Teaching objectives
1. Understand the characteristics of engineering problems and understand that the total workload can be expressed in "1". Work efficiency can be expressed as a fraction of the workload completed per unit time.
2. Understand and master the quantitative relationship and solutions of engineering problems.
3. Cultivate students' ability to use existing knowledge to analyze and answer new questions.
Teaching emphases and difficulties
Learn how to use the unit "1" to represent the total amount of work, and use a fraction of the total amount of work completed in a unit time to represent the work efficiency. Master the solutions to engineering problems.
teaching process
Review preparation
1. We have studied the work problem before. Who can remember which three quantities are involved in the question of work? (Total amount of work, working hours, working efficiency)
What is the relationship between them?
Students dictate and teachers show their projections;
Total amount of work = working efficiency × working time
Work efficiency = total workload ÷ working hours
Working hours = total amount of work ÷ working efficiency
2. a canal 120 meters, it was repaired in five days. How many meters will be repaired on average every day?
According to the relationship between the three quantities, what do you know about this problem? Ask for what? How to form? (120÷5=24 (m))
What does 24 mean? (work efficiency)
Some. Are obtained through workload/working hours. )
Work efficiency can be a specific quantity or a part of the total workload completed in a unit time.
Learn a new course
1. Give an example of 10.
A section of highway is 30 kilometers long. Team A/KLOC completed the repair in 0/0 and Team B/KLOC completed the repair in 0/5. How many days did it take for the two teams to complete the repair together?
2. Analyze the solution.
(1) Look at the questions, think, form, solve and write them in the exercise book.
(2) Tell me about your demonstration.
30÷(30÷ 10+30÷ 15)
According to what formula? (Total amount of work ÷ work efficiency and = working hours)
What do you want from 30÷ 10? What do you want from 30÷ 15?
What do these two quotients get by adding them up? (The working efficiency of Team A and Team B and. )
What do you get by dividing 30 by their sum? (Man-hours for joint repair. )
(3) blackboard writing problem solving process:
30÷(30÷ 10+30÷ 15)
=30÷(3+2)
=30÷5
=6 (days)
A: The two teams can complete the joint repair in six days.
3. Reanalyze the conditions in the transformation questions.
(1)30 km changes to 40 km, 45 km, 500 km, 10 km, 2 km. Please work in groups, and choose a data solution for each group.
(2) Who can tell us how many meters of works your group selected? What is the result of the solution?
Each group chooses one student to answer, and the result is 6 days.
(3) Since the total amount of work has changed and the result remains the same, can this question be answered by removing the specific amount of the total amount of work in the question?