List a case in teaching that reflects the development of students' data analysis concepts

Unit 7 "Fan Chart" P84~P85 of Volume 10, Fifth Grade, Beijing Normal University Edition

The teaching material first introduces the "Pagoda Chart of Balanced Diet of Chinese Residents" as the learning material It is helpful for students to understand the role of statistics in life, and also permeates the education of healthy diet. From the location and area of ??each floor of the pagoda, we can see the status and proportion of various foods in the diet. At the same time, the textbook presents a statistical table of the daily food intake of Xiaoli's family of three, requiring students to calculate the percentage of each food intake in the total intake. Then, the textbook presents bar charts and fan charts, mainly to allow students to understand statistical charts and understand fan charts through comparison with bar charts and fan charts. On this basis, organize students to communicate and talk about what information can be obtained from statistical charts? Understand the different characteristics and functions of bar charts and sector charts. When teaching, I mainly use these learning materials to organize students to learn, gradually understand the fan chart, and realize that the fan chart reflects the relationship between the whole and the part.

In teaching, I do this:

(1) Conversation review and transfer of new knowledge

The intention is to use the "Pagoda of Balanced Diet for Chinese Residents" to introduce, It is helpful for students to understand the role of statistics in life, and also permeates the education of healthy diet

(2) Comparative and induction to find out the characteristics

1. Present courseware: The teacher also collected small The daily intake of various types of food for Li’s family of three (the statistical table is shown on the right side of the dietary pagoda)

Ask questions to make students think

What did you find through observation? (Guidance and dietary pagoda) Chart scale (contact)

What statistical chart can we use to represent the data in the statistical table? (Courseware: Show the bar chart below the table)

What information can students get from the bar chart?

Why is it represented by a bar chart? (Experience the superiority)

That is, we can clearly see from the bar chart - "the intake of each type of food".

Let’s take a look at this statistical table again: What does “percentage of total intake” mean when we add a column? (Sheng: What percentage of each food intake accounts for the total intake?)

To ask this question, what do you need to ask first? (Total intake) Then ask each group of students to calculate the percentage of one food intake in the total intake (group cooperation and exchange) and see who can calculate correctly and quickly?

(3) Observation and discovery of the effect of experience

Can we use the bar graphs and line graphs we have learned to express the percentage of the total intake (cannot), then we Let’s study a new statistical chart together

What do you think is the most appropriate representation? Give reasons.

(Focus on the fan chart from the representation method students want)

This kind of statistical chart expresses the percentage of various types of food in ---- (a circle inside) (presenting a circle), that is, as the quantity of the unit "1", consider it as a whole (blackboard writing: whole)

① So ??how do you think it is expressed in a circle? (Divide the circle into several parts...)

②How to divide it? (How many percent of each type of food occupies, just draw what percent of the circle’s area it occupies) Based on the previously calculated data, divide the circle into 5 parts (show it is divided into 5 parts). Represents the various parts of the whole.

What shape does each part look like? (Like a fan) Yes, it's called a fan chart.

(Write on the blackboard)

What percentage of food do you think each part should represent? (Free answer for students: The biggest piece is cereal, the smallest...reason)

2. (Present a complete fan chart) What information can you get from this fan chart? (raw: cereals account for 47.4%...fats are the least...)

3. If you were a decision-maker, how would you like to decide on food intake

This paragraph is designed Intention: In order to cultivate students' mathematical awareness and spirit of exploration, I ask them to communicate and discuss in groups during the teaching process. They can explore the characteristics of fan charts and experience statistical ideas based on their own discoveries and ideas. Here I am just Play a guiding role, no longer the role of the absolute subject

(4) Layered exercises to consolidate application

1. Talk about it

Observe this statistical chart and talk about what information you got from it.

Given that the total land area of ??our country is 9.6 million square kilometers, let students use percentage multiplication to calculate the area of ??various types of terrain in tens of thousands of square kilometers

{Design intention: I further realized that this fan-shaped statistical chart only represents the percentage of various types of terrain in the total land area. It is not possible to directly see how many thousands of square kilometers the actual area of ??each type of terrain is. I also have a deeper understanding that the fan-shaped statistical chart can clearly express the quantity of each part. relationship to the total quantity. This is the characteristic of the fan chart and the difference from the bar chart and the line chart. }

(The courseware presents 3 questions in the book one by one)

Question (2): Let’s first look at this fan chart. This is a picture about the various types of eggs. Statistical chart of part weight as a percentage of egg weight

What do you know from this chart? (Predict: What percentage does each of them account for?)

In this picture, what is used to represent the weight of the eggshell, and what is used to represent the weight of the egg?

Then we can also say that this sector accounts for 15% of the entire circle

Summary: Sector statistical charts use a circle to represent the quantity of the unit "1", and use the sector to represent the Partial quantity reflects the relationship between the partial quantity and the total quantity.

Question (3): In addition to asking students to understand the fan chart, we also need to ask students to talk about their feelings?

2． Give it a try

The courseware presents the schedule of first and fifth grade students.

(1) Let’s see what are the differences in the allocation of work and rest time between first grade and fifth grade students? Look at the picture carefully and talk to each other at the same table.

For communication: first grade students have slightly more time for activities and sleep in and out of school, slightly more class time for fifth grade students, and more self-study time for fifth grade students. ...

(2) Can you calculate based on the statistical chart, the time these two students spend in class, self-study, activities inside and outside the school, three meals, washing, and sleeping every day? What is their total time? How can the time for each activity be calculated? Calculate in a notebook.

(3) Can you ask another math question? Who can help him answer it?

{Design intention: The exercise design is based on the students’ life experience and existing knowledge background, connects with life, and mathematicalizes life experience, embodying that "mathematics originates from life, resides in life, and is used in life." thoughts. }

(5) Summary.

What can be seen most clearly from this fan chart? What are the characteristics of a fan chart? (Discuss among classmates)

This is a case in my teaching. I teach according to the ideas of collecting data, organizing data, extracting information, and finally making decisions.