What is an algorithmic model? An algorithm is a clear and precise instruction to a specific performer to perform a final sequence of actions leading to a set goal. The stages of activity from determining the goal (setting the task) to obtaining the result are as follows: 1) Defining the goal 2) Planning the work of the performer 3) Work of the performer 4) Obtaining the result The algorithm is an information model of the performer’s activity. We will call such a model algorithmic.
System of executor's commands To build a real plan - an algorithm that turns out to be feasible, you need to know exactly the capabilities of the executor. These capabilities are determined by the system of executor commands (SKI). When composing an algorithm, one must not go beyond the framework of the SKI. This is the understandability property of the algorithm. For an automaton, SKI is a strictly defined finite set of commands put into it by its designers. Therefore, an algorithm is an accurate description of its operation, and the automaton performs the work by formally following the instructions of the algorithm. To control an automaton or computer, it is not difficult to come up with a formalized language for describing algorithms. Such languages are called programming languages, and an algorithm represented in a programming language is called a program.
Example of an algorithmic model The first player guesses an integer from a given range of numbers, for example, from 1 to 100. The second player must guess this number in the least number of questions. An algorithm for guessing a number using the halving method, aimed at a human performer. Algorithm Guessing a number Given: a range of numbers from A to B Must: guess the number X conceived by the player using the halves algorithm Start 1) Ask a question: Is X less than the average value between A and B? 2) If the answer is “YES”, then take the whole part of the average value as value B. 3) If the answer is “NO,” then take the nearest integer greater than the average as the value of A. 4) If the values of A and B are equal, then their common value is the desired number X. 5) If the values of A and B are not equal, then return to step 1. End This algorithm focused on the human performer, not the computer.
Algorithm “Half division” Alg Half division Whole A, B, X Start Enter A, B, X While A B, repeat Nc If X(A+B)/2 Then B:= Whole((A+B)/2) Otherwise A: = Integral ((A+B)/2)+1 kV Kc Output A End Start Start End Input A, B, X Output A AB X(A+B)/2 V: = INTEGRAL ((A+B )/2)A:=INTEGR ((A+B)/2)+1 no yes no yes
Flowchart A flowchart is a directed graph indicating the order in which algorithm commands are executed by the executor. The blocks - the vertices of this graph - indicate individual commands that are given to the performer, and the arcs indicate the sequence of transitions from one command to another. Commands - actions - are written in rectangles on block diagrams; conditions that determine the direction of further execution of commands are written in diamonds; in parallelograms – commands for input or output of information; in ovals – the beginning or end of the algorithm execution. Here we can talk about the path through the graph during the execution of the algorithm. Any path starts from the “Start” vertex and ends at the “End” vertex. Inside, the path can be different depending on the initial data and the results of checking the conditions. A flowchart is a graphical form, an algorithmic language - two different forms of representing an algorithmic model.
Structured programming The structure of the constructed algorithm is a loop with nested branching. Any algorithm can be built from a combination of three basic algorithmic structures: following, branching and looping. This statement is the basis of a technique called structured programming. Modern languages programming allow you to easily move from a description of an algorithm to a program if the algorithm is built structurally. Therefore, the most rational model of the performer’s activity is a structural algorithmic model.
Tracing an algorithm - a model of processor operation In order to check the correctness of an algorithm, it is not at all necessary to translate it into a programming language and perform tests on a computer. A person can also test the algorithm - by tracing. When performing manual tracing, a person simulates the operation of the processor, executing each command of the algorithm and entering the results of the commands into a trace table. It is a model of how the processor operates when executing a program. The program is executed step by step (first column of the table). The Algorithm Command column displays the contents of the processor command register. Where is the next command placed? The “Variables” column displays the contents of computer memory cells (or processor memory registers) allocated for variable values. The column “Performed actions” reflects the actions performed by the arithmetic-logical device of the processor.
Municipal budgetary educational institution
"Chubuklinskaya secondary school"
Zainsky municipal district of the Republic of Tatarstan
Algorithm as an activity model
(outline of a computer science lesson in 10th grade)
Computer science teacher: Safiullina R.I.
Topic: Algorithm as a model of activity
Objectives: Repeat the definition of an algorithm, recall the concept of a model and give a definition of an algorithmic model; Learn to represent any activity in the form of an algorithm graphically; recall the basic forms of representing the algorithm in the form of block diagrams. Develop the ability to plan a sequence of actions to achieve a goal. Formation of cognitive interest as a component of educational motivation.
During the classes
Organizing time
Greeting students
Updating the acquired knowledge
What is a graph? What does it consist of?
Which graph is called undirected (directed)?
What is a network? What characteristic features does the network have?
What systems are called hierarchical?
What is the convenience of tabular presentation of information?
What is a binary matrix? What information does it contain?
Problem solving
No. 2. The bottle, glass, jug and jar contain milk, lemonade, kvass and water. It is known that water and milk are not in a bottle, a vessel with lemonade is located between a jug and a vessel with kvass, there is neither lemonade nor water in a jar. The glass stands next to the can and the vessel with milk. Where is each liquid poured?
No. 3. In the gymnastics competition, Anya, Vera, Galya and Natasha took the first four places. Determine who took what place if it is known that Galya is second, Natasha, although she did not become the winner, was among the prize-winners, and Vera lost to Anya.
Learning new material
An algorithm is a clear and precise instruction to a specific performer to perform a final sequence of actions leading to a set goal.
Stages of activity from defining the goal to obtaining the result:
Examples of an algorithmic model
The first player guesses a whole number from a given range of numbers, for example from 1 to 100. The second player must guess this number in the least number of questions.
Let's write an algorithm for guessing a number using the halving method, focused on the performer - a person
Given: range of numbers from A to B
Necessary: guess the number X conceived by the player using the half division algorithm
Start
1. Ask the question: Is X less than the average between A and B?
2. If the answer is “yes”, then take the whole part of the average value as value B
3. if the answer is “no”, then take the nearest integer greater than the average as value A
4. If the values of A and B are equal, then their common value is the desired number X
5. If the values of A and B are not equal, then return to step 1
End
Let us present the algorithm in the form of a block diagram.
In order to check the correctness of the algorithm, you need to perform a trace.
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Algorithm command |
Variables |
Executed |
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actions |
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Input A,B,X |
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Reinforcing the material learned
A) Page 48 of the textbook describes an algorithm for finding the greatest common divisor (Euclidean algorithm), aimed at a human performer. Present it in the form of a block diagram and in an algorithmic language for the computer performer.
B) Having completed the previous task, trace the Euclidean algorithm to find the GCD of the numbers 128 and 56.
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Operation |
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| Document |
Lesson topic: “Algorithm as a model of activity.”
Goal: explain a new topic in an interesting and clear way.
Introduce students to the topic: “The concept of an algorithm. Types of algorithms and their properties”;
Students should know the concept of an algorithm, the properties of algorithms;
Students should be able to give examples of algorithms.
During the classes:
1. Organizational moment.
2.Study new topic.
Let's start repeating the concept of an algorithm by looking at an example. Let's say you want to cut out a model of a car from paper. The result will largely depend on your skills and experience. However, achieving your goal will be much easier if you first outline an action plan, such as the following:
1. Study the image of the car according to the existing model.
2. Draw the doors and car body on paper.
3. Cut out sketches.
4. Try to attach the sketches and correct errors.
5. Glue the parts of the model together.
By following the prepared plan, any person, even those who do not have artistic abilities, but who have patience, will definitely get a good result. Similar plan with detailed description actions necessary to obtain the expected result is called an algorithm.
The concept of an algorithm. ( Provide additional information)
The appearance of algorithms is associated with the origins of mathematics. More than 1000 years ago (in 825), a scientist from the city of Khorezm, Abdullah (or Abu Jafar) Muhammad bin Musa al-Khorezmi, created a book on mathematics in which he described methods for performing arithmetic operations on multi-digit numbers. The word “algorithm” itself arose in Europe after the translation into Latin of the book of this Central Asian mathematician, in which his name was written as “Algorithms”.
Algorithm- a description of a sequence of actions (plan), the strict execution of which leads to the solution of the task in a finite number of steps.
Algorithmization- the process of developing an algorithm (action plan) to solve a problem.
Examples of algorithms:
Any device purchased in a store is supplied with instructions for its use.
Every driver must know the rules of the road.
Mass production of cars became possible only when the procedure for assembling a car on an assembly line was invented.
Properties of algorithms.
We encounter algorithms at every step. We perform some of them automatically, without even thinking about it. When performing some actions, we do not even suspect that we are performing a certain algorithm.
These examples are nothing more than an algorithm. Despite the significant differences in the essence of the actions of these examples, one can find many similarities in them. These General characteristics are called properties of the algorithm. Let's look at them.
Discreteness(from Latin discretus - divided, intermittent) is a division of the algorithm into a number of separate completed actions (steps). What is common in the above algorithms is the need for strict adherence to the sequence of actions. Let's try to rearrange the second and third actions in the first example. You, of course, can perform this algorithm, but the door is unlikely to open. And if we swap, say, the fifth and second steps in the second example, the algorithm will become unfeasible.
Determinism(from Latin determinate - certainty, accuracy) - any action of the algorithm must be strictly and unambiguously defined in each case.
For example, if buses of different routes approach a stop, then the algorithm must indicate a specific route number - 5. In addition, it is necessary to indicate the exact number of stops that must be passed - say, three.
Limb- each individual action and the algorithm as a whole must be able to be completed. In the examples given, each action described is real and can be performed. Therefore, the algorithm has a limit, that is, it is finite.
Mass character- the same algorithm can be used with different source data.
Efficiency- there were no errors in the algorithm.
Types of algorithms.
There are 4 types of algorithms: linear, cyclic, branching, auxiliary.
Linear(sequential) algorithm - a description of actions that are performed once in a given order.
The algorithms for unlocking doors, making tea, and preparing one sandwich are linear. A linear algorithm is used to evaluate an arithmetic expression if it involves only addition and subtraction.
Round robin algorithm- a description of actions that must be repeated a specified number of times or until a specified condition is met. The list of repeated actions is called the body of the loop.
Many processes in the surrounding world are based on repeated repetition of the same sequence of actions. Every year spring, summer, autumn and winter come. Plant life goes through the same cycles throughout the year. By counting the number of complete turns of the minute or hour hand, a person measures time.
Condition- an expression located between the word “if” and the word “then” and taking the meaning “true” or “false”.
Branching algorithm- an algorithm in which, depending on the condition, either one or another sequence of actions is performed.
Examples of branching algorithms: if it rains, then you need to open an umbrella; if your throat hurts, then the walk should be cancelled; if a movie ticket costs no more than ten rubles, then buy a ticket and take your place in the hall, otherwise (if the ticket costs more than 10 rubles) return home.
In the general case, the diagram of a branching algorithm will look like this: “if a condition, then..., otherwise...”. This representation of the algorithm is called the full form.
An incomplete form in which actions are skipped: “if a condition, then...”.
Auxiliary algorithm- an algorithm that can be used in other algorithms by specifying only its name.
Homework. § 16,
1. Come up with your own examples for each type of algorithm.
2. Create an algorithm for crossing a road with and without a traffic light.
Lesson summary.
Children, what new did you learn today?
Today we learned what an algorithm is, we learned the types and properties of algorithms
To use presentation previews, create an account for yourself ( account) Google and log in: https://accounts.google.com
Slide captions:
Algorithm as a model of activity 900igr.net
What is an algorithmic model? An algorithm is a clear and precise instruction to a specific performer to perform a specific sequence of actions leading to a set goal. The stages of activity from determining the goal (setting tasks) to obtaining the result are as follows: defining the goal; planning the work of the performer; performer's work; getting the result.
An algorithm is a detailed plan for the performer’s work; it is a description of the sequence of elementary actions that the performer must perform. But every plan or description is an information model. Therefore: The algorithm is an information model of the performer’s activity
Algorithmic model: Defining the goal (setting tasks) Building a plan - algorithm Work of the performer Obtaining a result Model of the work of the performer
To build a real algorithm plan that will be executed, you need to know exactly the capabilities of the performer. These capabilities are determined by the system of executive commands (SKI). When composing an algorithm, one must not go beyond the framework of the SKI. This is the understandability property of the algorithm. A programming language is a formalized language for describing algorithms.
Example of an algorithmic model Algorithm: Guessing a number Given: a range of numbers from A to B Needed: guess the number X conceived by the player using the halves algorithm. Start Ask: Is X less than the average between A and B? If the answer is “yes”, then take the integer part of the average value as value B. If the answer is “no”, then take the value A as the nearest integer greater than the average If the values of A and B are equal, then their total value is the desired number X If values A and B are not equal, then return to step 1 End
no yes no Alg Half division Integral A, B, X Start Enter A, B, X While A≠B, repeat NC If X≤(A+B)/2 Then B: = whole (A+B)/2 Else A :=integer((A+B)/2)+1 kV Kc Output A End beginning end Input A, B, X A≠B X≤(A+B)/2 B: = integer(A+B)/2 A:=integer((A+B)/2)+1 Output A
Tracing an algorithm - a model of the processor's operation When performing manual tracing, a person models the operation of the processor.
Trace table of the “Half Division” algorithm Step No. Algorithm command variables Performed actions X A B 1 Input A, B, X 3 1 8 2 A≠B 1≠8, yes 3 X≤(A+B)/2 3≤4, 5, yes 4 V: = int((A+B)/2 4 V: =4 5 A≠B 1≠4, yes 6 X≤(A+B)/2 3≤2.5, no 7 A: =integer((A+B)/2)+1 3 A: =3 8 A≠B 3=4, yes 9 X≤(A+B)/2 3≤3.5, yes 10 V: = integer( (A+B)/2 3 B:3 11 A≠B 3≠3, no 12 Conclusion A Answer: 3
The trace table is a model of how the processor operates during program execution. The program is running (first column of the table). The “Algorithm Command” column displays the contents of the processor command register, where the next command is placed. The “Variables” column displays the contents of computer memory cells (or processor memory registers) allocated for variable values. The “Action to be performed” column reflects the actions performed by the arithmetic-logical unit of the processor. Thus, the algorithm, together with the trace table, completely simulates the information processing process occurring in the computer.
System of basic concepts Algorithm - model of activity Modeling object - purposeful activity of the performer Human performer Automatic performer (including a computer) Unformalized SKI Formalized SKI Forms of representation of algorithms Flowchart Educational algorithmic language Programming language Trace of the algorithm - step-by-step execution of the algorithm with a test version of the initial ones data “Manual” tracing – filling in the trace table Trace table – model of processor operation during algorithm execution
Completed by 10th grade students: Slobodenyuk Olesya Kudruk Victoria Prokopiv Olesya
On the topic: methodological developments, presentations and notes
Open lesson on computer science, grade 10 "Algorithm - model of activity"
This lesson covers all the stages of the lesson. The lesson is based on project technology. Students create mini projects in class...
Lesson topic: “An algorithm is a model of the activity of an algorithm executor. Performer Draftsman. Draughtsman management. Working in the Idol environment"
Lesson topic: “An algorithm is a model of the activity of an algorithm executor. Performer Draftsman. Draughtsman management. Work in the Idol environment"Lesson objectives: To systematize students' ideas about the...
Lesson summary
Item : Computer Science and ICT
Subject: Algorithm as an activity model
Lesson type : a lesson in developmental control
Lesson form– traditional
Goals:
Educational:
- continue to form ideas about algorithms;
––
recall the concept of a model and define an algorithmic model;- drawing up algorithms using conditions and cycles.
Educational:
- create conditions for the development of students’ cognitive activity;
- develop verbal and logical thinking; communication culture;
-
develop students’ personal qualities of self-control and self-esteem.
Educators:
- develop confidence in your abilities;
- foster a sense of camaraderie and mutual assistance.
Requirements for results
Subject:
- develop the ability to compose algorithms;
- learn to work with new data centers (arrows);
- form teams to achieve the goal;
- complete the task independently.
Universal learning activities:
Personal:
- the action of meaning-making;
- students establishing connections between teams and goals;
Regulatory:
- goal setting;
- developing the ability to plan any activity in the form of algorithms as a model of activity;
- formation of self-control and self-esteem;
- volitional self-regulation;
- forecasting;
- control;
- correction.
Cognitive:
- formation of logical actions of analysis, comparison, establishment of causality investigative connections;- formulation and formulation of the problem, independent search for its solution.
Communication
- develop the ability to collaborate;
- teach to speak, reason;
- learn to interact in pairs.
Forms of training: frontal, individual, in pairs.
Teaching methods: visual, verbal, practical, control.
Used educational technologies:
Dialogue technology,
Collaborative learning technology,
ICT.
Lesson equipment:
Interactive complex, presentation, digital design center “arrows”.
Decor
results
Localization of difficulties
Identify the location and causes of the difficulty and determine the goals of the lesson.
Recognize the need for control and self-monitoring of results, as well as identifying the causes of difficulties in activities.
Results of the task of compiling algorithms (presented on the slides)
Encouraging dialogue
Organizes the motivation of students for correctional activities.
Analyzes the correctness of students’ self-testing of their work.
Clarifies the algorithm and rules for eliminating errors.
Helps identify the causes of errors in various types tasks.
Determines student consultants (checking the correctness of the compiled algorithm).
Determine places
Indicate methods of action.
Compare with the standard and perform tasks of a creative level
Evaluate themselves
Understand the reasons for mistakes made based on
Write in a notebook and check the result on the screen.
Construction of a project for correcting identified difficulties
Launching the correct answer options on the screen.
Provocative dialogue, brainstorming, discussion.
Organizes the process of students discussing the goals of correction, and also helps to choose the necessary means and ways to achieve them.
Organizes work in pairs according to the types of mistakes made.
Formulate individual goals and an algorithm for corrective actions.
Choose a method and means of correction.
Implementation of project construction
Organization of corrective independent work on errors.
Creative tasks for students who completed the test without errors.
Independent work with checking against the standard.
Directs counselors to assist other students.
Students who complete the work without errors can complete creative tasks.
Work on bugs.
Select tasks according to errors;
do the work suggested by the teacher.
Working on mistakes in notebooks.
Generalization
Reinforce the methods of action that caused difficulty.
Encouraging dialogue.
Organizes a discussion of typical difficulties.
Speaks out the wording of the methods of action that caused difficulty
Formulate methods of action that caused difficulty.
Independent work with self-test according to the standard
Carry out independent work
Practical work.
Individual activity and work in pairs.
Organizes students' independent work.
Provides a symbolic record of overcoming difficulties.
Deriving student assessment criteria.
Perform independent work.
Perform a self-test. Shows results to teacher
The result is a properly designed program.
Reflection of activity
Conduct a self-assessment of performance results
Communicative influence, independent work.
Self-esteem card
Encouraging dialogue.
Organizes the discussion of the mechanism of control activities.
Organizes the evaluation of the results obtained, as well as the fixation of the goals of subsequent activities.
They discuss the mechanism of control activities.
Evaluate the results obtained.
The purpose of follow-up activities is fixed.
Evaluate activities in the lesson.
Lesson plan
Organizing time(2 minutes)1.Organizational moment
Everyone, good afternoon everyone!
Localization of difficulties
They brought me a box and gave me the task of figuring out what was in this box.
What could be in it?
Answer questions. They make assumptions.
Choose tasks of a creative nature.
Construction of a project for correcting identified difficulties
Where to begin? What do we call this sequence of actions? Why do you need instructions? Can it be called an algorithm and why?
Why do we need algorithms? How can we diagrammatically represent the algorithm?
An algorithm for corrective actions is formulated.
Choose a method and means of correction
Implementation of project construction
№2. The bottle, glass, jug and jar contain milk, lemonade, kvass and water. It is known that water and milk are not in a bottle, a vessel with lemonade is located between a jug and a vessel with kvass, there is neither lemonade nor water in a jar. The glass stands next to the can and the vessel with milk. Where is each liquid poured?
Answer:
Milk
Lemonade
Kvass
Water
Bottle
Cup
Jug
Jar
They do the work themselves.
Check against the standard. Evaluate the work.
Generalization of difficulties in external speech.
And so we have four different situations:
Situation 1: I am the director of a company and I need to draw a company logo in the form of the letter F. On the desktop in the folder executor task 1_1 (you need to make a list of commands to complete this task using the commands: step, turn, jump) Demonstrate to the teacher. 1 point for completing this task
Situation 2: As a director, I need to fence off the area. Using a procedure, you need to write commands to obtain the desired result. In a folder on the desktop, task 1_2 is worth 1 point
Situation 3: As a director, I need to send money via a safe route, for this I cannot change the route. Write commands using a cycle to deliver money from point A to point B. Task in the Executor folder on the desktop task 1_3. 1 point for completing this task
Situation 4: It is necessary to write an algorithm for the movement of a pizza delivery machine, with the condition that it does not drive into the wall. Use a conditional operator. Problem 1_4. For completing this task using conditional operator 2 points, for using the linear algorithm 1 point
Independent work with self-test according to the standard
Students: An algorithm is a clear and precise instruction to a specific performer to perform a final sequence of actions leading to a set goal.
Students evaluate their work independently and show the result to the teacher. Students: create algorithms.
Teacher: now let’s check whether we completed this task correctly (on the screen, one of the students runs the correctly composed algorithms, the rest check)
Perform independent work.
Perform a self-test (slide).
Evaluate.
Reflection
As the lesson progresses, we identify difficult situations.
Graphic artist stands intop left corner of the field. Direction -arbitrary . What will be displayed on the screen after the graphical performer performs the following algorithm (describeall possible options ): if there is an edge in front then turn, else jump jump end of branching until there is an edge ahead step end of cycle
