1. Learn to use the strategy of "reverse reasoning" to solve problems.

X. circle

1. Features of circle, center, radius and diameter;

2. Can use compasses to draw a circle with a specified size;

3. Be able to use the knowledge of circle to explain some phenomena in life and solve some simple problems;

4. The meaning of pi; Calculation of circumference and area of a circle. ?

General review of mathematics in the second volume of the fifth grade 1. Multiplication of numbers and operational fractions;

1, the meaning of fractional multiplication by integer: the meaning of fractional multiplication by integer is the same as that of integer multiplication, which is a simple operation to find the sum of several identical addends.

2. Calculation method of multiplying a fraction by an integer: the denominator remains the same, the product of multiplying a numerator by an integer is a numerator, the reducible offer is simplest fraction, and the calculation result that can be converted into an integer is converted into an integer. Note: Multiply 0 by any number to get 0.

3. The meaning of the score multiplied by the score: What is the score of this number?

4. Calculation method of fractional multiplication: numerator multiplies numerator, denominator multiplies denominator, and what can be reduced is reduced first. The calculation result needs the simplest score.

Note: Understand the meaning of discount. For example, a discount of 10% means that the current price is nine tenths of the original price. A 65% discount means that the current price is 65% of the original price.

5. Know what a number is and what is the score of this number? Such application problems can be solved by multiplication. decimal

1, reciprocal: If the product of two numbers is 1, then one number is the reciprocal of the other. The reciprocal is the reciprocal of two numbers, and it does not exist in isolation. Two numbers whose product is 1 are reciprocal. 2, the method of finding the reciprocal.

3. The reciprocal of1is still1; 0 has no reciprocal. (Reason: 0 has no reciprocal, because 0 cannot be the denominator of a fraction). 4. One number (a) divided by another number (b) (except zero) is equal to the reciprocal of this number (b). 5. Dividing a fraction by an integer means finding the fraction of this number. 6. Compare the quotient and the size of the bonus. The divisor is less than 1 and the quotient is greater than the dividend;

The divisor equals 1. Quotient equals dividend;

The divisor is greater than 1 and the quotient is less than the dividend. Mixed operation of fractions

1, the order of fractional mixing operation is the same as that of integer mixing operation. (If there are brackets, count them first and then count them out; Without brackets, multiply first and then divide, then add and subtract; Multiplication and division are calculated from left to right. Division is first converted into multiplication and then simplified, and the final result is the simplest fraction)

2. The law of integer operation is also applicable to decimal operation. 3. Solve the practical problems of fractional mixing operation with equations. 4, will use the line chart to analyze the quantitative relationship in the application problem, "percentage".

1, the meaning of percentage: the number indicating that one number is the percentage of another number is called percentage, and percentage is also called percentage and percentage.

2, the percentage of reading and writing.

3. Method of converting decimals into percentages: To convert decimals into percentages, just move the decimal point two places to the right and add hundreds of semicolons at the back.

4. Method of converting fractions into percentages: To convert fractions into percentages, you can first convert fractions into decimals (except for those that are inexhaustible, three decimal places are generally reserved), and then write them into percentages; You can also multiply the numerator and denominator by a number at the same time to become a percentage number, and then write it as a percentage.

5. Percentages are converted into decimals and fractions.

Percent the number of components, first rewrite the percentage into the number of components, and make a quotation that can be turned into the simplest score. When the percentage is converted to decimal, the percent sign should be removed and the decimal point should be moved to the left by two places.

6. Solve the practical problem of "how many percent of a number is known, and find this number" with equations. 7, the difference between percentage and score:

Different meanings: percentage only indicates the relationship between two quantities, and there is no unit; Fraction can represent the relationship between two quantities or a specific quantity, and can be added in units. The reading is different: the percentage is only a few percent, not a few percent. Different writing methods

Second, space and graphics.

1, characteristics of cuboids and cubes: 3. Know that a cube is a special cuboid.

4. Calculate the sum of the side lengths of a cuboid and a cube:

Sum of sides of a cuboid = (length, width and height)? 4 or long? 4 wide? 4 high? 4 The sum of the sides of a cube = the number of sides? 12 5, the surface area of a cuboid

Surface area of cuboid = length? Wide? 2 long? Tall? 2 wide? Tall? 2= (Long? Width and length? Height and width? High)? 2 Surface area of cube = side length? Side length? 6 6. When calculating the exposed surface area:

Count the number of exposed surfaces first, and then find the area of exposed surfaces = the number of exposed surfaces? The area of the surface.

Cuboid (2)

1, the concept of volume and volume.

Volume: The size of the space occupied by an object is called the volume of the object.

Volume: The volume that a container can hold an object is called the volume of the object. 2. unit of volume

Commonly used unit of volume are: cubic centimeter, cubic decimeter and cubic meter. Commonly used unit of volume are: liter and milliliter. Add special knowledge points: the volume of refrigerator is in liters; The tap water we drink is measured in cubic meters. 3, the cuboid volume

Volume of cuboid = length? Wide? high

Volume of cube = side length? Side length? edge

The volume of a cuboid (cube) = the bottom area? high

4. Measurement method and calculation method of irregular object volume. Object volume = rising water volume = container bottom area? The rising height of the water surface. (See the second question on page 55 of the textbook) 5. The rate of propulsion between volume and unit of volume.

1 dm3 = 1 l, 1 cm3 = 1 ml, 1 l = 1000 ml 1 m3 = 1000 dm3.

(The propulsion rate between two neighboring unit of volume and unit of volume is 1000) 6. The forward speed between other units.

1 m = 1 00cm1m3 = 100000 m3 length unit:

1 m = 10 decimeter 1 decimeter = 10 cm (the ratio between two adjacent length units is 10) Area unit:

1 m2 = 100 square decimeter 1 square decimeter = 100 square centimeter (the propulsion rate between two adjacent area units is 100) unit of volume:

1 cubic decimeter = 1000 cubic centimeter 1 cubic meter = 1000 cubic decimeter unit of volume: 1 liter = 1000 ml mass unit:

1 ton = 1 000kg1kg =1000g 3. statistics

1, fan chart: take a circle as a whole and express the percentage of each part in this circle. 2. Different characteristics of bar chart, fan chart and line chart: bar chart is easy to see the amount of data;

The fan-shaped statistical chart can clearly see the relationship between the whole and the part; The dotted statistical chart can show the changing trend (or situation) of data.

3. Median and mode

Arrange a set of data from small to large (or from large to small), and the middle number is called the median of this set of data. The number that appears most frequently in a set of data is called the mode of this set of data. 4. The solution of median and mode.

Arrange a set of data in order of size. If there are odd numbers of data, the middle number is the median of this set of data. If there are even numbers of data, the average of the middle two numbers is the median of this set of data. Mode is the mode with the highest frequency in a set of data.

Fourth, key topics