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Title of the Experience

Exponential functions and their function for the life

Name of the teacher

Katarína Javorová

Country where it took place

Slovakia

School typology

Lower Secondary School

Thematic Area

Maths

Experience typology

Teaching in class

Type of contact

Direct

Description of the Experience

My experience says that there is always at least one student at the beginning of the new curriculum topic that asks the question "What is it good for me? Where do I use it further? I want to be a lawyer or a doctor and mathematics I do not need ...". Similarly it is also in the case of the topic of exponential functions. Here I use an example from a daily life - annual interests in the banks. Students do not understand in the beginning what interests and exponential functions have in common. I give them a task: Find in different banks what the interest rates are for different time periods (monthly interest, quarterly interest, annual interest). Later in the class we work with these identified data. The given task #1 for students is as follows: At the beginning put into AB bank 1000 EUR with an annual interest of 10%.

A) How much will be in the account in AB bank AB after 10 years?

B) How would it be if we saved the money in XY bank account?

C) What is the difference in profit between the deposit to the bank AB and the bank XY?

D) Would you be able to figure out how much we would have in an account at the Bank AB (XY Bank) after n number of years?

The students realize the difference between banks (Bank AB is for easier counting, finding prescription for n-years and is a model, while the bank XY is an existing bank with real numbers).

Based on this example pupils can understand the importance of exponential functions, they can compare it with a power law function. All students get engaged in calculating, they are even willing to count without a calculator. Of course I have a positive experience from this lesson. Even the less thriving pupils get involved, the theme based on the correct choice of examples addressed them well.

There are other examples suitable for understanding the exponential function which pupils receive. Task #2 for the students is: "Is it more advantageous for the bank to provide citizens with lower interest rates for shorter periods or greater interest rates for a longer period?" Task# 3: “Why do we have to borrow money from various other companies or loan sharks?

I enter the issue task as an annual course activity.

A) How much will be in the account in AB bank AB after 10 years?

B) How would it be if we saved the money in XY bank account?

C) What is the difference in profit between the deposit to the bank AB and the bank XY?

D) Would you be able to figure out how much we would have in an account at the Bank AB (XY Bank) after n number of years?

The students realize the difference between banks (Bank AB is for easier counting, finding prescription for n-years and is a model, while the bank XY is an existing bank with real numbers).

Based on this example pupils can understand the importance of exponential functions, they can compare it with a power law function. All students get engaged in calculating, they are even willing to count without a calculator. Of course I have a positive experience from this lesson. Even the less thriving pupils get involved, the theme based on the correct choice of examples addressed them well.

There are other examples suitable for understanding the exponential function which pupils receive. Task #2 for the students is: "Is it more advantageous for the bank to provide citizens with lower interest rates for shorter periods or greater interest rates for a longer period?" Task# 3: “Why do we have to borrow money from various other companies or loan sharks?

I enter the issue task as an annual course activity.

Comments on this Teachers Experience

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Date: 2014.10.16

Posted by **Marieta Andreeva** (*Bulgaria*)

In secondary schools in Bulgaria math classes are just two hours per week, and exponential functions are not included in the curriculum at all. The extracurricular activities in maths can be 1 hour per week, which aslo is insufficient. I find the practice very interesting and if I have time I would use it in my teaching classes. But such examples would take a long time and in order to cover all the material in maths included in the curriculum we focus only on solutions of problems.

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