"Why Are Numbers Not Enough Again?" Real Number PPT Courseware 2

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"Why Are Numbers Not Enough Again?" Real Number PPT Courseware 2

Can you help?

a. Xiaohong is a freshman who has just entered eighth grade. One weekend morning, her father, who is an engineer, asked Xiaohong two math problems.

(1) Are the two numbers 3.252525... and 3.252252225... the same? What are the different among its?

(2) From a square wooden board with a side length of 6cm, cut off four identical right-angled triangles as shown in the figure. Please calculate the area of ​​the remaining square wooden board? What is the length of the side of the remaining square plank in centimeters? Can you help Xiaohong solve this problem?

b. Can you find the side length of a square with area 2? Do you know the exact value of pi? …can they be represented as integers or fractions (i.e. rational numbers)?

Discuss

group discussion:

Is it possible that a is an integer?

Could a be a fraction?

a²=2, 1

a must not be an integer;

Because a²=2,

So a must not be a fraction.

In the equation a²=2, a is neither an integer nor a fraction, so it must not be a rational number.

draw a picture

Use 16 small squares with a side length of 1 to form a grid as shown in the figure. If you connect any two grid points, you will get a line segment.

Try to draw a line segment whose length is a rational number and a line segment whose length is not a rational number.

summary:

1. Through puzzle activities, you can feel that rational numbers are no longer enough. Tell us what you gained and experienced from this class? What difficulties do you need others to help you solve?

2. If you feel that numbers are not enough, you will determine whether a number is a rational number or not.

3. This lesson uses basic methods: hands-on, operation, observation, thinking, conjecture verification, reasoning, induction and other processes to acquire mathematical knowledge.

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"Why Are Numbers Not Enough Again?" Real Number PPT Courseware:

"Why Are Numbers Not Enough Again?" Real Numbers PPT Courseware 1. Think about it 1. How are rational numbers classified? Rational integers (such as -1, 0, 2, 3): they can all be regarded as finite decimals. Fractions (such as -3/2, 2/5, 9/11): it is impossible to convert them all into finite decimals or infinitely recurring decimals. .

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Update Time: 2024-11-19

This template belongs to Mathematics courseware Beijing Normal University eighth grade first volume mathematics industry PPT template

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