content

How tall is this big tree?

teaching

target

1. Through the practice of measuring the shadow length of various targets, students can actively explore and master the proportional relationship between the shadow length and the actual height of the target.

2, through group cooperation, cultivate students' ability to use their hands and brains, solve practical problems and the spirit of unity and cooperation.

3. Through activities, students can feel the close connection between mathematics and real life, further stimulate their interest in learning mathematics, and cultivate innovative spirit in activities.

Emphasis and difficulty in teaching

Make students actively explore and master the proportional relationship between shadow length and actual height of target.

Teaching methods and means

Teaching methods: guide students to calculate and imagine.

Learning methods: group cooperation, discussion and induction.

Teaching preparation

Small blackboard

teaching process

First, create a situation to stimulate interest

1. Play a clip of the cartoon "Smart Two Generations-Selling Shades"

Synopsis: On a hot afternoon, a long-term worker is enjoying the cool under a big tree outside the Bayi Building with two generations of lovers. At this time, Mr. Bayi appeared and asked everyone to pay 100 yuan to buy a sunshade. The clever Avanti saw through Bayi's greedy intention and decided to play along and teach him a lesson. So everyone chipped in 100 yuan to Bayi, and Bayi left contentedly. In the evening, a full moon rose into the sky, and the bright moonlight shone on the big tree, and the long shadow of the big tree just fell on the courtyard and roof of Master Bayi. Long-term workers, led by two generations of love, poured into Bayi's home, and some even climbed onto the roof. Bayi got a fright and hurried to save everyone. At this time, two generations of love said, "We spent money to buy shade. Wherever the shadow goes, we follow it. If you want us to go out, you have to pay. " Master Bayi had to give up and beg for mercy. He not only returned 100 yuan, but also promised not to stop everyone from enjoying the cool in the shade. )

Teacher: After reading this story, what do you think of the relationship between the two generations?

Health: Smart and resourceful, dare to confront Master Bayi and seek happiness for the poor.

Teacher: However, the story is not over. Bayi is reluctant, and has been looking for opportunities for revenge. A few days later, the two generations hurried out. Bayi came to the tree with a few thugs, pushed the long-term workers aside, and then ordered the thugs to cut down the tree. There is only such a big tree nearby, with dense branches and leaves, which is the only place for long-term workers to escape the summer. It was his trick to beg Mr. Bayi not to cut down trees. I saw Bayi roll his eyes, grinned twice and said, "You don't have to cut down trees. As long as one of you can tell how tall this big tree is, the condition is that you are not allowed to climb it and measure it. Otherwise, you'd better scrape together enough 100 yuan and come here to enjoy the cool! " The long-term workers were shocked. You look at me, I look at you. I'm anxious. How everyone hopes that the two generations of love can appear here at this time!

Second, find the law and solve problems skillfully

Teacher: Smart students, are you willing to use your brains and give us an idea to help the long-term workers smash Master Bayi's tricks?

1. Think positively and express your opinions.

① Students discuss in groups and speak by name.

Health: You can sneak up the tree when Master Bayi is not paying attention, put down a rope as high as the big tree, and measure how long the rope is, and how high the big tree is;

Health: You can tie several bamboo poles into a long bamboo pole and stand beside the big tree. If it is as tall as a big tree, measure the length of the bamboo pole.

Health: Use shadows. When the sun shines, when our shadow is the same as our height, it means that the shadow of the big tree is also the same height as the big tree. Measure the shadow of the tree immediately.

Health: Send someone to find Avanti at once.

Health: using the media. First take a picture of a big tree or something, see how many times the height of the big tree is equivalent to this thing, and then measure the height of this thing. How many times is the height of the big tree?

Health: Tie a long plastic rope under the hydrogen balloon, put the hydrogen balloon in the air and measure the length of the plastic rope when it is the same height as the tree.

……

2, careful observation, looking for the law.

The teacher just heard a classmate mention the use of shadows. Yes, the whole incident was actually caused by the shade (that is, the shadow of the tree). Let's see if we can find a way to calculate the height of a tree from its shadow.

(2) (Courseware display) A picture: Father and son are facing the sunset and walking on the sidewalk, casting two shadows behind them, one long and one short.

Teacher: Have a look. What did you find?

Health: the father is tall and the shadow is long; A short son has a short shadow.

(3) Before class, the teacher also asked the students to measure the shadow length of the long stick and the short stick and their own height, and fill in the measurement results on this form (P78 form). Please tell me when and where you measured it, and what was the result. (Each group reports its own measurement data, which may be different. )

Teacher: Why do people measure different shadow lengths with sticks of the same length?

Note: Because the time and place of measurement in each group may be different (for example, some students measure in the morning, and some students measure in the afternoon or noon), the shadow length of upright wooden sticks with the same height also changes.

4 observation. Please carefully observe the three sets of data you have measured. Can anyone tell me what the shadow length has to do with the actual height?

⑤ Students observe and discuss in groups. At the same time, it is concluded that the higher the actual height of an object, the longer its shadow. By trying to calculate, it is found that bamboo poles are long and short, and the shadow length is long and short, but the ratio of pole length to shadow length of each bamboo pole is equal.

3. Use laws skillfully to solve difficult problems.

Teacher: The students found the relationship between the shadow length and the height of the object. How to use this relationship to help long-term workers solve difficult problems?

② Students discuss. According to the students' answers, the teacher will demonstrate the following process step by step:

A bamboo pole with a length of 1 m was erected vertically beside the big tree, and the shadow length of the bamboo pole was measured to be 0.5m, and the shadow length of the big tree was 2.8m.. According to the above data, please work out the height of this big tree in groups. See which group of students use the most methods.

(3) Each group of students reports their own problem-solving methods and ideas.

Method 1: Because the bamboo pole is twice as long as its shadow, the height of the big tree is twice as high as its shadow.

The formula is: 2.8×( 1÷0.5).

Method 2: Because the shadow length of bamboo pole is 1/2 of its height, the shadow length of big tree is also 1/2 of its height.

The formula is: 2.8(0.5) liters

Method 3: Because the shadow length of the big tree is 5.6 times that of the bamboo pole, the height of the big tree is 5.6 times that of the bamboo pole.

The formula is: 1×(2.8÷0.5)

Method 4: Because the shadow length of bamboo pole is 5/28 of the shadow length of big tree, the height of bamboo pole is also 5/28 of the height of big tree.

The formula is l \u( 0.5 \u 2.8).

Method 5: ...

Third, continue to explore and practice in depth

1. Teacher: The students really used their brains. Even two generations of love praised us. Look:

(Showing courseware) Two generations of love give everyone a thumbs-up and say, Class 6 (*), Jaaksi! .

Teacher: Are the students happy to see Bayi go with his head drooping?

Yes, we are really happy to use our wisdom to help the long-term workers smash the plot of August 1st again.

2. Next, we will use the method we have mastered today to arbitrarily select a target object on the playground, such as flagpole and basketball stand, measure its shadow length and calculate its actual height.

Preparatory work:

(1) Start the division of labor in groups.

② Thinking in the actual measurement process: Is there a more ingenious measurement method?

3. Field measurement, recording and calculation

4. Summary of situation feedback activities

Small errors are allowed in the measurement and calculation results of each group report. If there is a big discrepancy, help find out the cause of the error and correct it on the spot.

Fourth, incentive evaluation, problem extension

What have you learned through the activities and study in this class? How did you know? Do you like your study?

When you get home, choose the huge object you like, measure and calculate its height.

After teaching

modify

blackboard-writing design

Method 1: Because the bamboo pole is twice as long as its shadow, the height of the big tree is twice as high as its shadow.

The formula is: 2.8×( 1÷0.5).

Method 2: Because the shadow length of bamboo pole is 1/2 of its height, the shadow length of big tree is also 1/2 of its height.

The formula is: 2.8(0.5) liters

Method 3: Because the shadow length of the big tree is 5.6 times that of the bamboo pole, the height of the big tree is 5.6 times that of the bamboo pole.

The formula is: 1×(2.8÷0.5)

Method 4: Because the shadow length of bamboo pole is 5/28 of the shadow length of big tree, the height of bamboo pole is also 5/28 of the height of big tree.

The formula is l \u( 0.5 \u 2.8).

Method 5: ...