ICTeam lesson plans

ICT-based Educational Application for Mathematics - ICTeam Comenius Multilateral Project 2013-2015

Partners:

    

Silifke Cumhuriyet Ilkokulu, Turkey Goetheschule Wetzlar, Germany Основно училище "Любен Каравелов", Burgas, Bulgaria Osnovna Škola Mikleuš, Croatia Istituto tecnico industriale-liceo scientifico delle scienze applicate "Oreste del Prete"- Sava (ta)- Italy  Centrul de Excelență a Tinerilor Capabili de Performanță, Botoșani, România  Частна целодневна детска градина "Цветни песъчинки ", Varna, Bulgaria

This project has been funded with support from the European Commission.

This publication reflects the views only of the author, and the Commission cannot be held responsible for any use which may be made of the information contained therein

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Primary School Mikleuš LESSON PLAN SCHOOL: Primary School Mikleuš GRADE: 6th DATE: 2 December 2013 TEACHER: Ivana Tržić LESSON UNIT: Orthocenter TYPE OF LESSON: Developmental Lesson DURATION: 45 minutes AIM OF THE LESSON: To enable students to reveal the statement, that the intersection of the lines, on which the heights of the triangle lie, intersect in one point, which is called the orthocenter.

OBJECTIVES: EDUCATIONAL: · ·

Students should be able to define the term: the height of a triangle Students should be able to construct triangle heights with the use of GeoGebra dynamic geometry computer software.

FUNCTIONAL:

· · · ·

To develop examination and discovering new characteristics To develop the ability of extraction and connection of given data To learn how to apply the newly acquired knowledge To develop the ability to connect maths with everyday life PEDAGOGICAL:

· ·

To strengthen the feeling of responsibility of finishing tasks independently and to prepare students for further progress.

To develop concentration and thoughtful way of performing a task.

TERMS: the height of a triangle, orthocenter of a triangle METHODOLOGICAL TYPE OF WORK WITH STUDENTS: frontal, individual work, pair work TEACHING METHODS: dialogue, presentation, demonstration, computer work TEACHING DEVICE: students book, workbook TEACHING AIDS: blackboard, chalk, projector, computers

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LITERATURE: G. Paić, Ž. Bošnjak, B. Čulina- MATEMATIČKI IZAZOVI 6 – student book and work book for 6th grade, 1st term, Alfa, Zagreb, 2010.

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D. Glasnovć, Z. Ćurković, L. Kralj, S. Banić,M. Stepić- PETICA+6 – student book and work book for 6th grade, volume 1, SysPrint, Zagreb, 2010.

MAKRO LESOON PLAN 1.

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Introduction (10 minutes) The students have to define the term: the height of a triangle.

Students start the GeoGebra software. The teacher gives short instructions for work.

2.

Presentation (25 minutes)

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The students have to draw an acute angled triangle, obtuse angled triangle, a right angled triangle and their heights, using the GeoGebta software.

The students should be able to notice, while observing the drawings, that the lines, on which the heights of the triangle lie, intersect in one point.

To introduce the term: orthocenter

3.

Ending the lesson (10 minutes)

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To revise the most important facts, to save all the drawings into a computer file.

Homework: only for those students who find it really interesting – tasks for constructing triangles using GeoGebra software.

Evaluation of the lesson.

MICROPLAN OF THE DAILY LESSON PLAN 1. Introduction: The students understand the following terms: triangle, perpendicular, height of a triangle and height of foot. Students remind themselves of those terms during the introduction of the lesson. After that, students start GeoGebra software of dynamic geometry. The teacher gives the students short instructions for work: which buttons to use to draw line segments, lines and perpendiculars.

2. Presentation: The teacher hands out the work sheets.

Each student creates an acute angled triangle using the GeoGebra software. The teacher uses the overhead projector, so students can see what is to be done. After creating the acute angled triangle, each student draws the height of the triangle.

The students already know that the heights lie on the perpendicular, out of the vertex of an angle, to the opposite edge of the triangle, so students will use the button. The teacher asks the students what do they notice. Most of the students will probably answer, that all the three heights of the triangle intersect in one point.

The students have to work in pairs and create an obtuse and right angled triangle and their heights. The teacher helps the st udents to create the triangles. We don't have to create an obtuse triangle because, we can create one out of the acute angled triangle by moving one of the triangle vertex, till we get one obtuse angle. That way, we will save time and realize some advantages by using this dynamic geometry software. When creating a right angled triangle, the teacher helps the students to create the right angle. After students finish their tasks, we ask them, what did they notice? The students should say, that the lines, on which the heights of the triangle lie, intersect in one point. *We should ask the students, if they think that that always happens. For homework, the curious students can find data of Euclid, also known as "Father of Geometry" on the internet to find out more*.

Now, we can introduce the term orthocenter -the lines on which the heights of the triangle lie, intersect in one point which is called the orthocenter of a triangle.

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The students should also be able to realize, where the orthocenter of an acute angled, obtuse angled and right angled triangle is.

Conclusion: the orthocenter can stand within the triangle, outside the triangle and at the triangle vertex. We ask the students to move the triangle vertexes, to assure them into this theory.

WORKSHEET 1. Create an acute angled triangle.

2. Draw its heights.

3. What do you notice, according to its heights? ________________________________________________ 4. Create an obtuse angled triangle.

5. Draw its heights.

6. Create a right angled triangle.

7. Draw its heights.

8. What do you notice, according to their heights? _______________________________________________________________________________________ 9. Do their heights intersect? _______________________________________________________________ 10. Try to write down the correct definition. ___________________________________________________ _______________________________________________________________________________________ 11. Where is the orthocenter of the acute angled triangle? ________________________________________ 12. Where is the orthocenter of the obtuse angled triangle? _______________________________________ 13. Where is the orthocenter of the right angled triangle? _________________________________________ 14. To check your answers, move the triangle vertexes and observe what is happening to the orthocenter.

3. Ending the lesson Each student saves its work in a computer file.

Homework (just for curious students): worksheet: The construction of triangles using the software.

Students should fill out the evaluation sheets.

BLACKBOARD Acute angled triangle -orthocenter within the triangle

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Obtuse angled triangle –orthocenter outside the triangle

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Right angled triangle- orthocenter at the triangle vertex

The definitions and characteristics of geometry that the students discover by themselves, have a long- term effect rather than dictating the students readymade definitions. Using the software, students are able to try out more practicabilities, which is usually impossible with the use of only chalk, blackboard and geometrical kit. The students realize that there are more possible solutions by creating their constructions on the computer, and the accuracy in GeoGebra is 100%, unlike creating their constructions on paper. For example, if the students are not skilled to move the geometrical kit properly, there will be some deviations for 1° or 1 cm...

EVALUATION SHEET Put a + sign into the right column to describe your experience connected to the activities. Column 5 describes the best experience.

1 It is interesting to find out independently new mathematical claims and characteristics.

Now I understand more about the heights of triangles.

I would like to work on a computer more independently during math’s lessons I like GeoGebra

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I will try to use the dynamic geometry software, that we used today at school, at home.

I would like to check some other mathematical claims by using this software.

This lesson was interesting, because I have learnt something new in math’s by using the computer.

Goetheschule Wetzlar, Germany Teacher: Karsten Rauber

Use of the EIS-Principle in teaching Middleschool Grade 6 advanced course Topic: Fractional arithmetic, multiplication of two ordinary fraction numbers The EIS-Principle EIS: 

Enaktiv: Activity

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Ikonisch: Pictures

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Symbolisch: Symbols or language

Example: Addition of numbers 

E: Practical action using material such as two pencils and one pencil

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I: 7

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S: 2 + 1 = 3

The EIS-Principle derives from developmental psychology (Piaget) 

Enaktiv: Something concrete operative from childhood (unlocking reality)

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Ikonisch: Further development allows simultanious comprehension of chains of action

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Symbolisch: Acquisition oft he mother tongue

The Operative Principle is applied. Operations play an important role for the gaining of insights and the development of intelligence.

Features: 

The use of concrete material, drawings and texts that allow the students to act in real. Most important are the executed activities. (I hear and I forget – I see and I remember – I do and I understand)

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Reversable, sectional, associative

Fractional numbers as operators: 

Fractional numbers instruct multiplicative calculations

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Example: Take 2/3 of 3/8 litres of cream (backing recipy) Lessonplan

Time: 45 min Topic: Multiplication of two ordinary fractional numbers Material: Pencils Medien: Interactive SmartBoard with prepared pictures (see below)

Course of the lesson: At first the students work Enaktiv on the example: 2/5 of 2/3 

The students work in pairs of two, for each pair an operator 1 and 2 is determined 8

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15 pencils are put on the table

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Operator 1 takes away 2/3 of the 15 pencils (10 pencils) and passes those to Operator 2

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Operator 2 takes then 2/5 of the 10 pencils and puts the result (4 pencils) on the table in front of him

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The next task is to take 2/3 of 2/5, the Operators change places for that task

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Operator 2 first takes 2/5 of the 15 pencils (6 pencils) and hands those to Operator 1

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Operator 2 takes 2/3 (4 pencils) and puts those in front of him on the table

Those Enaktiv actions are then displayed as a drawing ikonisch:

=>

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Die ikonische display in symbolic display:

Practical experiences: The enaktiv example served as an introduction into the multiplication of fractional numbers ensuring a strong motiviation for the students. The transformation into iconic and symbolic writing was manages quickly and surely. One should ensure however that the process of drawing does not take too long, this is not an arts exercise.

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L.Karavelov Primary School Burgas, Bulgaria LESSON PLAN 1

Prepared by: Gergana Gineva Class: ІV „в” / Mathematics grade 4

Lesson theme: Division of whole numbers by a two-digit number Type of the lesson: Solidifying knowledge and skills Aims of the lesson: The students will solidify their knowledge and will improve their skills in dividing multi-digit numbers by a two-digit number.

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Tasks: Educational: - Revising the knowledge of already studied cases of division, and the analogy that can be found with some of them - Directing the students to a way to find the number of the digits in the quotient and the number which they will first divide by the given divisor; - Revising the knowledge of dividing by a two-digit number in the cases when there is remainder; - Revising the knowledge of the measures of length and time; - calculating of expressions; - solving text problems.

Educative: - Developing of keenness of observation; - Strengthening of the students’ curiosity/ studiousness/.

Methods: Lecture, exercise, presentation, demonstration, working with the program ‘Envision’.

Means: Mathematics Students book of ‘Bulvest’ 2000”publishing house, the classroom board, a multimedia system, laptop, a pre-prepared author lesson using ‘Envision’.

Course of the lesson: 1. Organizing the class for work: “ During the previous 3 lessons in mathematics we learnt the algorithm of dividing the numbers after 1000 by a two-digit number .

2.Checking the homework and revising students’ old knowledge and skills of dividing by a twodigit number: Students on duty report if everybody has homework, then I direct their attention to the board, where a rectangle is drawn and I ask about the solution of problem 6 from the homework, in which we know the surface of a rectangle orchard and one of the faces, and we seek how many meters the other face is long. A student writes the solution on the board, and after he gets the answer in meters, I ask the class what other units of measurement of length we know.

3. Motivating the study work and introducing the theme of the lesson: ‘During this lesson we will solidify our knowledge and improve our skills of dividing by a twodigit number as we study cases when there is a remainder. We will also revise the units of 15

measurement of length and time’. I write the theme of the lesson – ‘Division of whole numbers by a two-digit number’. Lesson 100.

4. Practice exercises for solidifying the knowledge and skills: Everybody opens the students’ book on page 115/ exer.1 а), in which we will revise the way in which we determine the number of digits in the quotient and the number, which we will first divide by the given divisor, and we will revise the knowledge of dividing by a two-digit number in the cases when there is a remainder. I write the expressions on the board, and remind of the respective algorithms.

After that we go on to exer. 1 б), where we have to calculate how many centimeters and how many millimeters are 85 mm. We remember that 1сm = 10mm, so 85:10=8сm 5mm and these are units of measurement of length and then I ask the students which are the units of measurement of time. After their answer I remind that 60min = 1h and three students go to the board to find out how many hours and minutes are 368 min, 435 min, 783 min.

‘As far as I can see, you do very well with the problems, so it is time we go on with our work, but this time with the mice (which are handed out before the beginning of the lesson), and each problem you will first solve in your notebooks, and then you will mark the correct answer. Let’s see who works the most quickly and the most correctly’. We begin the work with ‘Envision’. A picture 1 min = 60 sec appears on the screen, and on the next two slides are the problems: Write down in minutes and seconds 863 sec and 390 sec, and for each problem the given time is 1 min, and the answer is written through a virtual keyboard. A static screen follows – 1 day plus night = 24 hours, and the next two problems are in the form of text questions, to which the students must answer with only one correct answer: 745 hours are? 1493 hours are? The next problem is of the type showing on a picture: ‘The divident is 25 773, and the divisor is 33. The quotient is?’ On the screen there are pictures of three answers, and the students mark only the one they think is correct. A text problem follows, in which they not only have to give the correct answer, but also the numeric expression they used to reach the answer.

A static screen on the board –‘Problems for curious children’. The first problem is a text question with text answers: ‘Find out how many types of colibri are known in the world by calculating the expression (1000.20+735): 65= ‘Writing on the virtual keyboard follows, and the problem is: For one hour one colibri bird moves its wings 252 000 times. How many times does the colibri move its wings in one minute?’

‘Now we have to read carefully and think before we answer.’ On the next picture screen is the problem: ‘A candle on the cake burns down for 15 min. How long will it take for 11 candles to burn if they are lit simultaneously?’, and the students answer by marking only one correct answer.

The teacher gives in advance time limit for each of the problems, and the students solve the problems in the notebooks and then mark the answers with the mice.

The last picture screen prepares the children for the account of the results: ‘After your efforts let’s see your points!’

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5. Summary and conclusions from the lesson: Besides a summary in per cent which is done by ‘Envision’, I also express my impressions from the lesson and the work of the students.

6. Setting the tasks for homework: ‘For homework – workbook page 45 and from the book with problems in mathematics page 96/problem 4’.

LESSON PLAN 2

Prepared by Veska Krasteva, teacher at L. Karavelov Primary School Theme: ‘Roman numerals’ – lesson №20 from Mathematics students’ book, grade 4, ‘Bulvest’ Publishing House.

Type of the lesson: new knowledge Aims of the lesson: Introducing the Roman numerals and their putting into practice to the students.

Expected results: Students will be able to use Roman numerals in practice.

Inter-subject relations: Man and Society, Bulgarian language and Literature.

Didactic means and materials: Videoclip for the application of the Roman numerals and a lesson in ‘Envision’, prepared by me, historical facts, wireless mice.

Course of the lesson: Teacher’s activity 1. Checking the homework - Did you have any difficulties doing the homework? ( if yes, explanation follows) 2. Revising old knowledge - Draw a circumference with a center p.О and a radius/ r/ = 2 cm.

- Draw a circumference with a center p.О and a diameter /d / = 4 cm - What are these circumferences? What are their radii?

- Where in the room do you see circumferences?

Students’ activity Students share and comment

Students measure and draw

They explain that the circumferences have the same radius.

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3. Going on to the new theme I play a clip, in which there are different clocks, on the faces of which Roman numerals are drawn. There are coins, calendars, historical events, books and monuments, in which Roman numerals are used.

4. Introducing the theme. ‘Roman numerals.

- Part of the presentation included in the lesson is shown and historical facts about the origin of the Roman numerals are given, the way they are written and how they can be shown with the help of the fingers is explained.

Work with the students’ book - exer.2/page.32

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5. Explaining the symbols and the way the numerals are written Tasks on the board: Write in your notebooks the numbers from 1 to 10 with normal figures /digits/ and Roman numerals.

The rule that not more than three symbols are written one after the other is explained as well as the way of writing and reading the numerals. The number 0 doesn’t exist in the Roman numerals.

Read the numerals: XVI = 10 + 5 + 1 = 16 XIV= DIX = DCLXVI = MDXV = MMII = MMXIV = 6. Solving problems from the book exer. 3/page.32 exer. 5/page 32 7. Checking the knowledge with individual answer using ‘Envision’.

Students watch and share what they have seen.

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Students write down the theme in the notebooks

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Students look at the numerals in the book, and read exercise 2/page 32.

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Tasks on the board -students write in their notebooks and on the board

- Read from left to right: XVI = 10 + 5 + 1 = 16 XIV=10-1+5 =14 DIX = 500-1+10 =509 DCLXVI =500+100+50+10+5+1=666 MDXV=1000+500+10+5=1515 MMII=1000+1000+2=2002 MMXIV =1000+1000+10-1+5=2014

Problems are read and explained

Every student has a mouse and works alone.

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Problems: 1. Is it true that 11 is written like that IX ?

2. Which clock shows 10,10?

3. Write with Roman numerals: 25 and 55.

4. Calculate in your notebooks the numeric expression and write the answer with Roman numerals: 865 – ( 439 + 234) = = = 5. During which century was the Bulgarian state founded?

6. P. Hilendarski wrote ‘Slavic-Bulgarian history’ in 1762. Which century is this?

7. Match the numbers with the Roman numerals:

1.

yes

3.

4.

XXV, LV. 865 – ( 439 + 324) = = 865 – 763= =102( CII)

5.

VIIc.

6.

XVIIIc.

7.

25 19 XIX CIII 103 XXV 8. Which is the missing number?

XXVI, XXVII, XXVIII, …………., XXX. 8. Logical problem; Can we get thirty from the number twenty-nine by taking away one?

9. Summarizing the knowledge What do we use Roman numerals for?

Note: If time allows problems with sticks can be included.

2. no

25 XIX 103

19 CIII XXV

8.XXIX YES XXIX XXX With Roman numeral we write: - Centuries and months - the hours on the clock - Olympiads - Volumes of books - Value of coins

10. Assessment of the knowledge 11. Homework Workbook – Lesson 20

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Частна целодневна детска градина "Цветни песъчинки ", Varna, Bulgaria LESSON PLAN 1

The apple

Date/Day: Time/ Duration: 20 min Year- 5/6 Subject: Math Themes: Orientation into space, Numbers 1 - 4 Topic: Orientation into space, Counting from 1 to 4 Skills: - Developing the children’s orientation into space; - Developing precision hand motion; - Differentiation of the objects.

Objectives: In the end of the lesson children should determine correctly the different position of the object and counting the animals in the pictures.

Tasks: - Practicing the prepositions of place through orientation into space; -Practicing the numbers 1-4 trough counting from 1 to 4.

Interdisciplinary relation: Literature - “The apple”, V. Suteev Description of the lesson: Using the educational software “Envision” children determine the position of the apple in the picture and fix the number of the characters in it.

LESSON PLAN 2 THE NUMBERS; DIRECTIONS

The numbers. Counting to 10 – Lesson plan Pre-primary school 20

LESSON PLAN Date/Day:

Time/ Duration: 15 min

Year- 5/6 Subject: Math Themes: Students practice counting and number recognition from 1 - 10 Topic: Counting from 1 to 10. Orientation in supermarket.

Skills: - Developing the children’s orientation into space; - Developing precision hand motion; - Differentiation of the objects.

Objectives: In the end of the lesson children should determine correctly the different position of the object and counting the animals in the pictures.

Tasks: - Practicing the prepositions of place through orientation into space; -Practicing the numbers 1-10 trough counting from 1 to 10.

- Drawing and handwriting Interdisciplinary relation: Social skills, fine motor skills Description of the lesson:

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Using the educational software, the children determine the numbers and objects. They count and draw the numbers and fix the number of the characters in it. In the supermarket they buy goods, using money.

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Directions Pre-primary school 25

The lesson "Directions" are appropriate to help preschoolers to understand the concepts of what inside and outside are. This lesson plan gets the preschool class up and moving. It also involves a fun game for assessment that students will enjoy. 

The lesson are extremely helpful for the preschool teacher. Use this lesson for inside and outside to teach your students what the words mean and the concept that goes along with it.

After teaching this lesson the students will be able to identify whether an activity or item goes inside or outside.

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Prior Knowledge Take students for a walk. Go and visit different places inside the building, and then go outside. Visit various places outside on the school grounds. Before going back in the building, stop at the door and get each student the opportunity to stand inside and then outside. Watch the didactic introduction movie.

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Teach Divide the chart paper in half with a marker. Write inside on one side of the chart paper and outside on the other. Brainstorm things you do inside and things you do outside. Show students a cover of a book. Encourage them make predictions based on the cover.

Envision lesson ………………………………………….

Extend These pictures would make a great bulletin board. An appropriate title would be “Inside or Outside? Up or down? Left or right?”

Give students a task to make a book full of things that are done inside or meant to go inside, up or down, left or right.

LESSON PLAN 3 THE APPLE; INSIDE-OUTSIDE

The apple LESSON PLAN Date/Day:

Time/ Duration: 20 26

Year- 5/6 Subject: Math Themes: Orientation into space, Numbers 1 - 4 Topic: Orientation into space, Counting from 1 to 4 Skills: - Developing the children’s orientation into space; - Developing precision hand motion; - Differentiation of the objects.

Objectives: In the end of the lesson children should determine correctly the different position of the object and counting the animals in the pictures.

Tasks: - Practicing the prepositions of place through orientation into space; -Practicing the numbers 1-4 trough counting from 1 to 4.

Interdisciplinary relation: Literature - “The apple”, V. Suteev Description of the lesson: Using the educational software “Envision” children determine the position of the apple in the picture and fix the number of the characters in it.

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Inside -Outside: Lesson Plan Pre-primary school Pre-K lessons "Inside and Outside" are appropriate to help preschoolers to understand the concepts of what inside and outside are. This lesson plan gets the preschool class up and moving. It also involves a fun game for assessment that students will enjoy. 

Pre-K lessons "Inside and Outside" are extremely helpful for the preschool teacher. Use this Pre-K lesson for inside and outside to teach your students what the words mean and the concept that goes along with it. After teaching this lesson your students will be able to identify whether an activity or item goes inside or outside.

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Prior Knowledge Take students for a walk. Go and visit different places inside the building, and then go outside. Visit various places outside on the school grounds. Before going back in the building, stop at the door and get each student the opportunity to stand inside and then outside. Watch the didactic introduction movie “Inside – outside”.

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Teach Divide the chart paper in half with a marker. Write inside on one side of the chart paper and outside on the other. Brainstorm things you do inside and things you do outside. Show students a cover of a book. Encourage them make predictions based on the cover.

Envision lesson ………………………………………….

Extend These pictures would make a great bulletin board. An appropriate title would be “Inside or Outside?”

Give students a task to make a book full of things that are done inside or meant to go inside.

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Silifke Cumhuriyet Primary School LESSON PLAN 1 School:Silifke Cumhuriyet Primary School Lesson:Maths

Class: 1 Subject:Collection Process in Natural Numbers Teacher:Rahmi Sari Writing natural numbers as collection of two natural numbers Steps to be followed 1) 2)Sub-learning Area: Collection process in natural numbers 3)Subject:Writing natural numbers as collection of two natural numbers 4)Recovery:Writes natural numbers untill 7.20 as collection of two natural numbers 5) Method,technic and abilities:Study,practice,question-answer,reasoning, discussion, communication,individual studies,group studies,cognitive development 6)Tools and equipments:Counting bar,unit cube,beans,number cards,apple,plastic plate 7)Duration::2 lessons time 40’+40’ 8)Preparations:Bring 7 pieces of candies and two pieces of plastic plates with you to classroom 9)Put the candies and plastic plates on the table.Ask different students to seperate 7 pieces of candies in to two plates with random numbers.Collect the numbers in the plates.Make them understand they can write nuımber 7 as collection of two natural numbers Examine the Picture in the textbook with students.Ensure them the total numbers of apples in the basket and plates are equal.

10)The event aims to introduce the students that they can write numbers until 20 as collection of two natural numbers 11)Individual Event:Collected numbers can change but the total not Tools and equipments:Number cards,counting bar,notebook,pencil.

Process Steps:Take one of the cards with numbers 1 to 20.Ask the students to model the number on card as collection of two natural numbers with counting bars.

12)Writing a natural number as collection of two natural numbers Ezgi’s mother puts 8 pieces of apples in the basket,to plates as shown How can you seperate this 8 pieces of apples in to two plates?

13)Event: Tool:Unit cube Process Steps: *Create groups with 4 students 36

*Choose 3 numbers from numbers 1 to 20 *Model this numbers as collection of two numbers with unit cubes *Write math sentences of modelled processes *Select the leader group of the event that constitutes the largest number of models

I.I.S.S. “ORESTE DEL PRETE” – SAVA (ITALY) ACTIVITY 1 Think of a number ... a. b. c. d.

add 12 the result by 5 subtract 4 times the number in your mind add 40 to the result

Teacher asks some students the final result; subtracting 100 from this result, "guesses" the number. In the following activity-stimulating teacher, addressing the whole class, he offers each student to follow the instructions in the notebook; the teacher does not know what number was initially chosen by each student. a. Think of an integer let’s start: Teacher then justifies his "foresight" with symbolic computation.

He Invites some students to rewrite in order on the board the given operations, without actually doing them, as follows: n.

7

… + 12 7+12

…·5 (7+12)·5

…  4·…

(7+12)·5  4·7

… + 40 [(7+12)·5  4·7] + 40

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what do you get?

t n. a

…·5

…  4·…

(a+12)·5

(a+12)·5  4·a

… + 12 a+12

… + 40

what do you get?

[(a+12)·5  4·a] + 40

Finally he invites to fill out a table like this to reflect on how it is possible, with appropriate calculations, making the simplest expressions.

Before a+12 (a+12)·5

After Now you can’t write this expression in a a different way, : it is a simple expression But here you can apply the distributive property of the product.

And then:

(a+12)·5  4·a

a+12 a·5 + 12·5 5·a + 60

Using the just found result, let’s rewrite:

5·a + 60 − 4·a

Now we change the order (why can you do?)

5·a − 4·a + 60

Let’s add a parenthesis (why can you do?)

We can now apply the distributive property to the expression within parentheses: By performing the calculation we have: But 1 is a neutral element for the 38

(5·a − 4·a) + 60

(5 − 4)·a + 60 1·a + 60 a + 60

product, and then: [(a+12)·5  4·a]+40

Using the just found result, let’s rewrite: And finally, the final result will be:

a + 60 + 40 a + 100

Now you can reveal the "trick" of the teacher!

The teacher let his students observe that the rules of calculation are nothing but the application of the rules of arithmetic; in particular he highlights the role of the distributive property that allows you to "distribute" a product on a sum but also to "pick up" a common factor, depending on how you interpret the equality: a·(x + y) = a·x + a·y

LESSON PLAN

Title: Arithmetic helps algebra and algebra helps arithmetic

Teacher: Pichierri Cosimo Name of the school: "O. DEL PRETE " School Type: High School for Science and Technology Class involved: I A Experience started on 05/02/2014 Experience finished on 12/02/2014 Hours of experimentation in the classroom: 6 Hours of personal work outside the classroom: 3

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DESCRIPTION OF THE EXPERIENCE The class IA, where I carried out the experience, consisted of 23 pupils .

It wasn’t very homogeneous about basic skills, and about learning rhythms and all 'participatory attitude. The average profit was just enough with a few outstanding elements.

The chosen activity was proposed when I was getting ready to introduce algebraic calculation.

Many students remembered the technique of the sum of polynomials studied in Scuola Media, so they did not have particular difficulty in this.

I thought to make the experience as an introduction to the operation of multiplication of polynomials.

I proposed the Activity 1 : Think of a number ... as a class game: addressing the whole class, I suggested to each student to execute the instructions in the notebook.

I asked some guys the final result, and ... "magically" I "guessed" the starting number.

I repeated the experience, especially for those who had not performed calculations correctly and then I asked him how I had to guess the thought number.

Under my leadership on the blackboard, I invited the students to rewrite the operations, in order, without actually doing them.

After reflecting on what the sequences of operations had in common, regardless of the starting numbers, the expression has been generalized by writing it in a way independent of the thought number.

I highlighted the fundamental role of the distributive property in this game of numbers and letters.

Later, in the laboratory, I illustrated the geometric interpretation of this rule of calculation and asked them to draw separately with GeoGebra two rectangles with dimensions x, and y, b and a third rectangle with size and led them to consider that the area of the first two rectangles is equal to 'area of the third rectangle: ax+ay=a(x+y) 40

ORGANIZATION OF WORK Group work :

Yes

It involved the entire class

Yes

It made cross-connections with other disciplines / teachers

Yes

If Yes, What?

Italian, trying to get the correct language.

STUDENT BEHAVIOR Describe how the activity has been welcomed by the students and the way they have fulfilled their mandates. Describe the working climate.

Initially the boys felt immediately the diversity setting of "do" maths, highlighting insights sometimes relevant and fulfilling the proposed target that was reflection and justification of the proceedings, for me.

The working atmosphere was positive and constructive allowing full collaboration between students more oriented operation with others more likely to discussion and elaboration of concepts.

41

LEARNING: SUCCESSES AND DIFFICULTIES Detecting the positive results and the difficulties faced by students in the understanding of various mathematical concepts and methods of overcoming Comments to the results:

Positive results from the point of view motivational (attitude / interest / commitment)

They achieved a small improvement in the relations between them socializing and have increased their concentration time and participation in school activities by assuming a more educated behavior

Positive results from the cognitive point of view

they are learning, finally, that the PC is not just for play or connect to facebook but can also be used to study.

Methods of overcoming Difficulties from the point of view motivational (attitude / interest / commitment)

Difficulties in terms of cognitive point of view:

By setting the lesson as a game, starting from their everyday lives with small examples showing that mathematics is a part of their daily lives.

Simple exercises of calculation and gratify them their small successes.

(Increasing in the level of learning)

42

DIFFICULTIES IN ORGANIZATION Describe the difficulties faced in the activities during the experience.

Difficulties

Strategies of overcoming difficulties

Not many difficulties

Dividing the class into small groups and alternate them so that everyone can use and learn new educational software.

EVALUATION Which verification tests have been given?

1) Let x be the measure, expressed in cm, of the side of a square, with x>2. It decreases the side of 2 cm.

Among the three following algebraic expressions, what is that which expresses the decrease in the area of the square?

- x 2  22 - x2   x  2 -

 x  2

2

2

 22

Show that the decrease considered can be expressed by.....

2) Consider any integer number, multiply it by the number which is obtained by adding to it 2; add 1 to the obtained product.

The result you get is a perfect square. After verifying this property in two cases, show it in general.

 a  b   a  b 2

2

 4ab 43

3) Interpret geometrically and test the following equation: 4) Consider a triangle; how does its area change if the base is reduced by 10% and the height increases by 10%?

If we denote by p the rate of change of the base and height, what is the percentage change in the scope?

The results can be considered positive as only 30% reported insufficient votes, but if I think about the initial situation of the class I can consider myself satisfied.

The proposal work unit enabled the implementation of an effective support for students in difficulty.

Yes No How: with a different approach to the matter and with the group work.

The work unit has given permission to carry out an effective stimulating action for the brightest students.

Yes No How: taking responsibility even further, transforming their break times helping classmates in distress.

Using new educational software.

Referring to the experience related to this Work Unit, do you detect changes in your educational setting, in your attitude toward discipline, .... compared to the previous practice of teaching?

What do you consider to be the most significant?

44

Personally I didn’t do many changes in my teaching approach, but I think that sharing the strategies proposed by the project, I realize that you have to keep in your mind the times and available curricular hours and very often you can get caught by the rush and come back to the usual lecture.

THE GEOMETRIC INTERPRETATION

45

Centrul de Excelență a Tinerilor Capabili de Performanță, Botoșani, România

LESSON PLAN 1

Teacher: Daniela NelaIonasc Class VII them 05/20/2015 Learning Unit: Circle Lesson Title: Problem solving and appliedLemoine's circles 46

Type of lesson: training skills and abilities Time: 50 minits Venue: math lab General skills: 1. Identify data and mathematical relationships and their correlation to the context in which they were defined.

2. Data processing quantitative, qualitative, structural, contextual statements contained in math.

3. Using algorithms and mathematical concepts to characterize a local or global situations.

4. Expression of mathematical quantitative or qualitative characteristics of a concrete situation and their processing algorithms.

5. Analysis and interpretation of characteristics of a situation mathematical problem.

6. Mathematical modeling of various problematic contexts, integrating knowledge from different fields.

7. Using new technologies.

Specific skills: CG1-8. Recognition and description of the elements of a circle, a geometric configuration.

CG2-8. The calculation of segment length and appropriate measures angles using the methods geometrical configurations include a circle.

CG3-8. Use of information provided by a geometric configuration for deduction of some properties of the circle.

CG4-8. Expression of the properties of a circle into mathematical language elements.

Methods and processes: conversation, exercise, competition, logic modeling, work in groups, observation, problem solving, educational software.

Organization forms of the class: individual and groups of students.

Evaluation forms: observation, evaluation of students, checking drawings, student grading, encouragement, praise.

Means of education: geometric kit, rebus, typesetting, worksheets, whiteboard, computer, GeoGebra.

Preparing: 47

Stepslesson

Teacheractivity

Student activity

Organizatio nalpoints

Greetings.

The presence of students.

Ensure optimal.

Checknecessarymaterialstostud ents.

Correcting theme

Preparing for lesson

Introductio n Announcin gthe theme andobjectiv es Conducting activity

Presentatio n material Ensuring reverse connection Providingfe ed-back

Assessment

Home work

Note thetitle of thelessonandlessonobjectivesan nounced Students are dividedintogroups of 2 students per computer Announcesthat it willmake a quickcheck of theconceptslearned in previousclasses Studentsreceiveworksheet 1 Thiscrosswordisdrawn on theblackboard Studentsreceiveworksheet 2.

It willhold a competition. The groupwillfinishfirst in GeoGebrarealization of previouslyanalyzedfigures on record.

The teachernotedthatstudentsstooda ndencourageshystudents Tell a theme thatwillbeready for thenextclass

Methodsand processes conversatio n

Studentsannouncewhethertheyh avedoneyourhomework, take a notebook checkedrandom.

Students notes in notebooks

Organizati onforms front

Evaluation methods

front

Remark

conversatio n

front

Carefullyreadtherequirementsan d solve crossword Complete thecrossword

Logic modeling Workinggro ups

In groups Students at theblackb oard

Checkingk nowledge Praise encourage ment

Studentsstudythe document thefirstdemonstration Lemoinecircle.

The first design work GeoGebra.

Checkcorrectness.

Studentsstudythe document thefirstdemonstration Lemoinecircle.

GeoGebraisdone theseconddrawing.

Checkcorrectness.

competition exercise Problematic

In groups

Checkingdr awings encourage ment Praise Remark

front

Gradingstu dents

for of in

for of in

Note theme

Worksheet 1

Complete thecrosswordbelow, completinghorizontalcorrespondingdefinitionstowords.

Verticallyachieveyourword ...

48

horizontal: 1. Segment joiningtwopoints on thecircleiscalled ....

2. rope passing throughthecenter of thecircleiscalled ....

3. The portion of thecirclebetweentwo distinct points on thecircleiscalled ....

4. Iftwocircles are equalwhenthey are calledrayscircles ....

5. A tip angle in thecenter of a circleiscalled ....

6. segment joiningthecentercirclewith a point on thecircleiscalled ....

7. A measure of arc iscalled ....

Worksheet 2 Lemoine'scircles

 The firstcircle of Lemoine The K Lemoine'spoint of a triangle ABC go MN, PQ, RS paralleltothesides. Thenthepoints M, N, P, Q, R, S is a circlecalledLemoine'sfirstcircle of thetriangle ABC.

49

Figure 1. The first circle of Lemoine Demo: 

Parallels NM, PQ and RS sides BC and AB respectively to determine parallelograms AC ARKQ, BPKN and SCMK with diagonals means the simedians AK BK CK respectively.



It follows that RQ, NP, MS are antiparallel with BC, AB AC respectively. Looking quadrilaterals so PSRN, PSMQ and NMQR they are writeable.



Quadrangle NPQR is trapezoid (NR || PQ) isosceles (∢ARQ ≡∢ACB ≡ ∢BNP) so he is writable.



NMSP is trapezium quadrilateral (NM || PS) isosceles (∢CSM ≡∢CAB ≡ ∢BPN) so he is writable.



Quadrangle RQMS is trapezoid (NR || PQ) isosceles (∢SMC ≡∢ABC ≡ ∢AQR) so he is writable.



Considering C quadrilateral circumscribed circle PQRN have S ∈ C (RNPS) writable, M ∈ C (NMSP writeable) then C is the circle sought.

 The secondcircle of Lemoine The K Lemoine'spoint of a triangle ABC go MN, PQ, RS antiparalleltothesides (MN if BC isantiparallel∢ . Then the points M, N, P, Q, R, S is a circle called the second circle Lemoine of the triangle ABC. 50

Figure 2. The secondcircle of Lemoine

Demo: Or Q,S∈BC, N,P∈AC și R,M∈ABwhetherso MN, SR and PQ are antiparalleltothesides BC, CA, AB. ∆KRS because it is isosceles m(∢KQS)=m(∢KSQ)=m(∢BAC) => KQ≡ KS ∆KNP because it is isosceles m(∢KNP)=m(∢KPN)=m(∢ABC) => KN≡ KP ∆KRM because it is isosceles m(∢KRM)= m(∢KMR)= m(∢ACB)=> KR≡ KM. But because K is theintersection of simedianelor isthemiddle of threesegmentsnamely

calledthesecondcircle of Lemoine.

GivenhiscirclesLemoineabove, weshould note thefollowing: - Antiparalelele QP≡NM≡RS becausethey are in thesecondcirclediameters of Lemoine - Triangles∆QNR and ∆SPM havesides perpendicular tothesides as theQP, NM și RS are diameters.

51

- Triangles∆QNR ≡ ∆PMSand are similar to∆CAB. QN≡PM it QNPM isparallelogram (diagonals are halved) scored, so it rectangle. m(∢RQN)=m(∢C)=m(∢SPM)theangles of thesides perpendicular.

In

an isosceles triangle ∢

In

∢

∢

∢

∢

∢

an isosceles triangle ∢

In

∢

an isosceles triangle ∢

Given

LESSON PLAN 2 The Perimeter of a polygon (square, rectangle, triangle) 1. DESCRIPTION School: School Nr. 11 Botosani Class: 5th Grade Period A Teacher: Prof. Dr. Geanina Tudose Subject: Mathematics- Geometry Content: The Perimeter of a polygon (square, rectangle, triangle) MAIN GOAL Understand the concept of perimeter for polygon and their applications 52

OBJECTIVES The students are expected to    

use the ruler on their kit and the virtual ruler to calculate the segment length be able to solve problems involving lengths , distances and fractions use the formula for the perimeter of an equidlateral triangle, square and rectangle use these concepts in more complex problems that involve perimetres

RESOURCES AND ICT tools:

    

laptop and projector for a a Power Point presentation and text problems flip-chart for solving problems use of www.mathplayground.com to use a virtual ruler and compute the perimeters of rectangles cards Textbook: Arithmetic for 5th grade, by A. Balauca

2. PROCESS/ACTIVITIES 1. Introduction  Ask students for previous day homework; and check their notebooks  Ask volunteers to review the units of length measurements Introduction of new concepts   

Presentation on perimeter of rectangle, square, triangle (attached the ppt resentation) Use the virtual rule on www.mathplayground.com, to show how to compute perimeters Solicit one student to come to the computer, demonstrate and check answer 2. Interaction

   

Students draw on their notbooks a rectangle, use their rulers to find lengths and widths and calculate the perimeter.

Solicit students to solve questions on the flipchart Problem 1; Easy application of formula Problem 2: Given a certain relationship between length and width and a given perimeter, find 53

out the length and width Problem 3: An word problem that applies the concept of distance. Students must be able to compute a fraction from a given number and to be able to explain the distance of a road. Encourage two students to explain the same solution. 



I present a problem and two solutions for a composite figure.

3. Integration

 

Quiz: students sitting on the same desk (3) receive a problem of computing the perimeter figure of a composite. They are allowed to discuss and agree on the solution.

Ask for each desk representative to show and explain the solution 4. Final Remarks

 

Ask Students to briefly review the content of the lesson and the main formulas for perimeters Give the homework for the next day LESSON PROJECT 3

School „Mihai Eminescu” College, Botoşani Teacher: Maria Oniciuc Class: IX G Level: 7th year of study, L1 Textbook: English, my love! – Editura Didactică și Pedagogică Date: 14th May, 2015 Topic: Houses Type of lesson: mixed

Aim: developing vocabulary and critical thinking skills so that at the end of the lesson the students could attain the following objectives: I. Cognitive: 1. to write words related to the given topic; 2. to give at least two arguments to sustain their own point of view; 3. to identify advantages/disadvantages of living in a castle/block of flats; 4. to write a five-minute essay on the given topic.

54

II. Affective: The students should be stimulated to show interest and take active part in the development of the lesson.

Approach: communicative approach Skills: speaking, writing, listening Methods and procedures: dialogue, conversation, exercise, elicitation, compare and contrast, cluster, T-chart, essay.

Resources: - materials: textbook, copybooks, handouts, computer, sites: 1. http://www.cglearn.it/mysite/civilization/uk-culture/types-of-houses-in-england/ , 2. https://hagafoto.jp/templates/hagahaga/topics/house/house-e.html , 3. https://www.youtube.com/watch?v=rj3HU7_Y8Io , 4. https://www.youtube.com/watch?v=rL9sutnl9Zc - 29 students - time: 50 minutes Stage of

Teacher’s

Students’

activity

activity

Aim s

Met hods

Resou rces

Skills

organisati on

Inter actio n

lockstep

T

speakin g

lockstep

SS

speakin

lockstep

TS

lesson 1.

War m up

2.

Routine conversation: greetings, marking absents in the register.

Ss. answer the T’s questions.

T asks Ss to read their homework and correct it if necessary (My ideal room)

Ss. present their essays

-T invites Ss to think of

- Ss give examples

dialo 2 min gue

Class

speakin g listenin g

1 55

conv ersat ion

copyb ooks

clust

Board

3 min

Evoca different types of tion dwellings. She draws a cluster on the board and (prese fills in the spaces with ntatio the Ss’ help. Then, T. use n) the links 2. and 3. and show Ss. some types of houses.

of dwellings and draw the cluster in their copybooks.

-T instructs Ss to complete the cluster with various characteristics of different types of houses.

-Ss do the task and then discuss with T.

-T plays the videos (links 1 and 4) with houses in the UK and asks the students to describe one.

- Ss write their descriptions.

3.

Realis ation of meani ng

- T. draws a T-chart on the board and instructs Ss (pract to complete it with at ice) least three advantages and disadvantages of living in two types of dwellings.

4.

Refle ction

T asks Ss to write a paragraph to describe their ideal house.

(imm ediate creati vity) T. announces the 6.

Home homework: make an

- Ss draw the Tchart in their copybooks and fill in the columns.

When they finish, they discuss their opinions with T and classmates.

Ss write the essay.

A few volunteers read their essay aloud.

er

comp uter

g

5 min

2

3

10 elicit min ation

writing

T10 chart min

listenin g

Com pare and cont rast conv ersat ion

4

Ss. take notes.

essa y

the Intern et comp uter

Individual work

SS

Group work

SS

Pair work lockstep

SS TS

writing

board 15 min 5 min

Writing

individual

reading

work

SS

T 56

work

advertisement for a house in order to sell it.

LESSON PLAN 4 Date:25.02.2015 Class:IX-a B Teacher: Trisca Teodor Subject: Mathematics- Geometry Theme: Reduction Formulae to the First Quadrant Lesson type: mixed General competences 1. The identification of some mathematical data and relations and their correlation according to the context in which they were defined 2. The processing of the date of the quantity, quality, structure and context type which are included in mathematical statements.

3. The use of algorithms and mathematical concepts for the local or global characterization of a concrete situation 4. The expression of quantity or quality mathematical characteristics of a concrete situation and of the algorithms of its processing 5. The analysis and the interpretation of the mathematical characteristics of a problem-situation 6. The mathematical shaping of some various problematic contexts through the integration of knowledge in various fields.

Specific competences 1. The use of some charts and formulae for calculation in trigonometry and geometry 2. The translation of some practical problems in trigonometry and geometrical language.

3. The improvement of mathematical calculation through the proper choice of formulae.

4. The analysis and interpretation of the results obtained through solving practical problems    

Didactic methods and strategies: frontal, individual, reviewing conversation, explaining, problem-solving.

Teaching aids: Text books, ppt presentation, worksheets.

Organization : frontal and individual activity

Procedures: 57

1. Organising -the teacher asks about the absent students and registers them -the teacher makes sure that the atmosphere is the proper one for the lesson- 2 minutes 2. Checking the knowledge introduced in the previous lessons and reviewing those items which are necessary for the new topic -10 minutes I check a few homework notebooks, after I ask the students “What topic did we discuss about during our previous class?”

The expected answer is: During our previous class we talked about: “The sign of trigonometry functions.”

I ask the students the following questions:  What is a trigonometry circle?  The expected answer is :  The oriented circle with its center in the origin of the Cartesian reference point and with the radius equal to the unit is called trigonometry circle, marked with C.  Which is the sign of the trigonometry functions?  The expected answer is :  If……………… then…………

3.

4.

5.

Introducing the new items -30 minutes I introduce the students the title of the new lesson “Reduction formulae to the first quadrant”, PPT presentation The reinforcement of the newly introduced items and feed-back-6 minutes The students solve some applications on the worksheets.

Homework assignment -2 minutes

Worksheet: 1. Calculate: cos 300+cos450+cos600+cos 900+cos1200+cos1350+cos1500 2. ….. sin 1700 –sin 100 3. Calculate: a) sin 2250 ; b)sin 1350 c)sin

58

d)cos

e)tg

f) ctg 1500 g)sin

LESSON PLAN 5 Date: 13.04.2015 Grade XII-th Teacher: Buzduga Nicolai Topic of the lesson: The definite integral of a continuous function Type of lesson: Lesson for acquiring new pieces of knowledge General competences: 1. Identification of mathematical relations and data and their link depending on the context on which they were defined.

2. Processing of quantitative, qualitative, structural and contextual data, comprised in mathematical questions.

3. Use of algorithms and mathematical concepts for the local or global defining of a practical situation.

4. Expression of the quantitative and qualificative mathematical characteristics of a practical situation and its processing algorithms.

5. Analysis and interpretation of the mathematical characteristics of a practical situation.

6. Moulding of some various problematic contexts, by involving knowledge from different fields.

Specific competences to be acquired: C. 3. Use of algorithms to calculate definite integrals.

C. 4. Explanation of the calculating options of definite integrals, with the purpose of optimizing the solutions.

C. 6. Application of the differential or integral calculus in practical problems.

Values and opportunities: 1. Development of a creative, open mind and an independent system of thought and action.

2. Showcasing an initiative spirit, a disponibility to solve various tasks, a tenacity and preseverance, as well as a collectedness ability.

3. Development of an aesthetic and critical spirit, of a strong capacity of appreciating the rigour, the order and the elegance in the architecture of solving a problem or building up a theory.

4. Training the habit of turning to mathematical methods and concepts in dealing with common situations or to solve practical problems.

59

5. Building up motivation to study mathematics as a relevant field both in the personal life and in one’s career.

Development of the lesson

Lesson steps

Teaching strategies

Content of the lesson

1. Organizing moment

Ensuring the optimum working conditions (tidiness, light, dressing Conversation code..). Checking the students’ attendance.

2. Maintaining students’ attention

Frontal checking of the topic, both by quality and quantity (throughout a poll).

Conversation

3. Announcing the topic and tasks

We wish to discuss Conversation Definite integral of a continuous function Be it f : [a; b]  R a continuous function on the following interval

4. Refreshing previous knowledge

[a; b] and F , G : [a; b]  R two of f primitives on [a; b] . We note Conversation F ( x) |ba  F (b)  F (a) . Because G( x)  F ( x)  c, c  R, we have G( x) |ba  G(b)  G(a)  F (b)  c  F (a)  c  F (b)  F (a)  F ( x) |ba .

Definition. Be I an interval and a, b  I two numbers. Be F : I  R a primitive of the continuous function f : I  R . We call a definite integral of the f function from a to b the real number number noted

5. Presentation of the content and leading the assessment manner

b

through the relation:

 f ( x)dx  F ( x) |

b a

 F (b)  F (a) (Leibniz-

a

Newton formula).

Explaining

Observations: 

Integration variable plays no role in the definition of the integral: b

 a

Conversation

b

b

b

a

a

a

f ( x)dx   f (t )dt   f (u )du   f ( y )dy .

60



a

 f ( x)dx  F ( x) |

a a

 F (a)  F (a)  0.

a



a

 f ( x)dx  F ( x) |

b

a b

 F (a)  F (b)  F (b)  F (a)    f ( x)dx.

b



a

t

 f ( x)dx  F ( x) |

t a

is a primitive of f which is nule when t=a.

a

2

Example:

2  x dx  1

x3 3

2 1



2 3 13 8  1 7    3 3 3 3

Theoreme. Be the functions f , g : [a; b]  R continuous on [a; b] and be there   R .Therefore we have: b

a)

a

b)

b

b

a

a

  f ( x)  g ( x)dx   f ( x)dx   g ( x)dx; b

b

a

a

   f ( x)dx     f ( x)dx.

Example: To be determined:

 3x



2

1)

2

 2 x  2 dx;

1 4

2)



x dx;

0 1

3)

x

3

x dx;

0

 e 1

4)

x



 xe x dx .

0

6.

Strengthening the retention and providing an efficient transfer

Working sheet exercises from 1 to 20 Conversation Explanation

61

Working sheet exercises from 21 to 25 7. Providing a feedback

Independent work

The teacher solves the difficult exercises at the blackboard. Conversation Appreciation of the students that were outstanding throughout the Explanation lesson (+, -, and eventually a mark in the class book)

8. Evaluation

Teacher-book 9. Homework

Conversation Page 194 exercises from 36 to 40.

Annexe.Working sheet. Definite integral of a continuous function.

Using the Leibniz –Newton formula solve the following integrals: 2

1)

x

dx ;

2)

0

x

5

3)

dx ;

x

2

7

dx ;

 5

10)  10 x dx ; 1

6)



x x dx ;

0

0

4

1



3



3

8

x 1

1

8)

11)

1

4 1

7)

x

dx ;

e

1

x

x

2

x

2

4 3

dx ;

x 1 dx ; x 2



12)

2

13)

1 

1 dx ;  25 1 dx ; 3

14)  sin xdx ; 0



1

9)

  2  dx ; 2

4

5)

x

3

2

1

4)

3

3

5

x

dx ;

2

15)  cos xdx ; 0

62

7

dx ;



16)

1

 cos

2

x

3 4

dx ;

 2

17)

1

  sin

2

x

dx ;

6



18)

 tgxdx ;

2 3

2 2

19)

 0

2

20)

1 x2 1 1



3

x2  3

3



21)

 2 3 4

22)

 0

 3 1

23)

dx ;

dx

1 4  x2 1 9  4x 2

dx ;

dx ;



x  43 x dx ;

0

3 2   24)   x 5  4 x 3   2 dx x x  1 5  6 3  dx 25)   2   x2  9  4 x 9 e

63

DIDACTIC PROJECT Upstream Upper Intermediate Prof. Cătălina Melniciuc

Unit

PLANET ISSUES

Lesson

Vocabulary practice on environmental issues and Future Forms

Place

Theoretical Highschool “Nicolae Iorga” Botoşani

Target group Derived competences

Students from the 11th grade, Humanities O1 – use vocabulary connected to environmental problems O2 – bring arguments for and against the topic O3 – work together to carry out a task O4 – write down notes from a text they listen to O5 – explain and use the new words and phrases O6 – express personal opinions on environmental problems  Involvement  Communication  Cooperation - exercise, listening comprehension, communicative approach

Approach

Methods Means

- laptop, tape, textbook, workbook, cassette player

Time

50 minutes (8.00 – 9.00)

Organisers

Teacher, Catalina Melniciuc

Stage

Activity

Means

Role Participants

1.Warm-up

Organiser

Warm up(1’) Theme and purpose presentation The teacher introduces the topic and

Lecture

Listen

Introduces

gives the students the evaluating scheme which will help them to appreciate the homework. The students will listen to the indications of using it 2. Activity

1. Practice : 

Why the Antarctic is considered the key to Planet Earth? – consequences of pollution in this region Film presentation – air pollution 

Has the presentation impressed you?  Who is responsible for this phenomenon?  Which was the strongest impact that the presentation has had on you?  Will this change your attitude?

How? Film debating – global warming 

Can the material advantages replace the loss of stability on our planet?  Which are the resources you discovered in order to solve such problems?  What do you expect from school/society/authorities?  How can we improve the situation? Which are the solutions?

2. Production - independent activity : exercises focusing on vocabulary practice, ex 13/pag 162 - listening: ex 1b/pag 162

65

Frontal activity

Watch the videos

Watch

Facilitates

Listen

Lectures

Involve in the dialogue

Moderate s

Debate

- pair activity: ex 4/pad 162 3.

Follow-up (5’)

Evaluation

Final appreciation.

Lecture

Homework

listen selfassessment

Lectures Supervises

WORKSHEETS FOR PHYSICS LESSONS Prof. Adriana Vatavu

1. Determination of sliding friction.

Required materials: A pulley, a hook for notched discs, notched discs, a tribometer, an inextensible thread, a tray, standards weights, a rectangular piece PROCEDURE:

1. Make the installation in the figure above.

2. Add notched discs in the hook until the system formed by the rectangular piece on the horizontal plane and the tray begins to have a rectilinear motion. In this case, the weight G of the tray and of the standards weights on the tray (the thrust) is equal to the sliding friction Ff .

G = Ff

3. Place different bodies of known mass on the rectangular piece and then add notched discs in the hook until the system has a rectilinear motion.

Method I:

66

4. The experimental results obtained are presented in the table:

Number of

M

N=Mg

m

Ff = m g

determinatio

(kg )

(N)

( kg )

(N)



Ff N



m M

m



 m

ns 1 2 3 4

In which M - the weight of the rectangular piece + known weights ; m - the weight of the tray + known weights Method II:

The graphical determination of the coefficient of sliding friction  , represents the selection of two points, A and B, on the represented line, which are at some distance one from the other. In the right triangle ABC, the cathetus BC represents NA - NB , and the cathetus AC is FfA - FfB .

67



F fA  F fB NA  NB

 tg

5. Draw the grapf of the function Ff =f ( N ) on the graph paper.

Using a protractor determine the angle α, then with GeoGebra, determine the tangent of the angle, which is the spring sliding friction.

Conclusion : .................................................... .....................................................

2. Determination of elastic constant of a spring

Required materials: A spring, a hook for notched discs, notched discs, a support for the spring, a ruler.

PROCEDURE:

1.

Suspend the spring.

2. Measure the initial length of the spring (l0) in the undeformed state.

3. Add notched discs one by one at the free end of the spring.

4. For each notched disc added, measure the length of the spring in deformed state.

The elastic force is equal to the force that deforms the spring, in our case it is equal to the weight of the notched discs.

Fe = Fdef = G Method I: 5. The experimental results obtained are presented in the table: Number of discs

k Fe ( N ) =

l0

l

(m)

(m)

l

Fe l

km

G(N) (m)

(N/m)

68

( N /m )

k

km

k =km 

(N/ m)

( N / mk ) m)

Method II: 6. The experimental results obtained are presented in the table: Number of discs

7.

l0

l

l

(m)

(m)

(m)

Fe ( N ) = G ( N )

The data is transferred onto the graph paper, and the graph is drawn Fe= f( l):

69

Using a protractor determine the angle α, then with GeoGebra, determine the tangent of the angle, which is the spring constant.

Conclusion : ....................................................

Didactic activity project Determining elastic constant of a spring Study of spring grouping

School: C. N. „A. T. Laurian”, Botoşani Subject: Physics Grade: a IX-a Teacher: Bucătaru Magda Mihaiela Teaching unit: Principles and laws in classic mechanics Number of classes: 2 Lesson contents: Interaction and its effects. Hook law. Elastic constant of a spring. Questions, exercises, problems. (Physics curricula for 9th grade)

70

Lesson subject: Study of grouping springs. Determining elastic constant of two springs grouped in series and in parallel Learning model: Experiment Key competence: Theoretic and experimental scientific investigation applied in Physics Specific competences: derived from the learning pattern, according to the following table: Material resources: experimental activity hand-outs, mechanic kit, computer Sequences of learning unit Specific competences 1. Evoking – Anticipating Asking questions and giving alternative hypotheses, examining information sources, projecting investigation; 2. Exploring – Investigating Collecting samples, analyzing and interpreting information 3. Reflexing – Explanation Testing alternative hypotheses and proposing an explanation 4. Applying – Transfer Including other particular cases and communicating results; Impact of the new knowledge (values and limits) and valorizing results

Sequence IV Applying – Transfer Generic: What beliefs this information give me?

What else can I do if I have this information?

Specific competences (derived from the project model): Including other particular cases in communicating results. Impact of new knowledge (values and limits) and valorising results; Lesson type: Lesson of making/developing capacities to compare, analyze, synthesize, transfer, knowing values, make abilities to communicate, cognitive and social abilities, etc. Lesson to learn analogy by anticipating means. Lesson of systematizing and consolidation of new knowledge.

Cognitive process: deduction; Lesson script: deductive. Student notices a definition of the concept to be acquired/ a rule to solve a problem/ production instructions and apply them in in particular examples, explain characteristics that do not fit definition/rule/instruction. Student imagine different trials(experiments) of a concept to be learnt/problem to be solved/product to be made based on what he already know to do, notices and analyze partial achievements, successive representations of the expected result.

Teacher’s role Learning tasks Students (individually, in groups, with teacher) Show students a cognitive organizer Follow simulation and refresh knowledge (introductory lecture):reminds them notions The constant of spring elasticity can be 71

of elastic force, elastic constant, Hook law (presents interactive application) Offer students materials for the experiment implying them in solving new problems, evaluating procedures/adopted solutions.

Ask students: - To determine elastic constants of the two springs calculating and graphically.

- To draw the graphic of the force according to the absolute elongation for the two springs connected in series and parallel.

- To determine the equivalent elastic constant o0f the two springs connected in series and parallel.

- To compare the obtained results to the theoretic ones.

- To evaluate measure errors of the equivalent elastic constants

determined using spring characteristics (aria of cross section, length in original state, way of longitudinal elasticity), but also graphically, studying the deforming force and absolute elongation.

Make the experiment. Complete hand-outs table.

Calculates elasticity constant using tangent of the obtained angle in the graphic representing deforming force dependence to absolute elongation; compares it to the one obtained by calculation (according to the data table).

.

Guides students in obtaining relations for ks, Approach theoretically series/parallel respectively kp. grouping of more identical springs Implies students in making the final report and extends their activity outside the classroom (homework): ask students to make a short written report regarding the results of investigations; gives ideas for the structure and content.

Assume roles in the working group, type of product to be presented (lab works, experimental determinations, solving problems, essays, etc); establish modalities to present (posters, portfolios, PowerPoint presentations, own films made on computer, etc); Negotiate in the group content and structure of the final report and the way to be presented (paper, essay, poster, portfolio, multimedia presentation, own films, etc);

72

Simulation: https://phet.colorado.edu/ro/simulation/mass-spring-lab

Bibliography: (1) Sarivan, L., coord., Predarea interactivă centrată pe elev, M.E.C.T./ P.I.R., Bucureşti 2005; (2) Păcurari, O. (coord.), Învăţarea activă, Ghid pentru formatori, MEC-CNPP, 2001; (3) Leahu, I., Didactica fizicii. Modele de proiectare curriculară, M.E.C.T./ P.I.R., Bucureşti 2006; (4) Ailincăi,M, Rădulescu,L,Probleme-Intrebări de fizică, Editura didactică şi pedagogică, Bucureşti,1972 (5) https://phet.colorado.edu/ro/simulation/

Annex 1

Determining elastic constant of a spring. Study of spring grouping

Materials at disposition -

Support for suspending springs

73

-

Two springs with different elastic constants, having about the same initial length Hook with marked masses Rule

Demands: -

To determine the elastic constants of the two springs To determine the equivalent elastic constant of the two springs connected in parallel To determine the equivalent elastic constant of the two springs connected in series To compare the obtained results with the theoretic ones.

Theory and work way The initial length of the first spring is measured l0, then the hook is fixed (15g) and gradually a marked mass (10g) measuring the spring length l and calculating corresponding elongation The value of elastic constant is calculated for each attached mass

Data are written in the following table: m (g)

(cm)

(cm)

(cm)

k (N/m)

(N/m)

15 25 35 45 55 65 75 74

(N/m)

(N/m)

(%)

(N/m)

85 95

Same operations are done for the second spring and for the two types of grouping the springs, parallel and series.

Parallel grouping

Series grouping

G(N) is represented graphically according to the spring elongation (m) and the elongation constant is determined from the graphic slope. The result is compared to the one obtained from calculation.

Annex2 Experimental results Determining elastic k1

(cm) 0,7 1,1 1,5 2,1 2,6 3,1 3,6 4,2

m (g) 15 25 35 45 55 65 75 85

k1 (N/m) 21,43 22,73 23,33 21,43 21,15 20,97 20,83 20,24

(N/m)

21,37

(N/m) 0,00 1,84 3,86 0,00 0,05 0,16 0,29 1,28

(N/m)

(%)

(N/m)

0,313

1,5%

21,37Âą1,5%

75

4,7

95

20,21

1,34

K1 120

100

80

60

K1= 20,7N/m

40

20

0 0

0,5

1

1,5

2

2,5

3

3,5

4

4,5

Determining elastic constant k2

(cm) 0,85 1,4 2,05 2,6 3,2 3,8 4,4 4,95 5,55

m (g) 15 25 35 45 55 65 75 85 95

k2 (N/m) 17,65 17,86 17,07 17,31 17,19 17,11 17,05 17,17 17,12

(N/m)

17,28

(N/m) 0,37 0,58 -0,21 0,03 -0,09 -0,17 -0,23 -0,11 -0,16

(N/m)

(%)

(N/m)

0,085

0,5%

17,28Âą0,5%

76

5

K2 100 90 80 70 60 50

K2 = 17,1N/m

40 30 20 10 0 0

1

2

3

4

5

6

Determining elastic constant grouped in parallel kp

(cm) 0,4 0,65 0,9 1,2 1,45 1,7 2 2,25 2,5

m (g) 15 25 35 45 55 65 75 85 95

k1 (N/m) 37,50 38,46 38,89 37,50 37,93 38,24 37,50 37,78 38,00

(N/m)

37,98

(N/m) -0,48 0,48 0,91 -0,48 -0,05 0,26 -0,48 -0,20 0,02

(N/m)

(%)

(N/m)

0,143

0,4%

37,98Âą0,4%

77

K paralel 100 90 80

70 60 50

Kp = 37,9 N/m

40 30 20 10 0 0

0,5

1

1,5

2

2,5

3

Determining elastic constant grouped in series ks

(cm) 1,55 2,6 3,7 4,6 5,55 6,6

m (g) 15 25 35 45 55 65

k1 (N/m) 9,68 9,62 9,46 9,78 9,91 9,85

(N/m)

9,82

(N/m) -0,15 -0,21 -0,36 -0,04 0,09 0,02

(N/m)

(%)

(N/m)

0,066

0,7%

9,82Âą0,7%

78

7,4 8,6 9,4

75 85 95

10,14 9,88 10,11

0,31 0,06 0,28

K serie 100 90 80 70 60 50

Ks = 9,9 N/m

40 30 20 10 0 0

1

2

3

4

5

6

79

7

8

9

10

120

k1 = 20,7N/n

100

kp = 37,9 N/m 80

k2 = 17,1N/m

ks = 9,9N/m

60

40

20

0 0

1

2

3

4

5

6

7

8

9

10

Determining slip friction coefficient using mechanic energy variation of a body/object theorem Didactic activity project School: C. N. „A. T. Laurian”, Botoşani Subject: Physics Grade: a IX-a Teacher: Bucătaru Marius Daniel Learning unit: Mechanic energy. Theorem of mechanic energy 80

Number of classes: 2 Contents for the learning unit: Mechanic energy of a system of objects (physics system).

Theorem of mechanic energy variation. Isolated physics system. Conservation of an isolated a physics system mechanic energy. Determining slip friction coefficient using mechanic energy variation theorem. (Physics curricula for 9th grade).

Lesson subject: Determining slip friction coefficient using mechanic energy variation of a body/object theorem Learning pattern: Experiment.

Key competence: Theoretic and experimental scientific investigation applied in Physics Specific competences: derived from the learning pattern, according to the following table: (Calculating mechanic work made by the slip friction force, of kinetic and gravitational potential energy. Solving simple problems by applying mechanic energy variation theorem in different situations.

Learning unit sequences 5. Evoking – Anticipating

6. Exploring – Investigating 7. Reflexing – Explanation 8. Applying – Transfer

Specific competences Asking questions and giving alternative hypotheses, examining information sources, projecting investigation; Collecting samples, analyzing and interpreting information Testing alternative hypotheses and proposing an explanation Including other particular cases and communicating results; Impact of the new knowledge (values and limits) and valorizing results

The script present a lesson supposing making an experiment in lab conditions, learning new themes together with undertaking the experiment stages. The central cognitive process is induction or generalization (developing new knowledge based on examples of the already learnt concept).

Sequence I. Evocation – Anticipation 81

Generic: What I know or believe about this?

Specific competences (derived from project pattern): Giving hypotheses and planning the experiment Lesson type: Initial evaluation; communicating the tasks, presenting cognitive organizers (introductory lesson); learning the planning (anticipating) process.

Cognitive process/lesson script: planning or anticipating. The student tries in different ways to acquire a concept/solve a problem/make a product by anticipating demands, planning means and stages, adjusting them repeatedly Lesson 1 Teacher’s role

Learning tasks Students (individually in groups, with the teacher)

Presents students a cognitive organizer (introductory lecture): basic notions of a Physics system as a sum of kinetic and potential energy, unisolated or isolated Physics system.

Presents simulations. https://phet.colorado.edu/ro/simulation/energyskate-park

Give examples from personal experience, of objects that have kinetic and potential energy simultaneously.

Open and use simulations.

https://phet.colorado.edu/ro/simulation/rampforces-and-motion Guide students’ thinking to deduce Deduce the mechanic energy variation mathematical expression of the mechanic theorem by applying theorem of kinetic energy variation theorem. and potential energy for an unisolated Physics system.

Establish correspondence between mechanic energy variation of a physics system and mechanic work made by no conservative forces acting over the system.

Guides students’ thinking to particularize the Deduce energy conservation law for an

82

theorem of mechanic energy variation in an isolated physic system. . isolated physic system with the result of deducing mechanic energy conservation law.

Propose two problems to be solved referring to mechanic energy conservation in free fall without friction an in case of free slip on an inclined plan without friction

Solves the problems on the blackboard in two ways, the first one by using kinematic notions exclusively, the other one using mechanic energy conservation law.

Finds out that the two methods lead to the same result, hence the validity of the energy conservation law.

Extends students’ activity (with homework), Do the homework, give work asking them to make a paper on „Determining hypotheses, plan the experiment in team the coefficient of slip friction using the theorem and choose the necessary materials for the experiment. of mechanic energy variation.

Simulation: https://phet.colorado.edu/ro/simulation/energy-skate-park

83

Simulation: https://phet.colorado.edu/ro/simulation/ramp-forces-and-motion

Sequence II. Exploration – Experiencing

84

Specific competences: Making the experiment and collecting data Lesson type: Make/ develop capacities to explore, experiment, learning the analogy process and anticipating the effect, communicating and social abilities.

Cognitive process: analogy with anticipating the effect. The students find a certain difficulty of a problem, tries to correct it experiencing means.

Lesson 2 Teacher’s role

Learning tasks Students (individually in groups, with the teacher)

Stimulate students to present papers made at home and invites a student to present the theoretical part Offers students experimental materials Asks students to do the experiment

Presents theoretical part Evaluates the proposed hypotheses, material resources, time, group tasks, etc.

Annex 1.

Sequence III. Reflexion – Explanation Specific competences: Working data and elaborating conclusions Cognitive process: induction the student notices examples of the concept to be learnt, gives definitions/solving rules, improving them gradually.

Teacher’s role Learning tasks Students (individually in groups, with the teacher)

Invites students to synthesize Analyze experimental data and apply observations of the exploration stage, to calculus relations to calculate the two analyze the values table. friction coefficients.

Ask students to interpret the results and come to conclusions

85

Sequence IV Application – Transfer Specific competences: 4. Testing conclusions and predictions 5. Impact of the new knowledge and valorizing the results.

Cognitive process: deduction and analogy by anticipating the means. Students notice a definition of the concept, apply in particular examples, explain characteristics that do not fit the rule. He imagines different experimentations of a learnt concept, notices and analyze the partial achievements Teacher’s role Learning tasks Students (individually in groups, with the teacher)

Ask students to present the results of the Present their results (Annex 2) investigations regarding cognitive, esthetic, communication, social competences Final evaluation specifying instruments Communicate final conclusions (written test or oral assessment).

Projects, portfolio, etc.

Expand activity outside the classroom Make homework proposing solving problems.

Bibliography: (1) Anghel, S ş.a., Metodica predării fizicii, Ed. Arg-Tempus, Piteştii 1995 ; (2) Cerghit, I. ş.a., Prelegeri pedagogice, Ed. Polirom, Iaşi 2001; (3) Fălie, V ; Mihalache, R. Fizica, manual pentru clasa a IX-a, Ed. Didactică şi pedagogică, Bucureşti 2004;

86

(4) Gherbanovschi, C ; Gherbanovschi, N. Fizica, manual pentru clasa a IX-a, Ed. Niculescu, Bucureşti 1999; (5) Hristev, A ş.a., Fizica, manual pentru clasa a IX-a, Ed. Ed. Didactică şi pedagogică, Bucureşti 1994 ; (6) Păcurari, O. (coord.), Învăţarea activă, Ghid pentru formatori, MEC-CNPP, 2001; (7) Leahu, I., Didactica fizicii. Modele de proiectare curriculară, M.E.C.T./ P.I.R., Buc. 2006; (8) Păcurari, O. (coord.), Învăţarea activă, Ghid pentru formatori, MEC-CNPP, 2001; (9) Sarivan, L., coord., Predarea interactivă centrată pe elev, M.E.C.T./ P.I.R., Bucureşti 2005; (10) Ursu, S ş.a., Lucrări practice de mecanică pentru clasa a IX-a, Ed. All, Bucureşti 1995.

(11) https://phet.colorado.edu/ro/simulation/

Annex 1 Determining the slip friction coefficient using the theorem of mechanic energy variation of an object Materials at disposal -

Object of mass m=5g Metal inclined plan Paper Support for the inclined plan Ruler

Experimental device

Working mode:

87

Leaving the object to slip freely from A it will go on the inclined plan from A to B and continue horizontally till stop on distance AS We apply the theorem of kinetic energy variation between A and B and B and S respectively

We get:

We repeat it for a height h’ and determine friction coefficients

For experimental determination we fill in the table: ( s is determined as an average of, at least, five measurements h (mm)

l (mm)

220 230 240 250 260 270 280 290 300 310 320

543 543 543 543 544 545 546 547 548 549 550

s (mm) (mm)

ds'hs'dh'sd’ sh’ hd’ 2 2 (mm ) (mm ) (mm2)

Nr.

1 2 3 4 5 6 7 8 9 10

Error calculation:

88

Annex 2 Experimental results h (mm)

l (mm)

220 230 240 250 260 270 280 290 300 310 320

543 543 543 543 544 545 546 547 548 549 550

0,400

0,402

s (mm) (mm) 496,44 491,88 487,08 482,03 477,85 473,42 468,74 463,80 458,59 453,10 447,33

0,0021

42 65 87 109 131 153 175 198 222 246 271

ds'-sd’ (mm2)

hs'-sh’ dh'-hd’ (mm2) (mm2)

11609,27 11133,49 11155,7 11060,27 11092,5 11131,2 11645,54 12162,61 12224,39 12748,47

0,0021

4640 4410 4410 4410 4410 4410 4690 4980 4980 5290

0,53% 89

5966,06 6023,06 6084,31 5865,45 5929,40 5997,70 6070,67 6148,68 6232,17 6321,62

Nr. 0,400 0,396 0,395 0,399 0,398 0,396 0,403 0,409 0,407 0,415

0,402±0,53%

0,514 0,541 0,545 0,530 0,535 0,539 0,521 0,506 0,510 0,496

1 2 3 4 5 6 7 8 9 10

0,396 0,395 0,399 0,398 0,396 0,403 0,409 0,407 0,415

0,514 0,541 0,545 0,530 0,535 0,539 0,521 0,506 0,510 0,496

0,0057 0,0065 0,0031 0,0042 0,0056 -0,0009 -0,0076 -0,0056 -0,0131

0,524

0,0097 -0,0173 -0,0218 -0,0067 -0,0109 -0,0152 0,0024 0,0181 0,0138 0,0278

0,0053

1,02%

90

0,524±1%

Results obtained by graphic means 7000

6500

µ1 = 0,52

6000

5500

µ2 = 0,40 5000

4500

4000 10800

11000

11200

11400

11600

11800

12000

91

12200

12400

12600

12800

13000

DIDACTIC SCENARIO ”N. Iorga” Theoretical Highscool Botoșani Romania Teacher: Olivia Gornea, Roxana Vatavu Target group:9th degree Module: Life syle quality General competence: Practicing the management of a good quality life stylde.

Derived competences:. The analyse of some phenomena which have negative consequences on students’ life style.

Content:Personal life quality: - life style as resource for performance in school/professional activity Theme: ”A Healthy Life Style” Purpose: - Getting familiar with a healthy life style.

Objectives:  Reference Objective:Changing students’ mentality by making them aware and adopting a healthy life style.  OperationalObjectives: - To get basic notions which refer to a healthy life style after watching a movie; - To get basic notions which refer tothe ingredients of a healthy life style; - To correctly solve the group tasks from the annexes - To choose the images which they consider to illustrate the most appropriate means of spending the free time for a child of their age; Approaches and techniques: conversation,explanation, play role, group discussions to identify which are the factors which influence performance Didactic aids: flip chart, ball, marker, videoprojector,work sheets, glue, Organization: individual, group, frontal Time: 50 minutes Place: the classroom Bibliography and sources:  DRAGU, Mariana, BABAN, Marilena, POENARU, Camelia, Proiectul de lecţieîntretradiţionalşi modern – ghidmetodic, Didactica Publishing House, Bucureşti, 2011.  NADASAN, Valentin, AZAMFIREI, EdituraViaţăşisănătate, Bucureşti, 1999.

Leonard,Un

stil

de

viaţăpentrumileniultrei,

 The educationalsite: www.didactic.ro ACTIVITY PLAN Stages

Content Teacher’s activity

Students’ activity

92

Approaches and techniques

Didactic aids

1.

Organizatio n (1 min) 2. Warm-up ( 9 min)

T. prepares the didactic aids for the best organization of the activity.

3. Theme and objectives anouncemen t ( 5 min)

”Health is better than anything elsebut in order to enjoy itwe must have a healthy life style which involves discipline, work discipline, proper food, exercise and resting. The elements which influence health are: physical exercises, active games and trips, healthy eating, (vitamins , proteins, proper intake of bread, cereals, fruit, vegetables, dairy products, meat and fish)” ”Our discussion today starts with the balance between work and rest and about maintaining a correct and relaxing physical condition while working. We have chosen this topic as if we respect these rules, we will be able to protect our immune system and we will be able to avoid the diseases we might face in the cold season.

Ss. get ready to Conversatio start the activity n;

(flip-chart, videoprojector); Ice breaking exercise : ”The imaginary ball’’

93

The T. throws the ball to the Ss and they wil tell their name and favourite food.

Ss. pay attention and aswer the questions

Conversatio n

The ball

Conversatio n Explanation

flip-chart

Activity1 (5 minutes) T. will write on the flip-chart the ingredients of the previously mentioned life style.

Activity 2 ( 10 minutes) Using the video projector, the T. will show Ss. a film which shows images of the correct body posture while working and the alternation work – rest. Then s/he emphasizes the importance of proper posture and the need of breaks.

Ss. will dictate which the ingredients of a healthy life styleare.

Ss pay attention and follow the images to find out useful information.

5.

Assessment (15 min)

Ss. will form 3 groups, will solve the task and will write on a flip charter paper the ingredients of a healthy life style

Ss will fill in the work sheets.

Work sheets

6. Feedback and follow up (5 min)

Each S will receive a questionnaire for assessment (Annex 2).

S. will evaluate from 1 to 5 the degree they enjoyed the activity

Work sheets

4. Practice ( 15 min)

The grape flip chart cluster sheet

Explanation

Videoproj ector

Conversatio n

ANNEX NO.1Group ”__________________”

1. You are a pediatrician. What would you recommend to Florinel, (aged 9) who is overweight, has poor school results, spends most of his time inside in front of the TV, eats plenty of sweets, lacks energy and very often gets sick? _______________________________________________________________________________ _______________________________________________________________________________ _______________________________________________________________________________ 2. Which of the next means of spending the free time seems appropriate to you for a healthy life style?

94

COLEGIUL NATIONAL A.T.LAURIAN BOTOSANI

ANNEX NO. 2 Have you enjoyed the news, the information and the advice you received today about a healthy life style? How much have you enjoyed the activity? Cross the balloon you think it answers the question.

Yes, I enjoyed it a lot. I would like similar activities.

Yes, I liked them

So, so

Not too much.

No, I didn’t like it.

PEDAGOGICAL TECHNOLOGY PROJECT Date: 20.04.2015 Class: a XI a A Section : Real Specializing: mathematics-informatics Teacher: Cardas Cerasela Daniela Discipline: Informatics Learning unit: Elements of oriented programming in visual environment Theme: Graphic design applications for Second degree equation graphics Lesson type: enhancing of knowledge and skills General skills: implementing algorithms in a programming language

95

COLEGIUL NATIONAL A.T.LAURIAN BOTOSANI Specific skills: - Using the development app tools - Developing and implementing an application using Visual C # programming - Establishing an interdisciplinary mathematics-informatics application Learning activities: - Creating a graphical user interface consisting buttons, text boxes and setting their properties - Writing codes attached to controls Teaching methods: conversation, exercise, demonstration, independent work, problem solving, case study.

Means of education: computers, software Microsoft Visual Studio 2010 Express-C #, overhead.

Organization forms: face-to-face activity, individual Resources: - Pedagogical: Teaching computer science, modern user rating - Official: curriculum - Temporal: 1 hour CLASS ACTIVITIES 1. Arrangements Time: 3 min.

Teacher’s activity: The teacher checks the presence, ensures that students are prepared Student’s activity: Prepares the materials necessary for the lesson.

Teaching methods: face-to-face conversation 2. Updating the knowledge Time: 7 min.

Teacher’s activity: Teacher asks the students the following questions: - What are the necessary elements to build a GUI drawing application?

- What controls do we set in the design mode?

- What method will we implement for drawing the graph?

Student’s activity: Students listen to teacher's questions and prepare responses based on previously acquired theoretical and practical knowledge.

Teaching methods: face-to-face conversation 3. Statement of the new knowledge Time: 30 min Teacher’s activity: The teacher communicates the study topic „Graphic applications for drawing the chart of the II degree equations” and the objectives of the lesson: - Creating an application consisting 3 textboxes, 2 buttons; - Writing a code that must execute when loading the window (load).

- Writing a code for the Click button function Student’s activity: the students write down what the teacher presented and ask questions for clarifications. They run the Visual C# app and follow the steps to create the graphic interface.

Contents: Source code: using System; using System.Collections.Generic; using System.ComponentModel; using System.Data; using System.Drawing; using System.Linq;

using System.Text; using System.Windows.Forms; namespace Graph2 { public partial class Form1 : Form

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MessageBox.Show("Invalid iput", "Error", MessageBoxButtons.OK, MessageBoxIcon.Error); } private void timer1_Tick(object sender, EventArgs e) { p.Color = color[col]; if (i<200) g.DrawLine(p, x[i], y[i], x[i + 1], y[i + 1]); else timer1.Stop(); i++; } private void button2_Click(object sender, EventArgs e) { g.Clear(Color.WhiteSmoke); DrawAxis(); col = 0; }

public Form1() { InitializeComponent(); } int[] x = new int[1000]; int[] y = new int[1000]; int[] xL = new int[3] { 10, 280, 550}; int[] yL = new int[3] { 20, 50, 80 }; Label[] lbl = new Label[10]; Graphics g, g2; bool OK; Pen p = new Pen(Color.Black, 2); Pen p2 = new Pen(Color.Black, 1); Color[] color = new Color[10] { Color.Red, Color.Green, Color.Orange, Color.Cyan, Color.Blue, Color.DarkCyan, Color.Lime, Color.Purple, Color.Pink, Color.Yellow }; // V-varful parabolei int a, b, c, delta, Vx, Vy, i, j, col=-1 , k; string f; private void Form1_Load(object sender, EventArgs e) { g = this.panel1.CreateGraphics(); g2 = this.legend1.CreateGraphics(); } void DrawAxis() { g.DrawLine(p2, 0, 200, 800, 200); g.DrawLine(p2, 400, 0, 400, 400); for (i = 0; i <= 800; i += 10) g.DrawLine(p2, i, 197, i, 203); for (i = 0; i <= 400; i += 10) g.DrawLine(p2, 397, i, 403, i); }

void CheckImput() { OK = true; try { a= Convert.ToInt32(textBox1.Text); b = Convert.ToInt32(textBox2.Text); c = Convert.ToInt32(textBox3.Text); } catch { OK = false; } if (textBox1.Text == "" || textBox1.Text == "0" || textBox2.Text == "" || textBox3.Text == "") OK = false; } void AddFunctionToLegend(string f,Color c) { p.Color = c; g2.DrawLine(p, xL[k / 3], yL[k % 3]+10, xL[k / 3] + 40, yL[k % 3]+10); lbl[k] = new Label(); lbl[k].Size = new Size(200, 15); lbl[k].Text = f; lbl[k].Location = new Point(xL[k / 3] + 50, yL[k % 3]); legend1.Controls.Add(lbl[k]); k++; } }}

private void butto1_Click(object sender, EvenArgs e) { CheckImput(); if (OK) { f = "f(x) = " + a.ToString() + "*x^2 + " + b.ToString() + "x + " + c.ToString(); DrawAxis(); a *= -1; b *= -1; c *= -1; delta = b * b - 4 * a * c; Vx = -b / (2 * a); Vy = delta / (4 * a); for (i = Vx - 100, j = 1; i <= Vx + 100; i++, j++) { x[j] = i*10 + 400; y[j] = (a * i * i + b * i + c)*10 + 200; } i = 1; col++; timer1.Start(); AddFunctionToLegend(f, color[col]); } else

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Moments of the application

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Teaching methods: conversation, exercise, independent work, demonstration, a certain soft for creating the app.

IV. Consolidation of new information Time. 5 min Teacher’s activity: The teacher asks the following questions: - What kind of controls did we use in the previously apps for creating the graphic interface?

- How do we manage the events of the app?

- What is the class used for creating the graphic apps in C#?

Students activities: Students answer to teacher’ questions.

Teaching methods: face-to-face conversation.

V. Evaluation.

Time. 5 min Teacher’s activity: the teacher reviews the success of the students, he might as note them and clarifying the mistakes(?)

Student’s activity: They keep in mind the teacher’s observations.

Teaching methods: conversation.

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