Mathematics at every turn Little tricks

Material for students 10 - 14 years old

Some of the challenges below may seem too simple. But in such cases, I advise you not to rush into answering - you can get into trouble. Most of the situations described in the tasks occur in everyday life and are natural. However, they require some ingenuity and ingenuity to resolve them. This explains the name of this group of tasks. Tasks develop attention, thinking, and have a practical focus.
Since problems do not require knowledge of mathematical formulas, etc., they will be of interest to students of different ages, as well as their parents. These problems - of different difficulty levels. Some I use for warm-up, others require more time to solve. I mainly use them when conducting extracurricular activities and when conducting lessons in a playful way.

1. Economical account.

The seller has envelopes in stalls stacked in packs of 100. How can he count 75 envelopes faster?

2. Nails in a box.

How to roughly count the number of nails in a box?

3. Departure day - arrival day.

You left on a business trip on March 24th and returned on March 31st. How many days were you on a business trip?

4. Wood harvesting.

From three-meter and four-meter logs of the same thickness, you need to prepare a wood machine by sawing the logs into pieces one meter long. Which logs are more profitable to saw?

5. Walking along the steps.

How many times is the path up the stairs to 16 - floor of the house longer than the path to 4 - floor?

6. Necessary apartment.

One of the entrances 16 - of the floor building on the ground floor contains apartments with numbers 65, 66, 67, 68. in which entrance and on what floor is the apartment with number 165?

7. Pie without broth.

While in the dining room, you read on the menu that a portion of broth with a pie costs 31 rubles, and half a portion of broth with a pie costs 23 rubles. How much does a pie cost?

8. General safe.

Three engineers share a safe How to lock this safe To only be opened with the simultaneous presence or consent of all three engineers?

9. A pair of gloves.

There are 20 gloves in the chest of drawers in disarray: 5 pairs of browns and 5 pairs of blacks. What is the smallest number of gloves enough to take out without looking from the drawer so that you can probably choose a pair of gloves of the same color among them?

10. Buying tangerines.

Which tangerines - large or small - are more profitable to buy if their peel thickness is the same?

11. Figure volume.

How to calculate the volume of a small object of irregular shape (stone, ingot, etc.)?

12. Set stool.

The floor in the room is not very level, but the stool is completely even, that is, the lower ends of its legs lie in the same plane and form a square. How to install a stool in the easiest way so that it does not swing?

13. Huge hole.

Will you be able to cut a sheet from a school notebook so that you end up with a ring through which an adult can freely crawl?

14. Economical cutting.

Divide 5 apples into 6 people so. so that not a single apple has to be cut into 6 parts.

15. Measure without measurements.

How to cut off a piece of matter 8 m long without measuring instruments at hand?

16. Fire and water.

How to light a match with water and even light a fire?

17. Beetle.

Bug control - Weevil - one of the most important challenges in grain production To successfully fight this bug, you need to know its entire development cycle, body temperature and more.
How to determine the body temperature of a weevil7

18. Box of sugar.

Box of instant sugar - raffinade stands on the edge of the table so. that most of it hangs and it should fall, but it doesn't fall. Why?

Solutions.

1. It is better to count 25 envelopes, then there will be 75 of them left in the pack.
2. It is enough to count the number of nails in 100 g or 1 kg, and then weigh the box with nails and subtract the weight of the empty box. All that remains is to make the appropriate calculations.
3. 31-23=8 (days)
4. It is more profitable to saw shorter logs, since the ratio of the number of cuts to the number of pieces obtained for a short log is less. For example, to obtain 12 pieces from 3-meter logs you need to make 8 cuts. And from 4-meter logs - 9 cuts.
5. To climb to the 16th floor, you need to cover 15 distances between floors, which is 5 times more than the number of the same distances to climb to the 4th floor.
6. Apartment 165 is located in entrance 3 on the 10th floor.
7. Two halves of a broth with pies cost 46 rubles. This is a full portion and another pie. This means the pie costs 46-31=15 (p.)
8. Each of the engineers can cut their own personal lock into the safe, the key to which only they have. Then it will be impossible to open the safe without it.
9. You need to take at least 11 gloves: 6 of them will definitely be the same color, and among them, in turn, 2 will definitely come from different hands.
10. It is more profitable to buy large tangerines, because when the radius of a tangerine increases, its surface area (proportional to the square of the radius) does not increase as significantly as its volume (proportional to the cube of the radius).
11. Let's lower the object, for example, into a jar and pour water into it so that the object is completely covered with water. Then, after removing the object from the jar, we will measure how much the water level has decreased. The volume of the object will be equal to the product of the resulting value per the cross-sectional area of the jar.
12. If you turn the stool "in the plane" of the floor, then there will definitely come a moment when all 4 legs of the stool will touch the floor.
13. By folding the sheet in half, make cuts on both sides of the sheet in turn, the result is a large ring into which an adult can freely crawl.
14. Cut 3 apples in half and 2 apples into 3 pieces each, it will be 6 halves and 6 thirds, which can be equally distributed among 6 people.
15. It is enough to bend a piece of matter in half, then one of the halves in half again and. finally. The quarter that is closer to the middle is bent in half again. The last fold line will divide the length of the piece in a ratio of 3:5.

1 way:
You have to turn the water into ice and make a lens out of it. And then use it to light a fire.
2 way:
Place water between two watch glasses, thus obtaining the lens we need.

1. Place a full glass of bugs, cover it on top and insert a thermometer inside.
2. The box of sugar is incomplete, and it is all concentrated at one edge so that the center of gravity does not extend beyond the edge of the table.

Literature used:

1. Sergeev I.N, Olekhnik S.N, Gashkov S.B. Apply mathematics - M. "Science" 1990.
2. Tasks and exercises to develop students' creative imagination. - M. "Enlightenment", 1985..