Topicm6c3c9de826c40bde_1528449000663_0Topic

Applying rational functionrational functionrational function to interpret practical problems

Levelm6c3c9de826c40bde_1528449084556_0Level

Third

Core curriculumm6c3c9de826c40bde_1528449076687_0Core curriculum

V. Functions. The student:

13) uses the function $f\left(x\right)=\frac{a}{x}$, including its plot, to describe and interpret problems related with inversely proportional values, also in practical applications.

Timingm6c3c9de826c40bde_1528449068082_0Timing

45 minutes

General objectivem6c3c9de826c40bde_1528449523725_0General objective

Interpreting and operating information presented in the text, both mathematical and popular science texts, as well as in the form of graphs, diagrams, tables.

Specific objectivesm6c3c9de826c40bde_1528449552113_0Specific objectives

1. Communicating in English, developing basic mathematical, computer and scientific competences, developing learning skills.

2. Applying rational equations to solve text exercises.

Learning outcomesm6c3c9de826c40bde_1528450430307_0Learning outcomes

The student:

- applies rational equations to solve text exercises.

Methodsm6c3c9de826c40bde_1528449534267_0Methods

1. Chain of associations.

2. Situational analysis.

Forms of workm6c3c9de826c40bde_1528449514617_0Forms of work

1. Individual work.

2. Group work.

Lesson stages

Introductionm6c3c9de826c40bde_1528450127855_0Introduction

Students work with the method of the chain of associations. They fill empty links with terms, formulas and associations connected with rational equations. Students present their chains and discuss most important links.

The teacher verifies students’ words and clarifies doubts.

Procedurem6c3c9de826c40bde_1528446435040_0Procedure

The teacher introduced the subject of the lesson – applying rational functionrational functionrational function to solve practical problems.

Task
Students work in groups and analyse materials presented in the Slideshow. As conclusions, they write steps of solving the task.

[Slideshow]

Conclusions students should write down:

Steps of doing the text exercisetext exercisetext exercise:

1. Analysing the exerciseexerciseexercise.
2. Creating an equationequationequation.
3. Solving the equationequationequation.
4. Verifying conditions of the exerciseexerciseexercise.
5. Writing the answer.

Using obtained information, students take part in the task contest, by doing exercises on their own. For each correct solutionsolutionsolution they can get 4 points. Students that obtain most points get grades ‘very good’.

Contest task
Two workers do certain work in t days. The first worker would do this work alone in a days. In how many days would the second worker do this work, if he worked alone?

Contest task
Two trucks were supposed to transport building materials to the construction site in 10 days. The first truck broke down after 6 days and the second was transporting materials for 9 more days. In how many days would the first truck transport materials and in how many days the second one?

Contest task
When water gets to the swimming pool by first pipe, then the pool fills up in 2 hours, when with the second pipe, then it fills up in 4,5 hours more than when it gets filled with both pipes at the same time. In how many hours would it fill if the water was transported just by the first pipe and when it is transported just by the second pipe?m6c3c9de826c40bde_1527752263647_0When water gets to the swimming pool by first pipe, then the pool fills up in 2 hours, when with the second pipe, then it fills up in 4,5 hours more than when it gets filled with both pipes at the same time. In how many hours would it fill if the water was transported just by the first pipe and when it is transported just by the second pipe?

Contest task
Two pumps pump out a tank of oil in 3,75 hours. The first pump would pump out the tank alone in 4 hours less than the second. How much time would it take for each pump to pump out the cyst separately?

After finishing the contest, the teacher sum up results, rewards best students and clarifies doubts.

An extra task
A bath can be filled with water by two pipes. Time of filling the bath only by the first pipe is equal to 20 minutes and only by the second pipe is 30 minutes. Calculate the time of filling the bath while using both pipes at the same time.

Lesson summarym6c3c9de826c40bde_1528450119332_0Lesson summary

Students do the revision exercises.

Then together they sum‑up the classes, by formulating the conclusions to memorise:

Steps of doing the text exercise:
1. Analysing the exercise.
2. Creating an equation.
3. Solving the equation.
4. Verifying conditions of the exercise.
5. Writing the answer.m6c3c9de826c40bde_1527752256679_0Steps of doing the text exercise:
1. Analysing the exercise.
2. Creating an equation.
3. Solving the equation.
4. Verifying conditions of the exercise.
5. Writing the answer.

Selected words and expressions used in the lesson plan

equationequationequation

exerciseexerciseexercise

rational functionrational functionrational function

solutionsolutionsolution

task analysistask analysistask analysis

task solutiontask solutiontask solution

text exercisetext exercisetext exercise

verifying taks conditionsverifying taks conditionsverifying taks conditions