Mathematics knowledge points of fourth grade in Beijing Normal University
fractional arithmetic
1. Addition and subtraction of decimals
(1) does not carry forward or abdicate. 1.2+3.4 6.6- 1.3
(2) One in and one out. 20.6+3.7 19. 1-2.7
3 continuous carry and continuous abdication. 12.75+2.25 7 1. 13- 16.55
④ The digits are different. 16.3+2.75 60-2.88
2. Decimal multiplication
① general situation. 2.8× 1. 1
② There is a "0" in the middle of the multiplier. 1.06×3.3
③ There is a "0" at the end of the multiplier. 1.06×470
④ There is a "0" at the end of the product. 8.5×0.88
⑤ The relationship between products and factors. 0.49×0.9○0.49
⑥ The movement of decimal point causes the change of decimal size.
⑦ Properties of decimals. (Do not change the size of 1.3, and rewrite it to two decimal places)
3. Fractional division
The divisor is an integer.
② The divisor is a decimal.
③ There is a "0" in the middle of the quotient.
There is a "0" at the end of the quotient.
⑥ The relationship between quotient and dividend. 0.49÷0.9○0.49
⑦ Cyclic decimals.
The decimal representation of the cycle and the decimal representation of the business cycle will be judged.
⑧ Remainder problem. Cut a 3.6-meter-long rope into 0.6-meter pieces. How many pieces can I cut at most? How many meters are left? )
Pet-name ruby approximate figures. According to the actual situation, round or round, such as the end and the end (choose one method).
Unit 7 knowledge points in the first volume of fourth grade mathematics
1, pancake problem strategy:
When only two cakes can be baked at a time, and both sides should be baked:
(1) Bake three cakes: bake the front of 1 and No.2 cakes first, then bake the back of 1 cakes and the front of No.3 cakes, and finally bake the back of No.2 and No.3 cakes.
(2) Branding multiple cakes: If the number of cakes to be branded is even, two cakes are enough; If the number of cakes to be branded is odd, you can brand two and two cakes first, and then brand the last three cakes according to the above method, which saves the most time.
2, tea making strategy: First of all, we must make clear the general order of tea making, that is to say, what to do first, and then consider what we can do at the same time, and try to do what we can at the same time, which can save time.
3. Queuing theory problem strategy: Starting from things with less waiting time in turn can minimize the total waiting time.
4. "Tian Ji Horse Racing" problem strategy: Tian Ji used inferior horses against excellent horses in Wang Qi, and excellent horses against Zhongma and Zhongma in Wang Qi.
Yes, the bad horse of the King of Qi. Two out of three, Tian Ji wins.
The learning method of "from square centimeter to square kilometer" in the first volume of fourth grade mathematics
1, feel square kilometers
Students, do you think our school is big? Is our Sijing town big? What about Songjiang District? These areas are represented by our newly learned area unit km2. What is this? Please look at the big screen: (display)
Our beautiful campus covers an area of about 0.03 square kilometers.
Our hometown-Sijing Town covers an area of about 24.2 square kilometers.
Our Songjiang District has a total area of about 604 square kilometers.
What information did you get? How do you feel? What kind of area do you think square kilometers are generally used in? (Contrast, communication)
Summary: Square kilometers are often used to represent large areas.
Starting from the living environment of students, the strong contrast between "large area" and "small quantity" enriches the sense of quantity of square kilometers.
2. Perception of commonly used small area units
What other common units of area have we learned? Who can go from big to novel? What is the speed of progress between them? Let's use gestures to show their size! Can 1km2 be expressed by gestures? (Can't) Why? (1km2 is too large)
Write on the blackboard.
Km21m2 =100 dm21dm2 =100 cm2 【 Review the learned area units and reproduce the appearance of common area units by memorizing oral response and image gesture perception. ]
3. Perception exercises
Students have a good idea of area units, so let's open the textbook P23 and finish the third question. See who can fill it out quickly and accurately.
Fill in the appropriate area units in the following () (page 23 of the textbook).
The area of a stamp is about 9 square meters.
A table tennis table is about 4 10 ()
The area of a classroom is about 63 square meters.
The area of floppy disk is about 1 ()
A volleyball court covers an area of about 162 ()
Shanghai Wildlife Park covers an area of about 2 ()
Under the full perception of the previous regional units, by filling in the appropriate units, students will be familiar with a certain side or area of the object and establish contact with the regional units, which not only diagnoses the students' mastery of the knowledge they have learned, but also activates their sense of quantity in the existing unit areas. ]
Second, the inquiry stage.
1, scenario question: Students are familiar with the area unit through the unit filling just now. Next, let's solve the problems left over from the previous study: (Show) If 17 people can be squeezed into 1 m2, can 1 km2 squeeze all the people in Shanghai? (Shanghai population 16737700)
What do we need to know to solve this problem? Deskmate communication: We need to know how many m2 1 km2 is equal to, that is, the propulsion rate between km2 and m2, so that we can know how many people 1 km2 can squeeze in and finally solve the problem.
2. Cooperative exploration: We know that 1 km2 is the area of a square with a side length of 1 km (show a square figure with a side length of 1 km).
So what is the propulsion speed between km2 and m2? Can we find out the progress rate between them from the definition of 1 km2? Please cooperate with the team to complete.
(1) Try to solve problems in the group, and the teacher will patrol and guide.
(2) the whole class communication solution:
1 km×1km = 1 km2
1000m×1000m = 1000000
m2 1km2= 1000000m2
(3) Re-communication: In the relationship defined by 1km2, it is easy to find the relationship between them by converting km into m. Now let's share this process with each other at the same table.
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