"Basic Properties of Equations" PPT Courseware 3

Description

"Basic Properties of Equations" PPT Courseware 3

learning target

1. Experience the process of exploring the properties of equations and understand the basic properties of equations.

2. Be able to use the basic properties of equations to transform equations.

3. Cultivate students’ reasoning awareness through the exploration and application of the basic properties of equations.

Communication and discovery one

Think about the following questions and discuss them with your classmates.

(1) Xiaoying is a year old this year and Xiaoliang is b years old this year. How old will they be in c years?

Answer: Xiaoying is (a+c) years old; Xiaoliang is (b+c) years old

(2) If Xiaoying and Xiaoliang are the same age, (i.e. a=b), will they still be the same age in c years? What about C years ago? Why?

What conclusion do you find from (2)? Can you express it as an equation?

my discovery

If a=b, then a+c=b+c, ​​a-c=b-c

Basic properties of equations 1: If the same integer is added (or subtracted) to both sides of the equation, the result is still an equation.

Basic property of equation 2: If both sides of the equation are multiplied (or divided) by the same number (the divisor cannot be zero), the result is still an equation.

Combination of numbers and shapes: As shown in the figure, the line segments a, b, and c are known, where a=b and c

(1) If line segments a and b are added (or subtracted) to line segment c respectively, are the resulting line segments still equal? Drawing instructions.

(2) If the lengths of line segments a and b are expanded (or reduced) by the same multiple at the same time, are the resulting line segments still equal? Drawing instructions.

Apply what you learn

Example 1: Fill in the appropriate integers on the horizontal lines of each of the following questions to make the equation true, and explain which basic property of the equation is based on and how it is transformed.

(1) If 2x-5=3, then 2x=3+____

(2) If -x=1, then x=____

Answer the following questions:

(1) Can we get the equation a+3=b+3 from the equation a=b? Why?

(2) Can we get the equation a/2=b/2 from the equation a=b? Why?

(3) Can we get x=y from the equation x+5=y+5? Why?

(4) Can we get the equation x=y from the equation -2x+1=-2y+1? Why?

Expansion and extension

1. Among the following statements, which one is correct ( )

A. If ac=bc, then a=b B. If a/c=b/-c, then a=-b

C. If x-3=4, then x=3-4 D. If -1/3x=6, then x=-2

2. Among the following equations, what can be obtained by deforming equation 2x-3=x+2 is ( )

A. 2x-1=x B. x-3=2 C. 3x=3+2 D. x+3=-2

In-person testing

1. Which of the following equations is incorrectly deformed ( )

A. From a=b, we get a+5=b+5; B. From a=b, we get 6a=6b;

C. From 6+a=b-6, we get a=b-12; D. From x=y, we get x÷3=3÷y

2. It is known that the equation ax=ay, which of the following deformations is incorrect ( ).

A. x=y B. ax+1= ay+1 C. ay=ax D. 3-ax=3-ay

3. If x=3x+2, then x-___=2, according to __________

Keywords: teaching courseware on the basic properties of equations, Qingdao edition seventh grade mathematics volume PPT courseware download, seventh grade mathematics slide courseware download, basic properties of equations PPT courseware download, .PPT format;

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Update Time: 2024-11-19

This template belongs to Mathematics courseware Qingdao Edition Seventh Grade Mathematics Volume 1 industry PPT template

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