"Laws of Exploration and Expression" Integers and their addition and subtraction PPT (Lesson 2)

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"Laws of Exploration and Expression" Integers and their addition and subtraction PPT (Lesson 2)

Part One Content: Basic Knowledge Key Points

Knowledge points: Use letters to express and use operations to explain rules or phenomena.

1. There is a game rule: you think of a number, multiply it by 2, add 6, divide by 2, and finally subtract the number you think of, then I will know the result, then the result is (C)

A.1 B.2 C.3 D.4

2. When Xiao Ming was doing math problems, he found the following interesting results:

3-2=1;

8+7-6-5=4;

15+14+13-12-11-10=9;

24+23+22+21-20-19-18-17=16;

According to the above rules, it can be seen that the first number from the left in line 10 (C)

A.100 B.121 C.120 D.82

3. Point A starts to move from the point indicating +2 on the number axis. The first time it moves 1 unit to the left, and then 2 units to the right; the second time it moves 3 units to the left, and then 4 units to the right. units; for the third time, first move 5 units to the left, then 6 units to the right...

(1) After the first movement, the number represented by this point on the number axis is 3;

(2) After the second movement, the number represented by this point on the number axis is 4;

(3) After the fifth movement, the number represented by this point on the number axis is 7;

(4) After the nth movement, the number represented by this point on the number axis is n+2;

(5) If the number represented by this point on the number axis after the mth movement is 56, then the value of m is 54.

Exploring and expressing rules PPT, part 2: improvement of comprehensive capabilities

5. When we were very young, we practiced counting with our fingers. A child practiced counting according to the rules as shown in the picture. The corresponding fingers when counting to 2019 are (explanation: count 1, 2, 3, 4, 5 The corresponding finger names are thumb, index finger, middle finger, ring finger, and little finger) (B)

A. Index finger B. Middle finger

C.little finger D.thumb

6. Observe the pattern of numbers marked on the four vertices of the square in the figure. It can be seen that the number 2019 should be marked at (D)

A. The upper left corner of the 504th square

B. The upper right corner of the 505th square

C. The upper right corner of the 504th square

D. The upper left corner of the 505th square

7. As shown in the picture, when three sound pipes are struck, the sounds "1", "3" and "5" are produced in sequence. The two hammers start from "1" at the same time and strike back and forth with the same beat. The difference is that each hammer hammer The beat moves one place (left, center, right, center, left, center, right...), and hammer B does not move for one beat at each end (left, center, right, right, center left, center, right...). At the 200th beat, you hear is (B)

A. The same sound "1" B. The same sound "3"

C. The same sound "5" D. Two different sounds

Exploring and expressing rules PPT, the third part: Expanding exploration and breakthroughs

12. Read the following materials and solve the problems:

Materials: The famous ancient Greek mathematician Pythagoras discovered that the numbers 1, 3, 6, 10, 15, 21,... these numbers (stones) can be arranged into triangles, and numbers like this are called triangular numbers. .

Arrange the numbers 1,3,6,10,15,21,...in another way, that is

1=1;

1+2=3;

1+2+3=6;

1+2+3+4=10;

1+2+3+4+5=15;

Judging from the above arrangement, 1, 3, 6, 10, 15,... are called triangular numbers "deserving of their name".

(1) Suppose the first triangle number is a1=1, the second triangle number is a2=3, and the third triangle number is a3=6. Please directly write the expression of the nth triangle number an (where n is a positive integer).

(2) Based on the conclusion of (1), judge the relationship between the sum of the reciprocals of all triangular numbers T and 2, and explain the reason.

Keywords: Beijing Normal University edition seventh-grade mathematics PPT courseware free download, exploration and expression of rules PPT download, integers and their addition and subtraction PPT download, .PPT format;

For more information about the PPT courseware "Integral Formulas and Their Addition and Subtraction Exploration and Expression Rules", please click the Integer Expressions and their Addition and Subtraction PPT Exploration and Expression Rules PPT tab.

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Update Time: 2024-11-25

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