life. Improve oral and written computational, problem-solving, and quantity conversion skills.
- Develop mental operations, analysis, synthesis, classification, comparison, mathematical speech, attention, general outlook, creative imagination, design abilities.
- Cultivate perseverance, accuracy, mutual assistance, revenue, and the ability to work in a team.
EQUIPMENT: multimedia projector, screen, set of cards for differentiated work, self-assessment sheets, geoplans, magnetic board with geometric material, colored paper, scissors, glue, types of cubes, envelopes with homework, electrified stand, presentation - lesson accompaniment.
1. Organizational moment.
Good morning, guys and guests,
Everyone is welcome to the lesson,
Today's lesson is interesting and difficult,
But for those who work, nothing is impossible.
We have no English and no grammar
Math lesson.
2. Updating basic knowledge
A multimedia presentation appears on the screen.
Consider geometric shapes. They contain mathematical expressions. Calculate value numerical expression, which is :
a) at the intersection of a circle and a rectangle?
360:12=360:(6*2)= 360:6:2=30
What rule did you apply? (Dividing a number by a product)
b) An expression that is contained in the large square but not contained in the small square?
6300:100=63hundred:1hundred=63
c) The expression that is at the intersection of a square and a rectangle?
8*(720-120)=8*600=4800
d) The expression that is in the left semicircle?
25*12=25*(4*3)=100*3=300
What rule did you use?
(Multiplying a number by a product)
e) An expression that is contained in a rhombus, but not contained in a square.
8 dm 4 cm * 3= 84 cm *3= 252 cm = 25 dm 2 cm
- Which of these figures can we find the perimeter of?
For which figures can we determine the perimeter in several ways?
How?
A slide with formulas appears on the screen.
How to find the perimeter of a square?
How to find the area of a rectangle?
How to find the area of a square?
Generalization: You know geometric shapes well and evaluate expressions. Know the rules for finding area and perimeter. We need this to solve problems.
3. Statement of the educational task.
What do these figures have in common (Flat)
What other shapes can there be besides flat ones? (Volumetric)
Which geometric body are you already familiar with? (Parallelepiped)
Who will formulate the topic of today's lesson? (We will get acquainted with a new volumetric geometric body - a cube.)
4. Consolidation of what has been learned
Now let's solve the problem from the textbook.
Read the problem.
Can we immediately find the area of the square? (No)
Why? (We don’t know the side of the square)
How to find out? (36:4=9 mm)
What formula will we use to find the area of a square?
S square = a * a
Shall we solve this problem with commenting?
1) 36:4 = 9 (mm) - length of 1 side
2)9*9 = 81 (mm 2)
Answer: 81 mm 2 is the area of the square.
Draw this square.
What do you know about a rectangle?
*Rectangle is a quadrilateral with all right angles.
*Opposite sides are equal.
*The diagonals of the rectangle are equal.
*The diagonals of the rectangle intersect and are divided in half at the intersection point.
Solve the following problem.
Read the problem.
Can we answer the question right away? (Yes)
How? (area divided by width)
Let's decide at the board.
1) 3440:40=86(m)
Answer: 86 m is the length of the section.
D/v. What do you know about the square?
*A square is a quadrilateral in which all the angles are right and the sides are equal.
*The diagonals of a square are equal.
*The diagonals intersect and are divided in half at the point of intersection.
*The diagonals of a square intersect at right angles.
Compose inverse problems given.
5. Independent work
Option 1.
Land area rectangular shape 3440 m2. The length of the section is 86 m. Find the width?
Can we immediately respond to the task requirement? (Yes)
How? (area divided by length)
Option 1 will solve this problem.
Whoever completes the task will decide additionally. A task of your own ability, by choice?
Let's create a second problem.
Option 2
The length of the rectangular plot is 86 meters, width is 40 m. Find the area of the plot?
What formula will we use? (S square = a * b)
Additionally, solve another card of your choice
Each desk has differentiated tasks.
Red pocket is a task for strong students.
Green pocket - medium difficulty
The blue pocket is for low achievers.
P.T. - increased complexity.
Examination independent work.
When students answer, the named figures appear on the screen.
What is a trapezoid?
*This is a quadrilateral with only 2 sides parallel.
What is a parallelogram?
* This is a quadrilateral in which all opposite sides are equal and parallel.
6. Physical exercise.
Let's rest a little and work verbally with geoplans. (On each student’s desk) You need to recognize the figure from the description. Before we start working using the table, evaluate your knowledge, select a circle desired color. Be careful, we are learning self-control!
(A table appears on the screen)
(One student works on a magnetic board, the rest with geoplans)
7. TEST
Show me this figure on the geoplan.
- This figure has all sides equal and opposite angles equal. (Rhombus)
- All angles are equal to 90 degrees, opposite sides are equal. (Rectangle)
- A figure that consists of a point and two rays emanating from this point? (Corner)
- The figure that is obtained by drawing diagonals in a rectangle or square?
- (Triangle)
- "Crushed" rectangle?
(Parallelogram)
A rhombus with all right angles? (Square)
Checking on a magnetic board
KEY TO THE TEST:
Which figure is the odd one out here? Doesn't apply to polygons? (Corner)
What are the angles? (Acute, obtuse, rectangular)
Self-esteem check:
Who has the same self-esteem?
Who made a mistake in assessing themselves?
What mistakes were made?
CONCLUSION: Be careful, we are learning self-control.
8. Graphic dictation
New concepts appear on the screen.
Now we will do a graphic dictation and find out which geometric body we will get acquainted with in the lesson.
Place a point, mark it with the Latin letter A, then count 5 cells to the right, mark it with the letter B, from B five cells up, mark it with the letter C, from this point 5 cells to the left, mark it with the letter D; from A 3 cells diagonally to the right, mark E; from B diagonally to the right up 3 cells, designate F, from D to the right upward 3 cells diagonally designate K, from C to the right upward diagonally 3 cells, designate M. 9. Getting to know the cube.
What is this geometric body called?
(CUBE)
*This is a foreign word, otherwise it is called hexagon.
Where have you seen the cube? (Rubik's Cube game, game cubes, construction cubes.)
Here is a cube frame made of wire
(Helpers distribute cubes)
Take the cube. place it on your left hand. 1) Is a cube a geometric body? )
What shape is the face of a cube? (
Square
The surface of each cube consists of squares called FACES.
Why is it called a regular hexagon? Count the faces of the cube. How many are there? (6)
Two adjacent faces of a square (polyhedron) are called
RIB.
Use your pen (pointer) to show the edge
Count how many edges does a cube have? (12) Are the ribs equal in length? (Yes)
How many edges intersect (converge) to one vertex? (3)
Count how many vertices does a cube have? (8)
Remove the cubes.
Work in a printed notebook (page 8, tasks 12,13)
Making a cube development according to technological instructions.
Appears on screen:
Now we will make the cube scan ourselves. What is a sweep?
*It's like a cut cube on paper. (Show)
REMIND you to be careful with scissors, glue, and save paper.
Show the cube its vertices, edges, faces.
Is it possible to say that a cube is a rectangular parallelepiped whose length, width and height are equal to each other (YES)
Building from cubes in groups
(groups by color)
Let's remember the rules of working in groups (listen carefully to a friend, speak in turns, do not interrupt a friend, help a friend.
Who do you think the success of our lesson depends on? (From the work of each of us)
You each got a cube. Now, working in groups, try to construct something from cubes.
Options for student work
10. Lesson summary (on an electrified stand)
a) - How many faces does a cube have? (6)
How many vertices does a cube have? (8)
How many k cubes of edges? (12)
What is a regular hexagon called? (cube)
What is the face of a cube? (square)
b) Reflective-evaluative activity
11. Homework.
Complete the task using cards of your choice,
Color the figure that is the net of the cube.
Solve a geometric puzzle.
Thanks for the work!
Answers to p. 23
61. The picture shows the same dice in two positions.
How many different options points are indicated on all sides of the dice? How many sides does a cube have?
There are 6 scoring options on all sides of the cube. The cube has 6 sides. It turns out that each face has one non-repeating set of points.
62. On the left is a drawing of a geometric figure called a CUBE, and on the right is a drawing of a cube. 
What is the difference between drawing a cube and drawing it? How many faces of the cube are visible in the picture? Show the front, right and top faces of the cube in the drawing. In the drawing, show the back, left and bottom faces of the cube.
What shape is the face of a cube? Are all the faces of the cube equal?
What is the vertex of a cube?
How many vertices does a cube have?
What is the edge of a cube? How many edges does a cube have?
How many edges come from one vertex of a cube?
The number of faces - they are shown in the drawing with a dotted line. Only 3 faces are visible in the drawing, but 3 more hidden faces are visible in the drawing.
The face of a cube is a square. All faces of the cube are equal to each other.
The vertex of a cube is the point at which the edges of the cube meet. The cube has 8 such points.
An edge of a cube is one of the sides of a face. A cube has 12 edges.
There are 3 edges coming out of one vertex of the cube.
