Mathematics at every turn. Little tricks.

Material for students 10 - 14 years

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

1. Savings account.

The seller in the kiosk envelopes are stacked in packs of 100 pieces. How can he count 75 envelopes faster?

2. Nails in the drawer.

How to calculate the number of nails in a box?

3. The day of departure is the day of arrival.

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

4. Firewood.

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

5. Walk the steps.

How many times is the 16th floor of a house longer than the 4th floor?

6. The right apartment.

In one of the entrances of the 16-storey building on the first floor there are apartments with numbers 65, 66, 67, 68. In which entrance and on which floor is the apartment number 165?

7. Pie without broth.

While in the dining room, you read on the menu that a serving of broth with a cake costs 31 rubles, and a half serving of broth with a cake costs 23 rubles. How much is a cake?

8. Shared safe.

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

9. A pair of gloves.

In the drawer of the drawer are in a mess of 20 gloves: 5 pairs of brown and 5 pairs of black. What is the least number of gloves is enough to get without looking out of the box, so you can definitely choose a pair of gloves of the same color?

10. Buying tangerines.

Which tangerines – large or small – are more profitable to buy if the skin thickness is the same?

11. Volume of figure.

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

12. Set up a stool.

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

13. Huge hole.

Will you be able to cut a sheet from a school notebook so that the end result is a ring through which an adult can freely climb?

14. Economical cutting.

Divide 5 apples into 6 people so that no apple has to be cut into 6 pieces.

15. Measure without measurement.

How can a piece of matter 8 m long be cut off from a piece 5 m long without measuring instruments at hand?

16. Fire and water.

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

17. Beetle.

The fight against the bug - weevil - is one of the most important problems in the production of grain. To successfully fight this bug. You need to know the whole cycle of its development, body temperature and much more.
How to determine the body temperature of a weevil7

18. A box of sugar.

A 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 in the pack.
2. It is enough to count the number of nails per 100 g or 1 kg, and then weigh the box with nails and subtract the weight of the empty box. It remains to make the appropriate calculations.
3. 31-23=8 days
4. It is more profitable to cut shorter logs, since the ratio of the number of sawings to the number of pieces obtained for a short log is smaller. For example, to obtain 12 pieces from 3-meter logs, you need to make 8 saws. And of the 4-meter - 9 saws.
5. To climb to the 16th floor, you need to overcome 15 distances between floors, which is 5 times the number of the same distances for climbing to the 4th floor.
6. Apartment 165 is located in 3 entrance on the 10th floor.
7. Two halves of a serving of broth with cakes cost 46 r. It's a full serving and another cake. So the cake costs 46-31=15 (R).
8. Each of the engineers can enter his personal lock into the safe, the key to which only he has. It would be impossible to open the safe without it.
9. You need to take at least 11 gloves: 6 of them will necessarily be the same color, and among them, in turn, 2 will fall on different hands.
10. It is more profitable to buy large mandarins, because with an increase in the radius of the mandarin, the surface area (proportional to the square of the radius) does not increase as much as its volume (proportional to the cube of the radius).
11. Let’s drop an object, for example, in a jar and pour water into it so that the object is completely covered with water. Then, taking the object out of the jar, measure how much the water level has decreased. The volume of the object will be equal to the product of the obtained value per section area of the bank.
12. If you turn the stool "in the plane" of the floor, then there will come a time when all 4 legs of the stool will touch the floor.
13. Folding the sheet in half, make incisions on both sides of the sheet alternately. You will get a large ring into which an adult can freely climb.
14. Cut 3 apples in half and 2 apples into 3 pieces each. It turns out 6 halves and 6 thirds, which can be equally distributed to 6 people.
15. It is enough to bend a piece of matter in half, then one of the halves again in half and finally. That quarter, which is closer to the middle, bend in half again. The last line of the fold will divide the length of the piece in the ratio of 3:5.

1 way:
Turn water into ice and make a lens out of it. And then using it to light a fire.
2 way:
Put water between two watchglasses, thus obtaining the desired lens.

1. Dial 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 go over 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 the creative imagination of students. - M. "Education", 1985.