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Learning Scenario
Logarithms are not difficult
Last updated 16/07/2014, by Sladjana Trajkovic
Language(s):
Domain: Mathematics>Numbers and Computation>Arithmetic>Number
Learning objectivesCognitive - Knowledge:
Factual
Conceptual
Procedural
Meta – cognitive
Cognitive - Process:
To remember
To understand
To apply
To think critically and creatively
Affective:
To pay attention
To respond and participate
To organize values
To form and follow a system of values
Psychomotor:
To imitate and try
To perform confidentially following instructions
To perform independently, skillfully and precisely
To adapt and perform creatively
Grade & AgeAge 15-16
15-16 godina
Grade: secondary education
Keywords/subjectlogarithm, the use of logarithms, the decimal logarithms, natural logarithms
logaritam, primena logaritama, dekadni logaritmi, prirodni logaritmi
Prerequisites Exponential functions
Eksponencijalne funkcije
Difficulty Levelmedium
Duration1 Hours & 15 Minutes
Special needVisual, Auditive, Psychomotor
Author(s)Name: Slađana Trajković Organization: Tehnička škola ,,15.maj" Prokuplje, Serbia Role: nastavnik matematike
Description/ main idea

The logarithm is perhaps the single, most useful arithmetic concept in all the sciences; and an understanding of them is essential to an understanding of many scientific ideas. Logarithms may be defined and introduced in several different ways. This is one of the way to learn them easier.


New function

The teacher introduce students to some examples from the world of science through which observed a new function

Nova funkcija

Nastavnik upoznaje učenike sa nekim primerima iz sveta nauke preko kojih uočavaju novu funkciju

I want to know
Hoću da znam

Description

Teacher lesson begins with a presentation I want to know. It contains a number of questions: how to measure the strength of earthquakes, how to determine the age of archaeological finds? , how to measure the brightness of a star? how to determine the neutrality of the solution, etc. 

Through discussion, students talking about earthquakes and how they begin to lead a task which should be determined that the earthquake was stronger. To solve the task, students should be familiar with the formula for determining the magnitude of the earthquake. In this formula, the students perceive the function of the logarithm. 

Another problem that the teacher presents to students the process of determining the age of archaeological finds. 

The teacher introduces students to the method of determining the age ogranskih samples using radiocarbon C14 (in archeology, but also in other sciences) used since the mid-twentieth century. The task for students is to help archeologists to estimate how old a tree from which he made a tool that served early man if physicists measure the value of the isotope S-14 four times smaller than that of living things today? 

The problem of determining how to measure the brightness of a star? 

The teacher presents to students the concept of apparent stellar size or magnitude. Teacher ask students how can to determine the absolute magnitude of the Sun.

Next question is: how to know which is the wind speed near the centar of tornado. 

Here is the presentation: https://www.youtube.com/watch?v=s1mPo8epXu8

Homework: Students should look at  the video tutorial about logarithm and law logarithms and try to do the examples they give.

Video tutorial is here: https://www.youtube.com/watch?v=y1IyTQmiIJI 

Through discussion, students talking about earthquakes and how they begin to lead a task which should be determined that the earthquake was stronger. To solve the task, students should be familiar with the formula for determining the magnitude of the earthquake. In this formula, the students perceive the function of the logarithm. 

Teacher lesson begins with a presentation I want to know. It contains few questions: how to measure the strength of earthquakes, how to determine the age of archaeological finds, how to measure the brightness of a star, how to determine the neutrality of the solution, how to know which is wind speed near the centar of tornado. 

Students noticed a new function - logarithm.

Presentation is here: https://www.youtube.com/watch?v=s1mPo8epXu8

Types and Techniques

Receptive Type: Reading, Viewing
Information Type: Analyzing, Manipulating

Resources


Educational objects (as file):
1. I want to know

Educational objects (as url):
1. https://www.youtube.com/watch?v=s1mPo8epXu8
2. Logarithms - video tutorial

Duration

45 Minutes

Laws of logarithms
Pravila logaritmovanja

Description

Start  discussion about the lessons that students are supposed to look. Repeat what logarithms and which are the basic rules Logarithmic. If it was an example that students were unable to do so, the teacher works with the students or for example a student who has done the examples. 

Students divided into four groups. 

he task for the first group: 2,4,8,16,64,256 using numbers and mathematical operations of addition, subtraction, multiplication and division, assemble logarithmic expressions (7 - 10 posting expression). 

The task for the second group: 3,9,18,27,63,81,6561 using numbers and mathematical operations of addition, subtraction, multiplication and division, assemble logarithmic expressions (7-10 terms). 

The task for the third group: Using the numbers 5.10, 25,625,64,15625 and mathematical operations of addition, subtraction, multiplication and division, assemble logarithmic expressions (7 - 10 posting expression). 

The task for the fourth group: Using the numbers 7.14, 28,49,343,2401 and arithmetic operations of addition, subtraction, multiplication and division, assemble logarithmic expressions (7-10 terms). 

he third part of the class: Students choose a group to do the tasks that they are put together. Each group sets the selected group task 4. Winning group that has most accurately performed tasks. 

Homework: Each group solved tasks was compiled. View video tutorial on decadal and natural logarithms. Solved examples that students saw the first class using knowledge: 

1 To measure the strength of earthquakes? 

2 To determine the age of archaeological finds? 

3 to determine the absolute magnitude of the Sun 

4 Determine the pH value of the solution. 

Find similar examples of the application of logarithms. 

Duration

45 Minutes

What we learned?

Discussion about homework. Examples from the world of science that students get, now can do. Students represent and solve the examples they found that use of logarithms.

Šta smo naučili?

Čas početi diskusijom o domaćem zadatku. Primere iz sveta nauke koje su učenici dobili , sada uraditi. Učenici predstavljaju i rešavaju primere koje su pronašli u kojima se koriste logaritmi.