Unit 1: Fractional Multiplication
Fractional multiplication (1)
Knowledge point: 1, understand the meaning of fractional multiplication by integer. Fractional multiplication of integers, like integer multiplication, is a simple operation to find the sum of several identical addends.
2. Calculation method of integer and decimal multiplication. The denominator remains the same, and the product of a molecule multiplied by an integer is a molecule. Can be reduced to the simplest part of the quotation.
3. When calculating, you can divide the calculation first.
Fractional multiplication (2)
Knowledge point: 1. Combined with the specific situation, further explore and understand the meaning of multiplying fractions by integers and calculate them correctly.
2. Can find the score of a number.
3. Understand the meaning of discount. For example, a discount of 10% means that the current price is nine tenths of the original price.
Fractional multiplication (3)
Knowledge point: 1, the calculation method of multiplying the score by the score, and it can be calculated correctly.
Molecules are multiplied to be numerator, denominator is multiplied to be denominator, and what can be reduced is reduced first. The calculation result needs the simplest score.
2. Compare the product of fractional multiplication with the size of each multiplier.
The product of true scores is less than any multiplier; The product of true score and false score is greater than true score and less than false score.
Unit 2: Cuboid (1)
Understanding of cuboids
Knowledge point: 1. Know cuboids and cubes, and know the names of each part.
2. The characteristics of cuboids and cubes.
Top edge
Number-shape size relation
8 6 are all rectangles, especially the two opposite faces are squares, and the other four faces are all identical rectangles. The opposite is exactly the same rectangle. 12 can be divided into three groups, and the opposite sides are parallel and equal.
8 6 are all squares. Every face is a square. 12 are all equal in length.
3. Know that cubes are special cuboids.
4. Can calculate the sum of edges of cuboids and cubes.
The sum of the sides of a cuboid = (length+width+height) *4 or length *4+ width *4+ height *4.
Sum of cube sides = side length * 12
By using the formula flexibly, the length, width and height of a cuboid or the side length of a cube can be obtained.
Expand and fold
Knowledge point: 1. Know and understand the plane expansion diagrams of cuboids and cubes.
2. Understand several forms of cubic plane expansion diagram, and judge by it.
Surface area of cuboid
Knowledge point: 1. Understand the meaning of surface area. Refers to the sum of the areas of six faces.
2. Calculation method of surface area of cuboid and cube.
3, can be combined with the actual situation in life, calculate the surface area of graphics.
free end/face
Knowledge point: 1. In the process of observation, different observation strategies are adopted.
For example, one is to look at the exposed surface of each carton and add it together; The other is to look at different angles from the front, top and side to see how many faces can be seen at each angle, and then add them together.
2. Discover and find out the changing law between the number of stacked cubes and the number of exposed faces.
Unit 3: Fractional Division
reciprocal
Knowledge point: 1. Discover the characteristics of reciprocal and understand the meaning of reciprocal.
If the product of two numbers is 1, then we call one of them the reciprocal of the other. The reciprocal is the reciprocal of two numbers, and it does not exist in isolation.
2, the method of finding the reciprocal.
Exchange the numerator and denominator of this number.
3. The reciprocal of1is still1; 0 has no reciprocal.
0 has no reciprocal, because 0 cannot be the denominator of a fraction.
Fractional division (1)
Knowledge point: 1, the meaning and calculation method of dividing a fraction by an integer.
Dividing a fraction by an integer is to find the fraction of this number.
A fraction divided by an integer (except 0) is equal to the reciprocal of this number.
Fractional division (2)
Knowledge point: 1, the meaning and basic arithmetic of dividing a number by a fraction.
The meaning of dividing a number by a fraction is the same as integer division; Dividing a number by a fraction is equal to multiplying the reciprocal of this number.
2. Master the calculation method of dividing a number by a fraction.
Dividing by a number (except 0) is equal to multiplying the reciprocal of this number.
3. 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.
Fractional division (3)
Knowledge point: 1, column equation "What is the score of a number".
2. Use the properties of the equation to solve the equation.
3. Understand the meaning of discount.
A 20% discount means that the current price is eight tenths of the original price.
Mathematics and life
whitewash a wall
Knowledge point: 1. Make clear the conditions that must be known when painting classroom walls.
2. Calculate the corresponding area according to the actual situation.
Fold:
Knowledge point: 1, understand the relationship between three-dimensional graphics and unfolded graphics, and develop the concept of space.
2, can correctly judge the plane expansion diagram corresponding to the simple three-dimensional figure.
Unit 4: Cuboid (2)
Volume and volume
Knowledge point: 1, volume and the concept of 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.
volume unit
Knowledge point: 1, knowing volume and unit of volume.
Commonly used unit of volume are: cubic centimeter, cubic decimeter and cubic meter.
2. Feel the practical significance of 1 m3, 1 m3, 1 cm3, 1 liter, 1 ml.
Supplementary knowledge points: the volume of refrigerator is in liters; The tap water we drink is measured in cubic meters.
Volume of cuboid
Knowledge point: 1. Combined with the specific situation and practical activities, explore and master the calculation method of cuboid and cube volume.
Cuboid volume = length * width * height
Volume of cube = side length * side length * side length
Volume of cuboid (cube) = bottom area * height
2. Two conditions such as cuboid (cube) volume can be used to solve the problem. For example, the height of a cuboid = volume/length/width.
Supplementary knowledge: cuboid volume = sectional area * length
Unit of volume's transformation
Knowledge point: 1, the ratio between volume and unit of volume.
The propulsion rate between two neighboring unit of volume and unit of volume is 1000.
Interesting measurement
Knowledge point: 1, measurement method of irregular object volume.
2. Calculation method of irregular object volume.
Unit 5: Fractional Mixing Operation
Fractional mixed operation (1)
Knowledge point: 1, recognizing that the operation order of fractional mixed operation is the same as that of integer.
Fractional Mixed Operation (2)
Knowledge point: the operation law of integer is also applicable to decimal operation.
Fractional Mixed Operation (3)
Knowledge point: 1, using equations to solve practical problems related to fractional operation.
2. Estimation in the score.
3. Analyze the quantitative relationship in the problem with a line chart.
4. Check the final result.
Unit 6: Percentage
Significance of percentage
Knowledge point: 1, the meaning of percentage.
Percentage refers to the percentage of one number in another. Percentage is also called percentage, percentage.
2. Be able to read and write correctly.
3. Understand the meaning of percentage with concrete examples in life.
Qualified rate (application percentage 1)
Knowledge point: 1. Solve the practical problem that one number is a few percent of another.
This part of knowledge is the same as finding the fraction of a number in fractional division.
2. Decimals and fractions can be correctly converted into percentages.
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; To turn a fraction into a percentage, you can first turn the fraction into a decimal (usually keep three decimal places when you can't use it up), and then write it as a percentage; 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.
Protein content (application of percentage II)
Knowledge point: 1. Find the percentage of a number. The method is the same as finding the fraction of a number.
2. 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.
I'm in charge this month (percentage application 3)
Knowledge point: 1. Solve the practical problem of "knowing a few percent of a number and finding this number" with equations.
2. Understand the relationship between percentage and statistics.
Mathematics and shopping
Budget cost
Knowledge points: according to the actual problems, choose a reasonable estimation strategy and make an estimation.
Shopping strategy
Knowledge points: According to the actual needs, analyze and compare several common preferential strategies, and finally choose the most favorable scheme.
Packaging knowledge
Knowledge point: 1. Explore the best strategy to minimize the surface area of multiple identical cuboids after stacking.
2, master the basic methods and processes to solve the problem.
Unit 7: Statistics
Fan statistics chart
Knowledge point: 1. Understand the fan-shaped statistical chart and its characteristics and functions.
2. Be able to read the fan-shaped statistical chart and get the corresponding mathematical information.
Olympic Games (Selection of Statistical Chart)
Knowledge point: 1. Understand the characteristics of bar chart, fan chart and line chart.
Bar charts are easy to see the amount of data; The fan-shaped statistical chart can clearly see the relationship between the whole and the part; Line charts can show the changing trend of data.
2. You can choose the most intuitive and effective statistical chart to represent the data according to your needs.
Median and mode
Knowledge points: 1, median, meaning of 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.
2. 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 most frequent mode in a set of data, which may be multiple modes.
3. According to specific problems, we can choose appropriate statistics to represent different characteristics of data.
Get to know your classmates
Knowledge points: comprehensively apply the learned statistical knowledge to cultivate students' statistical concepts.
Summary table of knowledge points listed in the fifth volume of mathematics published by Beijing Normal University
Unit Directory Every unit should know something.
First unit
Fractional multiplication Fractional multiplication (1) 1, Fractional multiplication of integers "What is a fraction?"
2. Calculation method of integer and decimal multiplication
3. Solve the practical problem of multiplying the corresponding score by an integer.
Fractional multiplication (2) 1, fractional multiplication of integers "What is the fraction of a number?"
2. Solve the practical problem of multiplying the corresponding score by an integer.
Fractional multiplication (3) 1, the significance score of fractional multiplication
2, the score multiplied by the score calculation method
3. Solve the practical problem of multiplying the corresponding score by the score.
Second unit
Cuboid (1) Understanding of Cuboid 1, Names of Cuboid and Cube Parts
2. The characteristics of cuboids and cubes
3. Solve the corresponding problems of using cuboid and cube features.
Expand and collapse 1, the expansion diagram of cuboid and cube,
2. Re-understanding the characteristics of cuboids and cubes.
Surface area of cuboid 1, surface areas of cuboid and cube.
2. Calculation method of surface area of cuboid and cube
3. Solve the corresponding problems of using the surface areas of cuboids and cubes.
Exposed surface 1. Solve the problem of the number and area of exposed surfaces of objects.
Third unit
The reciprocal of fractional division is 1. The meaning of reciprocity.
2. Find the reciprocal of a number
Fractional division (1) 1, the meaning of dividing a fraction by an integer
2, the calculation method of fraction divided by integer
3. Solve the practical problem that the corresponding score is divided by integer.
Fractional division (2) 1, integer divided by the meaning of fraction
2. Calculation method of dividing a number by a fraction
3. Solve the practical problem of dividing a corresponding number by a fraction.
Fractional division (3) 1, solving simple fractional equation: ax=b
2. Solve simple fractional practical problems with equations.
mathematics
Use the living partition wall 1 to calculate and solve the problems in life by comprehensively using the area of the graph.
The relationship between folding 1, three-dimensional diagram and plane expansion diagram
2. Judge the simple three-dimensional figure corresponding to the flat expansion diagram.
Fourth unit
Cuboid (2) volume and volume 1, meaning of volume
2, the meaning of volume
Unit of volume 1, unit of volume: cubic meter, cubic decimeter, cubic centimeter.
2. unit of volume: liters and milliliters.
Calculation methods of 1, cuboid and cube
The volume of cuboid 2. Solve the practical problem of cuboid cube volume.
1 volume conversion unit, the ratio between volume and unit of volume.
2. Conversion between volume and unit of volume.
An interesting method for measuring 1 and the volume of irregular objects.
Fifth unit
Fractional mixing operation Fractional mixing operation (I) 1, Fractional mixing operation sequence
2. Mixed practical application of "a fraction of one number is a fraction of another number"
Fractional mixing operation (2) 1, fractional mixing algorithm
2. Mixed practical application of "how much more (less) one number is than another"
Fractional mixing operation (3) 1, solving slightly complicated fractional equations: ax b = c, ax bx = c,
2. Use equations to solve practical problems related to fractional operation.
Percent understanding 1, percent meaning
2. Correct reading and writing ratio
The qualified rate is 1, decimal, and the score is percentage.
2. The significance of qualified rate, survival rate and attendance rate.
3. The practical application of "how many percent does one number account for another"
Protein content is 1, and the percentage is converted into decimals and fractions.
2. Find out the practical application of "what is the percentage of a number"
This month I am responsible for the relationship between 1, percentage and statistics.
2. The practical application of "what percentage of a number is known"? Find this number. "
3. Solve simple percentage practical problems with equations.
mathematics
Estimate the cost of shopping with 1 and choose a reasonable estimation strategy.
Shopping strategy 1, according to the actual needs, several common preferential strategies.
Packaging knowledge 1, the optimal strategy of minimizing the surface area after stacking multiple identical cuboids.
These are knowledge points, copy them down. Lace can be painted beautifully and simply.