"The relationship between variables represented by tables" The relationship between variables PPT courseware 4

Description

"The relationship between variables represented by tables" The relationship between variables PPT courseware 4

learning target

1. Experience the process of exploring the relationship between variables in certain graphics, and be able to understand variables, independent variables, and dependent variables in the process, and further develop symbolic sense and abstract thinking.

2. Be able to use tables or relational expressions to express the relationship between variables according to specific situations.

3. Be able to evaluate based on relational expressions and initially understand the numerical correspondence between independent variables and dependent variables.

【Reveal new knowledge】

In the time test of the car sliding down:

The height h of the support and the time t for the car to slide are both changing, and they are both variables.

The time t for the car to slide down changes with the change of the height h of the support.

The height h of the support is an independent variable,

The time t for the car to slide down is the dependent variable.

In this process, quantities such as the length of the board that remain unchanged during the change are called constants.

【Think about it】

Boil a pot of water and the water boils ten minutes later. What are the variables in this process? What are the independent variables? What are the dependent variables?

The time to boil water and the temperature of water are variables, the time to boil water is the independent variable, and the temperature of water is the dependent variable.

What examples in life reflect the relationship between variables?

Communicate with your peers. Point out which are the independent variables? What are the dependent variables?

【Tracking Training】

1. Research shows that when the application amounts of potash and phosphorus fertilizers are constant, the potato yield has the following relationship with the application amount of nitrogen fertilizer:

(1)The above table reflects the relationship between which two variables? Which is the independent variable? Which is the dependent variable?

Nitrogen fertilizer application amount and potato yield Nitrogen fertilizer application amount Potato yield

(2) When the nitrogen fertilizer application rate is 101 kg/ha, what is the yield of potatoes?

What if no nitrogen fertilizer is applied?

32.29 tons/ha 15.18 tons/ha

(3) Based on the data in the table, what do you think is the appropriate amount of nitrogen fertilizer? Tell me your reasons.

336 kg/ha, because the yield is maximum at this time.

【Do it】

1. As shown in the figure, the height of the cone is 4 cm. When the radius of the base of the cone changes from small to large, the volume of the cone also changes accordingly.

(1) In this change process, the independent variable is _______________ and the dependent variable is ______________.

(2) If the radius of the base of the cone is r (cm), then the relationship between the volume of the cone V (cm3) and r is ______________.

(3) When the radius of the base changes from 1 cm to 10 cm, the volume of the cone changes from _______ cm3 to ________3 cm.

2. As shown in the figure, the radius of the base of the cone is 2 cm. When the height of the cone changes from small to large, the volume of the cone also changes accordingly.

(1) In this change process, what are the independent variables and dependent variables?

Independent variable: Height of the cone Dependent variable: Volume of the cone

(2) If the height of the cone is h (cm), then the relationship between the volume of the cone V (cm3) and h is .

(3) When the height changes from 1 cm to 10 cm, the volume of the cone changes from _______ cm3 to ________3 cm.

Practice in class

1. As shown in the figure, the number m of matchsticks required to use matchsticks to piece together a pattern changes as the number n of squares is changed. During this change process, which of the following statements is incorrect ( )

A. m and n are both variables B. n is the independent variable and m is the dependent variable C. m is the independent variable and n is the dependent variable D. m changes as n changes

[Analysis] Choose C. From the meaning of the question, we can see that in this change process, m and n are both variables, and m changes with the change of n, so n is the independent variable and m is the dependent variable.

2. In the process of using solar water heaters to heat water, the water temperature in the water heater changes with the length of time it is exposed to the sun. The dependent variable in this problem is ( )

A. Sunlight intensity B. Water temperature C. Sun exposure time D. Water heater

[Analysis] Choose B. The water temperature changes with the length of time in the sun.

3. (Zigong High School Entrance Examination) In order to welcome the Provincial Games to be held in our city, the city organized a ladder-shaped flower team to participate in the opening ceremony. It is required to stand in 60 rows, with 40 people in the first row, and each subsequent row is better than the previous row. If there is one more person standing, the functional relationship between the number of people in each row y and the number of rows in that row x is _____.

[Analysis] According to the meaning of the question, the functional relationship between the number of people in each row y and the number of rows x is y=40+�x-1�=39＋x

Answer: y＝39＋x (x=1,2,3,…,60)

Class summary

Through the study of this class, we need to master:

1. Explore variable relationships in graphs.

2. Be able to express the relationship between variables using relational expressions.

3. Able to evaluate based on relational expressions.

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Update Time: 2024-06-30

This template belongs to Mathematics courseware Beijing Normal University Edition Seventh Grade Mathematics Volume 2 industry PPT template

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