2. Learn to use letters to represent numbers in specific situations, understand the properties of equations, use the basic properties of equations to solve simple equations, and use equations to represent equivalence relations in simple situations to solve problems.
3. Be able to explore and master the area formulas of parallelogram, triangle and trapezoid;
4. Can see the shape and relative position of the object from different directions;
5. Understand the meaning of median and find the median of data.
The surface area of a cuboid = (length× width+length× height+width× height )× 2s = (AB+AH+BH )× 2.
Volume of cuboid = length× width× height V=abh
Surface area of cube = side length × side length× 6 s = 6a?
Volume of cube = side length × side length × side length V=a?
Volume of cuboid (or cube) = bottom area × height V=sh
The minimum multiple and maximum factor of a number is itself.
The number of factors of a number is limited.
The multiple of a number is infinite.
Among natural numbers, those that are multiples of 2 are called even numbers (0 is also even numbers), and those that are not multiples of 2 are called odd numbers.
Numbers in units of 0, 2, 4, 6 and 8 are all multiples of 2.
A number with 0 or 5 is a multiple of 5.
The sum of the numbers on each digit of a number is a multiple of 3, and this number is a multiple of 3.
If a number has only two factors: 1 and itself, it is called a prime number.
A number is called a composite number if it has other factors besides 1 and itself.
1 is neither prime nor composite.
The unit of volume is used to measure the volume. The commonly used unit of volume has cubic centimeters, cubic decimeters and cubic meters, which can be written as cm? ，dm？ And m? .
1dm？ = 1000cm？ 1m？ = 1000dm？
The volume that an object can hold is usually called its volume. Unit of volume is generally used to measure volume.
The volume of liquid is usually measured in liters and milliliters, and can also be written as L and ml.
1L = 1000ml 1L = 1dm？ 1ml= 1cm？
Fractions with numerator less than denominator are called true fractions. The true score is less than 1.
Fractions with numerator greater than denominator or numerator equal to denominator are called false fractions. False score is greater than or equal to 1.
The numerator and denominator of a fraction are multiplied or divided by the same number (except 0) at the same time, and the size of the fraction remains the same. This is called the basic nature of fractions.
Changing a fraction into an equal fraction with smaller numerator and denominator is called divisor.
Dividing the scores of different denominators by the scores of the same denominator equals the original score, which is called the total score.
Add and subtract fractions with the denominator, the denominator remains the same, and only the numerator is added and subtracted.
bonus
Dividends = —————
divisor
In a set of data, the number with the highest frequency is the pattern of this set of data.
In a set of data, there may or may not be multiple patterns.
1, distance, speed and time formula: s = vtv = s ÷ t t = s ÷ v.
2. Square perimeter formula: C=4a
3. Formula of square area: S=a2
4. Rectangular perimeter formula: C=2(a+b)
5. Rectangular area formula: S=ab
Additive commutative law: A+B = B+A.
7. Additive associative law: a+b+c=a+(b+c)
8. multiplicative commutative law: ab = b a.
9. Law of multiplication and association
10, multiplication and distribution law: [a+b] c = a c+b c.
1 1, classification of angles, from small to large: acute angle, right angle, obtuse angle, right angle and rounded corner.
12, acute angle less than 90 degrees, right angle 90 degrees, obtuse angle greater than 90 degrees but less than right angle, right angle 180 degrees, fillet 360 degrees.
13. Triangles are classified by angle: acute triangle, right triangle and obtuse triangle.
14. A triangle with three acute angles is called an acute triangle. A triangle with a right angle is called a right triangle; A triangle with an obtuse angle is called an obtuse triangle.
15. Triangles are divided into equilateral triangles, isosceles triangles and equilateral triangles.
16. Draw a vertical line from the vertex of the triangle to its opposite side. The line segment between the vertex and the vertical foot is called the height of the triangle, and the opposite side is called the bottom of the triangle.
17, the counting unit of decimals is one tenth, one hundredth, one thousandth -0. 1, 0.0 1, 0.00 1-
18. Properties of decimals: Add "0" or remove "0" at the end of decimals, and the size of decimals remains unchanged.
20. 1 angle =2 right angle 1 fillet =2 angle =4 right angle.
2 1, the triangle is stable.
22. The sum of any two sides of a triangle is greater than the third side.
23. The sum of the internal angles of a triangle is 180 degrees.
24. Learn to draw corners
25, will compare the size of decimals.
26, unit conversion
Unit of length: 1 m = 10 decimeter 1 decimeter = 10cm = 1 0mm10 decimeter =
Mass unit:1k g =1000g1t =1000kg =100000g.
Currency conversion: 1 yuan = 10 minute = 100 minute = 10 minute.
Time unit: 1 hour =60 minutes =3600 seconds 1 minute =60 seconds.
1 year = 65438+ February =365 days or 366 days 1 day =24 hours.
135780 wax, 3 1 day never goes bad. Four, six, nine, one, thirty, February 28th in a normal year and February 29th in a leap year.
Area unit: 1 m2 = 100 square decimeter 1 square decimeter = 100 square centimeter 1 m2 = 10000 square centimeter.
1 ha = 1 0000m21km2 =100ha =100000m2
Conceptual arrangement of the first volume of fifth grade mathematics
1, cut along the height of the parallelogram and put it into a rectangle by shifting. The length of the rectangle is equal to the base of the parallelogram, the width of the rectangle is equal to the height of the parallelogram, and the area of the rectangle is equal to the area of the parallelogram. Because the area of the rectangle is multiplied by the width, and the base of the parallelogram is multiplied by the height. If S is used to represent the area of a parallelogram, and A and H are used to represent the base and height of the parallelogram respectively, the area formula can be written as: S=ah.
2. Two identical triangles can be combined into a parallelogram, the base of which is equal to the base of the triangle, which is higher than the height of the triangle, and the area of each triangle is half that of the parallelogram. Because the area of a parallelogram is equal to the base multiplied by the height, the area of a triangle is equal to the base multiplied by the height divided by 2. If S is used to represent the area of a triangle, and A and H are used to represent the base and height of the triangle respectively, the area formula can be written as: S=ah÷2.
3. Two identical trapeziums can be spliced into a parallelogram, the base of which is equal to the sum of the upper and lower bases of the trapezium, the height of the parallelogram is higher than the height of the trapezium, and the area of each trapezium is half that of the trapezium, so the trapezium is equal to (upper base+lower base) × height ÷2. If s is used to represent the area of a trapezoid, a and a are used.
4. Fractions with denominators of 10, 100, 1000 ... can be expressed in decimals. One decimal place indicates a few tenths, two decimal places indicate a few percent, and three decimal places indicate a few thousandths. ...
5. The first digit to the right of the decimal point is ten, and the counting unit is one tenth, (0.1); The second digit to the right of the decimal point is the percentile, and the counting unit is one percent (0.01); The third digit to the right of the decimal point is one thousandth, and the counting unit is one thousandth (0.001); ..................................................................................................................................................................................
6. Add "0" or remove "0" at the end of the decimal, and the size of the decimal will remain unchanged. This is the essence of decimals.
7. Divide a decimal by 10, 100,1000 ... Just move the decimal point of this decimal to the left by one place, two places and three places.
8. Multiply a decimal by 10, 100, 1000… Just move the decimal point of this decimal to the right by one, two or three places …
9. A decimal, starting from somewhere in the decimal part, with one number or several numbers repeating in turn. Such decimals are called cyclic decimals.
10, dividend and divisor are expanded (reduced) by the same multiple at the same time, and the quotient remains unchanged.
1 1, how many times the dividend is expanded (reduced), and how many times the quotient is expanded (reduced) when the divisor is unchanged.
12, the dividend is constant, how many times the divisor is expanded (reduced), and how many times the quotient is reduced (expanded).
13, how many times one factor is enlarged and the other factor is reduced by the same multiple, and the product remains unchanged.
14, if one factor remains unchanged, the product will expand (shrink) many times with the expansion (shrink) of another factor.
15, length unit rate
1km = 1000m 1m = 10DM 1DM = 10cm 1cm = 10mm
Rmb 1 yuan = 10 angle 1 angle = 10 minute.
Mass unit rate 1 ton = 1000 kg 1 kg = 1000 g.
Area unit rate 1 km2 = 100 hectares 1 hectare = 10000 square meters.
1 m2 = 100 cm2 1 cm2 = 1 0000 cm21m2 = 10000 cm2.
16, high-level units are converted into low-level units multiplied by the forward speed, and the decimal point is moved to the right. Low-level units are converted into high-level units divided by the forward speed, and the decimal point is moved to the left.
17、a+b = b+ a a+b+c = a+(b+c)a-b-c = a-(b+c)a+b-c = a-c+b
a×b = b×a(a×b)×c = a×(b×c)a×b+a×c =(b+c)×a
a÷b÷c=a÷(b×c) (a+b) ÷c=a÷c+b÷c
18, measuring the land area, generally in hectares.
19 square land with side length 100 m, area 1 hectare.
20. When one factor is greater than 1, the product is greater than another factor. (Another factor ≠0)
When one factor is less than 1, the product is less than another factor. (Another factor ≠0)
When one factor equals 1, the product equals another factor.
2 1, when the divisor is greater than 1, the quotient is less than the dividend. (Dividend ≠0)
When the divisor is less than 1, the quotient is greater than the dividend. (Dividend ≠0)
When the divisor equals 1, the quotient equals the dividend.
22, decimal multiplication calculation rules:
① Calculate the product by integer multiplication first, and then put a decimal point on the product point.
(2) To see how many decimal places there are in a factor, just count a few times from the right (or one place) of the product and click the decimal point.
(3) When the number of decimal places of the product is not enough, you should add 0 in front, and then calculate the decimal point.
23. When a number (except 0) is multiplied by a number greater than 1, the product ratio is the original number ().
Such as: 3.4× 1.5 > 3.4 0.9× 3 > 0.9.
When a number (except 0) is multiplied by a number less than 1, the product ratio is the original number ().
Such as: 3.4× 0.74 < 3.4 0.9× 0.3 < 0.9.
24. Decimals whose integer parts are non-zero numbers are called decimals. For example:1.34,453.5643, etc. Decimals whose integer part is zero are called pure decimals. For example: 0.34, 0.56643, etc.
4. The difference between pure decimal and decimal is that pure decimal is less than 1 and decimal is greater than 1. For example, 0. 1 < 1 is a pure decimal.
1. 1 > 1, with decimal 4.5234 > 1, with decimal.
5. The order of four decimal operations is the same as that of integers.
① The order of decimal multiplication is: from left to right;
② The order of multiplication, addition, multiplication and subtraction of decimals is: multiply first, then add or subtract.
6. The commutative law, associative law and distributive law of integer multiplication are also applicable to fractional multiplication.