Its symbolic language: (1)∵AC=BC= 1/2AB, ∴ point C is called the midpoint of the line segment.
(2)∵ Point C is the midpoint of line segment AB, ∴AC=BC= 1/2AB (or AB = 2ac = 2bc);
Type 1 (single midpoint model)
Example 1, as shown in the figure, if the line segment AB=8Cm and point C is the midpoint of the line segment AB, find the lengths of AC and BC.
Teacher: Analysis: As can be seen from the figure, the total number of line segments is known, and the components are found. You can use the former expression, and if the component is known, you can use the second expression. The answer process is very short.
Tracking exercise: As shown in the figure, it is known that AC=3cm, and point C is the midpoint of line segment AB. Find the length of lines BC and AB.
Reflection, the span here is a bit too big for these students with poor foundation, and students can't accept it. Therefore, it is necessary to set the exercise 1 and the example 1 to 1, and only change the length of line AB.
But only students can always keep this requirement. Most students can't express themselves.
Type 2 (double midpoint model)
Example 2 As shown in the figure, point C is a point on line segment AB, point M and point N are the midpoint of line segments AC and BC, with AC=6cm and BC=4cm. Find the length MN of the line segment.
Teacher: Analyze: What is the meaning of the sentence "Points M and N are the midpoint of line segments AC and BC, respectively"?
Health: Shake your head.
Teacher: This sentence can be divided into two sentences: 1, point M is the midpoint of line segment AC, 2, and point N is the midpoint of line segment BC.
What can we know from the sentence 1? What about the second sentence?
Health: I can't say it clearly.
Most students are at a loss, at a loss. Still can't understand the meaning!
Reflection: It shows that students don't understand the essential meaning of the midpoint of the line segment.
Another example is needed to help students understand the meaning of the midpoint of a straight line.
Variant exercise:
1, as shown in the figure, it is known that point C is a point on line segment AB, point M and point N are the midpoint of line segments AC and BC respectively, line segment AB= 15cm, BN=3cm, and the length of line segment MN is found.
Reflection: this road is difficult to walk again, and the students can't find the north. No one can do it!
Tracking exercise 1 should be set to only change the length of AC and BC, and other conditions remain unchanged.
Although it is my own class, I always overestimate the students' understanding level.
I don't know why, I'm always uncertain about preparing students and teaching methods.