Topic analysis: this is a common problem of knowing the sum, knowing the difference and seeking the quantity in grade one and grade two. Many students are at a loss when they see this kind of topic, and there is nowhere to start. Some students directly formulated: 26-8= 18, but what does 18 mean? What should we do next? Let's use drawing to understand.
First, we draw a line graph (minimum or fixed quantity first), then draw a line segment representing pears, and then draw a line segment representing apples. The total number of these two lines is 26, because there are 8 more apples than pears (marked with a red pen), so 26-8= 18 represents the sum of two fruits when the number of pears and apples is equal (marked with a black line segment). So we only need to divide 18 equally, and we can know that there are 9 pears, so there are 9+8= 17 apples.
Formula (1):26-8= 18 (pieces)? Half of 18 is 9, 9 pears and 17 apples. Because the first-year students haven't learned division, they have to calculate half of 18, so everyone can understand and calculate.
Formula (2): Pears have (26-8)÷2=9 (pieces).
Apples have 9+8= 17 (pieces)
This kind of topic is the most basic method to solve the problem of drawing line segments. Students must be flexible and try to do the following question well.
Exercise 1. Children's school 1 (2) class has 50 students, with fewer boys than girls 10. How many male students are there? How many girl students are there?
Example 2. The sum of the numbers a, b and c is 360. As we all know, A is three times as big as B and B and twice as big as C. What are a, b and c respectively?
Topic analysis: This is a common problem for junior three students. The sum of several numbers and the multiple relationship between several numbers are known. When encountering such problems, it will be easier to understand and calculate by drawing a line segment diagram first. As shown in the figure below:
By observing the line graph, we can know that 360 is divided into 9 parts on average, and C accounts for 1 part, so we can get:
c？ 360÷( 1+2+2×3)=40
b？ 40×2=80
Answer? 80×3=240
Interested students can do exercise 2.
Exercise 2. Dad is five times as old as Xiao Ming, and grandpa is nine times as old as Xiao Ming. It is understood that grandpa is 35 years older than dad. How old are the three people?
The above questions will be better understood and calculated by drawing line segments. Drawing is a method we often use to solve mathematical problems, so we should use it flexibly at ordinary times.