one

First unit

Hours and minutes

1. There are three hands on the clock face. They are (hour hand), (minute hand) and (second hand). The fastest is the second hand, and the slowest is the hour hand.

2. There are (12) numbers, (12) large squares and (60) small squares on the clock face; There are (1) large cells between every two numbers, that is, (5) small cells.

3, clockwise 1 grid is (1) hours; It takes (5) minutes to walk 1 square and (1) minutes to walk 1 square. It takes (5) seconds for the second hand to go 1 and (1) seconds for the second hand to go.

4. When the hour hand goes 1, the minute hand just goes (1) laps, and the minute hand goes 1 laps for (60) minutes, that is, (1) hours. Clockwise 1 turn, minute hand (12 turn).

5. The minute hand goes 1, the second hand just goes (1) laps, and the second hand goes 1 laps for (60) seconds, which is (1) minutes.

6. When the hour hand turns from one number to the next, it is (1 hour). The minute hand moves from one number to the next (5 minutes). The second hand turns from one number to the next (5 seconds).

7. The time when the hour hand and the minute hand are at right angles on the clock face is (3 o'clock sharp) and (9 o'clock sharp).

8. Formula. (The advance rate between every two adjacent time units is 60)

1 = 60min1min = 60s.

Half an hour =30 minutes, 60 minutes = 1 hour

60 seconds = 1 minute 30 minutes = half an hour.

two

Unit 2 and Unit 4

Addition and subtraction within ten thousand (1) and (2)

1 and the minimum number of digits.

One digit of is 9, and the minimum digit is 0.

The two digits of are 99, and the smallest two digits are 10.

The three digits of are 999, and the smallest three digits are 100.

The four digits of are 9999, and the smallest four digits are 1000.

The five digits of are 99999, and the smallest five digits are 10000.

The three digits of are less than the smallest four digits 1.

2. Read and write numbers (write Chinese characters when reading and Arabic numerals when writing numbers).

No matter whether there is a zero or several zeros at the end of a number, this zero will not be read.

② There is a zero or two consecutive zeros in the middle of a number, and both of them read only one zero.

3. Comparison of figures:

① Numbers with different digits are larger, and those with more digits are larger.

(2) Compare the sizes of numbers with the same number of digits. First, compare the numbers on the numbers of these two numbers. If two digits are the same, compare the next digit, and so on.

4. Find the approximate value of a number:

Memory: Look at the last digit. If it is 0-4, use the four-shed method. If it's 5-9, use the decimal method.

Its three digits are 999, the smallest three digits are 100, the fourth digits are 9999, and the smallest four digits are 1000. The three digits of are less than the smallest four digits 1.

5, the minuend is a three-digit continuous abdication subtraction steps:

① When the columns are vertical, the same numbers must be aligned;

(2) When subtracting, which digit is not reduced enough will be1of the previous digit; If the previous digit is 0, it is 1 of the previous digit.

6. Pay attention to the middle 0 when doing the problem, because it is abdicated continuously, so you should retreat from one hundred to ten at 10, and then from ten to one at 10, and lend one, so there are only nine left in the ten, not 10. (Sum of two three digits: it may be three digits or four digits. )

7. When adding and subtracting with a pen: the same numbers should be aligned; From the number of units. When the number on which bit adds up to 10, go to the previous bit and input1; Where the number of digits is not reduced enough, take 1 from the previous digit as 10, and then reduce it after adding the standard; If the previous digit is 0, it is 1 of the previous digit. (Sum of two three digits: it may be three digits or four digits. )

Special attention: abdication subtraction with 0 in the middle, for example: 309-189; 1000-428 and so on

8、

⑴ Addition formula: addend+another addend = sum.

Check the calculation of addition:

① Exchange the positions of two addends and recalculate.

Another Addendum+Addendum = Sum

② Sum-Another Addendum = Addendum

⑵ Subtraction formula: minuend-minuend = difference.

Check the calculation of subtraction:

① Difference+Subtraction = Subtraction

② subtraction+difference = minuend

③ minuend difference = reduction

Special attention: don't forget to write "checking" when checking! ! !

three

Third unit

measure

1. In daily life, relatively few items can be used as units (millimeters, centimeters, decimeters); Large objects are usually measured in meters; Generally, the unit for measuring long distances is (km), also called (km).

2. There are (10) units in the length of 1 cm, and the length of each unit (equal) is (1) mm. ..

3. 1 The thickness of coins, rulers, magnetic cards, buttons and keys 1 min is about1mm..

4. When calculating the length, you can only add or subtract the same length unit.

Tip: When converting length units, change large units to small units, and add 0 at the end of the number (if there are several 0s in the relationship, add several 0s); Changing a small unit to a large unit will remove the zeros at the end of the number (if there are several zeros in the relationship, remove several zeros).

5. The relationship between length units is as follows: (the propulsion rate between every two adjacent length units is 10).

(1) The rate is 10:

1 m = 10 decimeter, 1 decimeter = 10 cm,

1 cm = 10mm,10 decimeter = 1 m,

10cm = 1 decimeter,10mm = 1 cm,

② The propulsion rate is 100:

1 m = 100 cm, 1 decimeter = 100 mm,

100 cm = 1 m, 100 mm = 1 decimeter.

③ The propulsion rate is 1000:

1 km = 1 000m,1km = =1000m,

1000m = 1km， 1000m = 1km。

When we express the weight of an object, we usually use (mass unit). In life, the weight of lighter items can be measured in grams. According to the quality of general goods, it is usually a unit (kg); Measure the mass of heavy or bulk goods, usually in tons.

Tip: in the conversion of "ton" and "kilogram", converting tons into kilograms means adding three zeros at the end of the number;

Converting kilograms into tons is to remove the three zeros at the end of the number.

7. The ratio of two adjacent mass units is 1000.

1 ton = 1 000kg1kg =1000g

1000kg = 1 ton1000g = 1 kg

four

Fifth unit

Understanding of the times

Meaning of 1 and multiples: To know the relationship between two numbers, first determine who is the multiple of 1, and then compare it with another number. There are several multiples of 1 in another number.

2. Find how many times one number is another by division: one number ÷ another number = multiple.

3. How many times is a number multiplied? This number × multiple = several times this number

five

Sixth unit

Multiply multiple numbers by one number.

1, the written calculation method of multiplying multiple digits by one digit (carry): the same digits are aligned, and the digits on each digit of multiple digits are multiplied by one digit respectively. If the product of the best digits is more than several tens, go to the previous digit, and the product is written under which digit.

2. Multiply by 0 in the middle of the factor:

① Multiply 0 with any number to get 0;

(2) There is a 0 in the middle of the factor, and the number on each bit of the multi-digit is multiplied by one digit. When multiplying with the middle 0, if it is not followed by a number, this bit will be occupied by a 0, and if it is followed by a number, it must be added.

(3) Simple calculation of multiplication with 0 at the end of a factor: When calculating with a pen, you can align one digit with the number before the multi-digit 0, and then see how many zeros are at the end of the multi-digit and add several zeros at the end of the product.

3.① Multiply 0 with any number to get 0;

② Multiply 1 by any number other than 0 to get the original number.

4. Three digits multiplied by one digit: the product may be three digits or four digits.

Formula: speed × time = number of people per car × number of cars = number of people in the whole car.

Distance/time = speed

Distance/speed = time

5. (About) Application:

There are "approximate", "approximate", "estimate", "estimate" and "estimate" in the questions. Are there any approximate figures in the conditions? Estimate. (Use ≈ in estimation)

For example: 387×5≈.

Take 387 as 390 (the unit is 7, rounded, 7 is greater than 5, so it is 1, which is regarded as 390) and then calculate 390×5= 1950.

So: 387×5≈ 1950

six

Unit 7

Rectangular and square

1. A closed figure with four straight sides and four corners is called a quadrilateral.

2. Features of quadrilateral: It has four straight sides and four corners.

3, the characteristics of the rectangle: the rectangle has two lengths and two widths, the four corners are right angles, and the opposite sides are equal.

4. Characteristics of a square: it has four right angles and four equal sides.

5. Rectangular and square are special parallelograms.

6. Features of parallelogram: ① The opposite sides are equal and the diagonals are equal.

② Parallelogram is easy to deform. (Triangle is not easy to deform)

7. The length of a closed graph is its perimeter.

8. Formula:

The circumference of a rectangle = (length+width) ×2

Variant: ① Length of rectangle = perimeter ÷2- width

② Width of rectangle = perimeter ÷2- length

Circumference of a square = side length ×4

Variant: side length of a square = perimeter ÷4

seven

The Eighth Unit

A preliminary understanding of scores

1, the meaning of fraction: divide a whole into several parts, which means that several parts are parts of the whole, the divided part is the denominator, and the taken part is the numerator.

Molecular representation: several kinds

The denominator means: how many shares are divided equally?

2. Fraction: divide an object or a figure into several parts on average, and each part is a fraction of it.

Score: divide an object or figure into several parts, and take a few parts, which is the score of the object or figure.

3. The more shares a whole is divided equally, the smaller the number each share represents.

4. Method of comparing sizes:

① When the numerator is the same, the smaller the denominator, the greater the score, and the larger the denominator, the smaller the score.

(2) When denominators are the same, scores with large molecules are large and scores with small molecules are small.

5. Decimal addition and subtraction:

① Calculation method of addition and subtraction of fractions with the same denominator: the denominator is unchanged, and the numerator is added and subtracted.

(2) Calculation method of how many fractions are subtracted from 1: When calculating how many fractions are subtracted from 1, write1as the denominator of the subtraction before calculation. (1 can be regarded as a fraction with the same denominator for all numerators)

6. How to calculate the fraction that one number is another number:

Example: Let 3/4 circles of 12 have () circles;

Analysis: Find the integer12 first; Then find the denominator 4, that is, divide it into 4 parts on average; Find 12÷4=3, which means that each copy has three; Finally, find the molecule 3, which means three of them, so: 3× 3 = 9; So 12' s three-quarters cycle has nine cycles.