Master class “Simple. Complex. Interesting”
Master Class
"Just. Difficult. Interesting"
(Slide 1)
I will begin my master class with the following epigraph: “The subject of mathematics is so serious that it is useful not to miss the opportunity to make it a little entertaining” (Blaise Pascal). So, the master class is called “Simple. Difficult. Interesting."
The practice of my work has shown that the more interesting the game actions that I use in lessons, the more imperceptibly and effectively the acquired knowledge is consolidated.
Children are active in the perception of problems - jokes, puzzles, logical exercises, so in my work, to activate children, I try to use entertaining material, because it not only entertains children, gives them the opportunity to relax, switch, but also makes them think, develops initiative, stimulates development non-standard thinking, logic, imagination. After all, no modern science can do without mathematics.
Oh, earthly mathematics,
Be proud of yourself, beautiful one.
You are the mother of all sciences,
And they value you.
Dear colleagues, I invite you to the wonderful world of mathematics, where it is simple, difficult, and very interesting.
Try your hand at math all-around.
(Slide 2)
- Warm-up
(carried out in order to maintain a good mood, good spirits, and a mathematical attitude).
I offer you problems, the correct solution of which most often does not require any additional knowledge - carefully read the conditions of the problem and try to avoid the traps set.
(Slide 3)
- One gentleman wrote about himself: “...I have twenty-five fingers on one hand, the same number on the other, and ten on my feet...” Why is he such a freak? (Answer: Mr. didn’t put a colon in one place. Which one?)
(Slide 4)
(Slide 5)
- Two travelers approached the river at the same time. There was a boat tied to the shore, in which only one person could cross. The travelers did not know how to swim, but each of them managed to cross the river and go their own way. How could this happen? (Answer: They approached the river from different sides.)
(Slide 6)
- Why is a hairdresser in Geneva more willing to cut two Frenchmen's hair than one German's? (Answer: Because he will earn more.)
- "Origametry". (Slide 7)
- Let's look at an ordinary sheet of paper as a means of teaching one of the complex subjects - geometry. I want to share with you how the art of origami helps solve many geometric problems. Now we will do a little work with you:
Take an orange triangle, let's try to bend it to build a bisector of one of the corners. Construct the bisectors of the other two angles. Unfold the sheet of paper. Look carefully at the fold marks. What can you say?
All three folds passed through one point.
If you performed all the steps correctly, then the bisectors intersected at one point.
Take the blue triangle. We will do similar work, only we will bend it a little differently. As a result, we built the height. Repeat for the other two sides. Unfold the sheet of paper. What can you say now?
All three folds passed through one point.
If you performed all the steps correctly, then the heights also intersected at one point.
Take the green triangle. To build the next line, we need to divide the side of the triangle in half; to do this, we combine the two vertices of the triangle and make a slight fold, thereby marking the middle of the side. Now we bend the triangle so that the fold line passes through the vertex of the triangle and the marked point. As you remember, such a segment is called the median of a triangle. Construct two more medians of the triangle. Let's look at the drawing of the lines again and make sure that the medians also intersect at one point.
Looking at all three triangles again, what general conclusion can be drawn?
So, within one minute, we have learned how to construct the main lines in a triangle, and also formulated theorems about the three remarkable points of the triangle. Most importantly, by completing these practical tasks, we mastered the simplest techniques of the art of origami - folding paper figures.
(Slide 
- "Tangram":
For the next task you will need both ingenuity and knowledge of the proverb “Measure twice, cut once.” A set is given consisting of seven figures: three pairs of isosceles right triangles and one square.
Exercise.
From these seven figures, form a square and a triangle.
Answer:
(Slide 9)
- Puzzles with matches. (Slide 10)
A box of matches is an excellent tool for geometric entertainment that requires resourcefulness and ingenuity. You can make all sorts of rectilinear figures from matches, and transform one figure into another by rearranging the matches.
(Slide 11)
- There are 6 matches on the table. Arrange them so that in each horizontal row there are: a) 4, b) 6. (Slide 12)
(Slide 13)
- From six matches, make 4 triangles with sides equal to the length of the match. (Answer: The solution can only be obtained by “exiting” into space.) (Slide 14)
(Slide 15)
- The figure shown in the figure is made up of 8 matches superimposed on each other. Remove two matches so that 3 squares remain.
(Slide 16)
- Correct the equation so that it becomes true without touching a single match (you cannot light it, move it, move it, etc.).
(Slide 17)
- "Mathematical Disappearance":
There are 3 triangles on the table. Remove 2 matches so that there are no triangles.
(Answer: We remove 2 matches and make an equal sign out of them. One triangle minus one triangle equals zero - there are no more triangles.) (Slide 18)
(Slide 19)
- Everything ingenious is simple!
“Fun Math” can make the most “boring” things in the world interesting, like the multiplication tables.
But multiplying by 9 on your fingers is something special. The photo above demonstrates the multiplication of 9 by 7. We bend the 6th finger and immediately see the answer: the first number is the number of fingers to the left of the bent one, the second is to the right. Total 54!
(Slide 20) Conclusion:
During our lives we solve many problems. And if each separately solved problem is considered like a blooming flower, then as a result we will get a huge, beautiful bouquet.
May all the tasks that confront you be solved, and may the bouquet be made only of blooming flowers.
Thank you for your fruitful work.
