Mathematical clock handwritten newspaper

First, understand mathematical clocks and watches

1, know the clock face

Clock face: There is a number 12 on the clock face, with an hour hand and a minute hand.

Minute hand: The slender hands on the clock face are called minute hands.

Hour hand: The short hands on the clock face are called hour hands.

2. Types of watches and clocks:

There are generally two kinds of clocks in daily life, one is a wall clock with the number 12, minute hand and hour hand on the dial. The other is an electronic watch, which has two dots on its surface and numbers around it.

3. Know all the time:

The minute hand points to 12, and the hour hand points to what time; On the electronic watch, when the right side of ":"is "00", it means the hour time, and the left side ":"means the time.

4, the whole period of writing:

There are two ways to write the whole time: when writing or in the form of an electronic watch. Like 8 o'clock or 8 o'clock.

Second, what is the problem of clock travel?

The stroke problem of the clock face is to study the relationship between the hour hand and the minute hand on the clock face. There are two common types:

(1) Study the problem that the hour hand and the minute hand form a certain angle, including overlapping, straight line, right angle or a certain angle;

⑵ Study the time error.

On the clock face, every hand rotates clockwise, but because of the different speeds, the minute hand always catches up with the hour hand, or the minute hand exceeds the hour hand, so the common clock face problem is often transformed into the problem of catching up.

3. What are the types of clock face problems?

The first category is the problem of traceability (there are often two situations when paying attention to the relationship between the hour hand and the minute hand); The second is the problem of meeting (the hour hand and the minute hand will never meet, but when the angle between the hand and the minute hand is equal to a certain scale, the distance sum can be found); The third is the problem of inaccuracy, the most critical point of this kind of problem: finding the proportional relationship between the watch and the real time.

4. What is the key problem of the clock face?

① Determine the initial positions of the minute hand and the hour hand;

② Determine the distance difference between the minute hand and the hour hand;

5. What are the basic methods to solve the clock face problem?

(1) framework method:

The circumference of the clock face is divided into 60 cells on average, and each cell is called 1 cell. The minute hand walks for 60 minutes every hour, which is a week; The hour hand only moves for 5 minutes, so the minute hand moves 1 minute, and the hour hand moves112 minutes.

② Degree method:

Viewed from the angle, the circumference of the clock face is 360, the minute hand turns 360/60 degrees per minute, which is 6 degrees, and the hour hand turns 360/ 12*60 degrees per minute, which is 1/2 degrees.

Six, the clock problem knowledge points

The clock problem can be regarded as a special problem that two people catch up or meet in a circular orbit, but the two "people" here are the minute hand and the hour hand of the clock respectively.

We usually call the problem of studying the hour hand and minute hand on a clock a clock problem, including the speed of the clock, the period of the clock, the angle formed by the hour hand and minute hand on the clock and so on.