ICT-based Educational Application

for Mathematics

- ICTeam -

Comenius Multilateral Project 2013-2015

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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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

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Primary School Mikleuš, Croatia

LESSON PLAN - Ivana Tržić

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

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TEACHING DEVICE: students book, workbook

TEACHING AIDS: blackboard, chalk, projector, computers

LITERATURE:

G. Paić, Ž. Bošnjak, B. Čulina- MATEMATIČKI IZAZOVI 6 – student book and

work book for 6th grade, 1st term, Alfa, Zagreb, 2010.

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. 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)

-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

Ending the lesson (10 minutes)

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.

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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 students 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.

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.

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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.

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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

Right angled triangle- orthocenter at the triangle vertex

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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 2 3 4 5

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

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.

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Goetheschule Wetzlar, Germany

Use of the EIS-Principle in teaching. Karsten Rauber

Middleschool Grade 6 advanced course

Topic: Fractional arithmetic, multiplication of two ordinary fraction numbers

The EIS-Principle

EIS:

Enaktiv: Activity

Ikonisch: Pictures

Symbolisch: Symbols or language

Example: Addition of numbers

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

I:

S: 2 + 1 = 3

The EIS-Principle derives from developmental psychology (Piaget)

Enaktiv: Something concrete operative from childhood (unlocking reality)

Ikonisch: Further development allows simultanious comprehension of chains

of action

Symbolisch: Acquisition oft he mother tongue

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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)

Reversable, sectional, associative

Fractional numbers as operators:

Fractional numbers instruct multiplicative calculations

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

15 pencils are put on the table

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

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

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

Operator 1

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:

=> =>

Die ikonische display in symbolic display:

2

5∗

2

3=

4

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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 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.

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’.

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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 two-digit 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 two-digit number as we study cases when there is a remainder. We will also

revise the units of 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

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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!’

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’.

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LESSON PLAN 2

Prepared by: Veska Krasteva

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 Students’ activity

1. Checking the homework

- Did you have any difficulties doing the

homework? ( if yes, explanation follows)

Students share and comment

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 measure and draw

They explain that the

circumferences have the same

radius.

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.

Students watch and share what

they have seen.

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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

- Students write down the

theme in the notebooks

- Students look at the

numerals in the book, and read

exercise 2/page 32.

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 =

- 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

6. Solving problems from the book

exer. 3/page.32, exer. 5/page 32

Problems are read and explained

7. Checking the knowledge with

individual answer using ‘Envision’.

Problems:

Every student has a mouse and

works alone.

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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:

25 19

XIX CIII

103 XXV

8. Which is the missing number?

XXVI, XXVII, XXVIII, …………., XXX.

1. yes 2. no

3. XXV, LV.

4.

865 – ( 439 + 324) =

= 865 – 763=

=102( CII)

5. VIIc.

6. XVIIIc.

7. 25 19

XIX CIII

103 XXV

8.XXIX

8. Logical problem;

Can we get thirty from the number twenty-nine

by taking away one?

YES

X X I X X X X

9. Summarizing the knowledge

What do we use Roman numerals for?

Note: If time allows problems with sticks can be

included.

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: Orientation into space, Numbers 1 - 4

Prepared by: Tanya Ivanova, Stanka Aleksandrova

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.

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LESSON PLAN: THE NUMBERS; DIRECTIONS

Prepared by: Tanya Ivanova, Stanka Aleksandrova

The numbers. Counting to 10 – Lesson plan

Pre-primary school

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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Pre-primary school

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.

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.

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 ………………………………………….

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.

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LESSON PLAN: THE APPLE

Prepared by: Tanya Ivanova, Stanka Aleksandrova

The apple

LESSON PLAN

Date/Day: Time/ Duration: 20

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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LESSON PLAN: Inside –Outside

Prepared by: Tanya Ivanova, Stanka Aleksandrova

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.

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”.

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 ………………………………………….

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 TURKEY

LESSON PLAN: Collection Process in Natural Numbers

Prepared by: Rahmi Sari

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.

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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 separate this 8 pieces of apples in to two plates?

13) Event:

Tool: Unit cube

Process Steps:

*Create groups with 4 students

*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

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I.I.S.S. “ORESTE DEL PRETE” – SAVA (ITALY)

ACTIVITY 1

Think of a number ...

a. add 12

b. the result by 5

c. subtract 4 times the number in your mind

d. 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. +12 …·5 … 4·… … + 40 what do you

get?

7 7+12 (7+12)·5 (7+12)·5 4·7 [(7+12)·5 4·7] + 40

n. …+12 …·5 … 4·… … + 40 what do you

get?

a a+12 (a+12)·5 (a+12)·5 4·a [(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.

39

Before After

a+12

Now you can’t write this expression

in a a different way, : it is a simple

expression

a+12

(a+12)·5

But here you can apply the

distributive property of the

product.

a·5 + 12·5

And then: 5·a + 60

(a+12)·5 4·a 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?) (5·a − 4·a) + 60

We can now apply the distributive

property to the expression within

parentheses:

(5 − 4)·a + 60

By performing the calculation we

have: 1·a + 60

But 1 is a neutral element for the

product, and then: a + 60

[(a+12)·5

4·a]+40

Using the just found result, let’s

rewrite: a + 60 + 40

And finally, the final result will be: 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 .

40

LESSON PLAN: Arithmetic helps algebra and algebra helps Arithmetic,

Prepared by: Pichierri Cosimo

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

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.

41

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)

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 ulfilling 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.

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

42

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)

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.

Difficulties in terms of cognitive

point of view:

(Increasing in the level of learning)

Simple exercises of calculation and

gratify them their small successes.

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?

43

- 2 22x

- 22 2x x

- 2 22 2x

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.

2 2

4a b a b ab

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.

44

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?

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: Circle

Teacher: Daniela Nela Ionasc

Class VII them

05/20/2015

Learning Unit: Circle

Lesson Title: Problem solving and appliedLemoine's circles

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.

46

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

48

49

Worksheet 1

Complete the cross word below, completing horizontal corresponding definitions to

words.

Vertically achieve your word ...

Horizontal:

1. Segment joining two points on the circle is called....

2. Rope passing through the center of the circle is called ....

3. The portion of the circle between two distinct points on the circle is called ....

4. If two circles are equal when they are called rays circles ....

5. A tip angle in the center of a circle is called ....

6. Segment joining the center circle with a point on the circle is called ....

7. A measure of arc is called ....

50

Worksheet 2

Lemoine'scircles

The first circle of Lemoine

The K Lemoine's point of a triangle ABC go MN, PQ, RS parallel to the sides.

Then the points M, N, P, Q, R, S is a circle called Lemoine's first circle of the triangle

ABC.

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 medians 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.

51

Considering C quadrilateral circumscribed circle PQRN have S ∈ C (RNPS)

writable, M ∈ C (NMSP writeable) then C is the circle sought.

The second circle of Lemoine

The K Lemoine's point of a triangle ABC go MN, PQ, RS antiparallel to the sides

(MN if BC is antiparallel∢𝐴𝑀𝑁 = ∡𝐶). Then the points M, N, P, Q, R, S is a circle

called the second circle Lemoine of the triangle ABC.

Figure 2. The second circle of Lemoine

Demo:

Or Q,S∈BC, N,P∈AC and R,M∈AB whether so MN, SR and PQ are antiparallel to

the sides 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.

52

But because K is the intersection of medians is the middle of three segments

namely

{𝐾𝑄 ≡ 𝐾𝑃 𝐾𝑁 ≡ 𝐾𝑀𝐾𝑅 ≡ 𝐾𝑆

⟹ 𝑄, 𝑆, 𝑁, 𝑃, 𝑅 𝑎𝑛𝑑 𝑀 belong to acircle with centerK

Called the second circle of Lemoine.

Given his circles Lemoine above, we should note the following:

- Antiparallel QP≡NM≡RS because they are in these cond circle diameters of

Lemoine

- Triangles ∆QNR and ∆SPM have sides perpendicular to the sides as the QP, NM

and RS are diameters.

- Triangles ∆QNR ≡ ∆PMS and are similar to ∆CAB. QN≡PM it QNPM is

parallelogram (diagonals are halved) scored, so it rectangle.

m(∢RQN)=m(∢C)=m(∢SPM) the angles of the sides perpendicular.

𝑄𝑆

cos 𝐴=

𝑁𝑃

cos 𝐵=

𝑅𝑀

cos 𝐶

In ∆𝐾𝑄𝑆an isosceles triangle

𝑚(∢𝐾𝑄𝑆) = 𝑚(∢𝐾𝑆𝑄) = 𝑚(∢𝐵𝐴𝐶) ⟹𝑄𝑆

2𝐾𝑄= cos 𝐴 ⟹

𝑄𝑆

cos 𝐴= 2𝐾𝑄

In ∆𝐾𝑁𝑃an isosceles triangle

𝑚(∢𝐾𝑃𝑁) = 𝑚(∢𝐾𝑁𝑃) = 𝑚(∢𝐴𝐵𝐶) ⟹𝑁𝑃

2𝐾𝑁= cos 𝐵 ⟹

𝑁𝑃

cos 𝐵= 2𝐾𝑁

In ∆𝐾𝑅𝑀an isosceles triangle

𝑚(∢𝐾𝑅𝑀) = 𝑚(∢𝐾𝑀𝑅) = 𝑚(∢𝐴𝐶𝐵) ⟹𝑅𝑀

2𝐾𝑅= cos 𝐶 ⟹

𝑅𝑀

cos 𝐶= 2𝐾𝑅

Given

𝐾𝑄 = 𝐾𝑁 = 𝐾𝑅 ⟹𝑄𝑆

cos 𝐴=

𝑁𝑃

cos 𝐵=

𝑅𝑀

cos 𝐶

53

LESSON PLAN: The Perimeter of a polygon (square, rectangle, triangle) -

Teacher: Prof. Dr. Geanina Tudose

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

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 equilateral triangle, square and

rectangle

use these concepts in more complex problems that involve perimeters

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

54

Introduction of new concepts

Presentation on perimeter of rectangle, square, triangle (attached the ppt

presentation)

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 notebooks 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 out the length and width

Problem 3: A 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

55

LESSON PLAN: Houses - Teacher: Maria Oniciuc

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.

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

56

57

58

LESSON PLAN: The reduction formulas to the first quadrant - Teacher: Trișcă

Teodor

Date:25.02.2015

Class:IX-a B; 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

59

Procedures:

1. Organizing

-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. Introducing the new items -30 minutes

I introduce the students the title of the new lesson “Reduction formulae to the first

quadrant”, PPT presentation

4. The reinforcement of the newly introduced items and feed-back-6 minutes

The students solve some applications on the worksheets.

5. 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 5𝜋

4 d)cos

5𝜋

4 e)tg

11𝜋

6 f) ctg 1500

g)sin11𝜋

6

60

LESSON PLAN: The definite integral of a continuous function - Teacher:

Buzduga Nicolai

Date: 13.04.2015

Grade XII-th

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 qualitative mathematical characteristics of a

practical situation and its processing algorithms.

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

situation.

6. Molding 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.

61

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 perseverance, as well as a collectedness ability.

3. Development of an aesthetic and critical spirit, of a strong capacity of appreciating

the rigor, 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.

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

62

63

64

65

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

Using the Leibniz –Newton formula solve the following integrals:

1) 2

0

5dxx ;

2) 3

2

5dxx ;

3) dxx

3

3

7 ;

4) dxx

1

5

7 ;

5) dxxx4

0

;

6)

1

43

1dx

x;

7)

1

83

1dx

x;

8)

1

2

2 1dx

x

x;

9)

1

1

dxe x;

10) 2

1

10 dxx;

11) 2

0

2 dxx

;

12)

4

4

2 25

1dx

x;

13)

3

1

2 3

1dx

x;

14)

0

sin xdx ;

15) 2

0

cos

xdx ;

16)

4

32cos

1dx

x;

17) 2

6

2sin

1

dxx

;

18)

3

2

tgxdx;

19)

22

02 1

1dx

x;

20)

2

32 3

1dx

x

21)

3

224

1dx

x;

22)

4

3

0249

1dx

x;

23)

1

0

343 dxxx ;

24)

e

dxxx

xx1

2

35 234

25)

5

422

9

3

9

6dx

xx

66

LESSON PLAN: Upstream Upper Intermediate - Teacher: Cătălina Melniciuc

Unit PLANET ISSUES

Lesson Vocabulary practice on environmental issues and

Future Forms

Place Theoretical Highschool “Nicolae Iorga” Botoşani

Target group Students from the 11th grade, Humanities

Derived

competences

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

Approach

Involvement

Communication

Cooperation

Methods - exercise, listening comprehension, communicative

approach

Means - laptop, tape, textbook, workbook, cassette player

Time 50 minutes (8.00 – 9.00)

Organisers Teacher, Catalina Melniciuc

Stage Activity Means Role

Participants Organiser

1.Warm-up

Warm up(1’)

Theme and purpose

presentation

Lecture

Listen

Introduces

67

Stage Activity Means Role

Participants Organiser

The teacher introduces the

topic and 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

Frontal

activity

Watch

the

videos

Debate

Watch

Listen

Involve in the

dialogue

Facilitates

Lectures

Moderates

68

Stage Activity Means Role

Participants Organiser

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

- pair activity: ex 4/pad

162

3.

Evaluation

Follow-up (5’)

Final appreciation.

Homework

Lecture

listen

self-

assessment

Lectures

Supervises

69

LESSON PLAN - WORKSHEETS FOR PHYSICS LESSONS - Teacher: 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:

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

Num

be

r o

f

de

term

inatio

ns

M

(kg )

N =

M g

( N

)

m

( kg

)

Ff =

m g

( N

)

M

m

N

F f

m m

1

2

3

4

5

70

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 .

tgNN

FF

BA

fBfA

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

71

Method I:

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

Num

be

r o

f

dis

cs

Fe (

N )

= G

(N

)

l 0

( m

)

( m

)

l

( m

)

l

Fk e

(N/m)

km

( N

/m

)

k

(N/

m)

k

m

(N /

m)

k =

km

km

Method II:

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

Number of

discs Fe ( N ) = G ( N )

l0

( m )

l

( m )

l

( m )

72

7. The data is transferred onto the graph paper, and the graph is drawn Fe=

f(l):

Using a protractor determine the angle α, then with GeoGebra, determine the

tangent of the angle, which is the spring constant.

Conclusion :

....................................................

73

LESSON PLAN: Determining elastic constant of a spring Study of spring

grouping, - Teacher: Bucătaru Magda Mihaiela

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)

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?

74

Specific competences (derived from the project model): Including other particular

cases in communicating results. Impact of new knowledge (values and limits) and

valorising results;

Teacher’s role Learning tasks

Students (individually, in groups, with

teacher)

Show students a cognitive

organizer (introductory

lecture):reminds them notions 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.

Follow simulation and refresh knowledge

The constant of spring elasticity can be

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).

75

Teacher’s role Learning tasks

Students (individually, in groups, with

teacher)

- To evaluate measure

errors of the equivalent elastic

constants

Guides students in obtaining

relations for ks, respectively kp.

Approach theoretically series/parallel

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);

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.

76

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/

77

Annex 1

Determining elastic constant of a spring. Study of spring grouping

Materials at disposition

- Support for suspending springs

- 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

�⃗� + 𝐹𝑒⃗⃗⃗⃗ = 0

𝑚𝑔 − 𝑘 ∙ ∆𝑙 = 0

𝑘 =𝑚𝑔

∆𝑙 (𝑁 𝑚⁄ )

78

Data are written in the following table:

m

(g)

𝑙 0

(cm

)

𝑙

(cm

)

∆𝑙

(cm

)

k

(N/m

)

𝑘

(N/m

)

∆𝑘

(N/m

)

𝜎

(N/m

)

𝜀=

𝜎 𝑘 (

%)

𝑘=

𝑘±

𝜀

(N/m

)

15

25

35

45

55

65

75

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 ∆𝑙(m) and the

elongation constant is determined from the graphic slope. The result is compared to

the one obtained from calculation.

79

Annex2

Experimental results

Determining elastic k1

∆𝑙

(cm)

m

(g)

k1

(N/m)

�̅�

(N/m)

∆𝑘

(N/m)

𝜎

(N/m) 𝜀 =

𝜎

�̅� (%)

𝑘 = �̅� ± 𝜀

(N/m)

0,7 15 21,43

21,37

0,00

0,313 1,5% 21,37±1,5%

1,1 25 22,73 1,84

1,5 35 23,33 3,86

2,1 45 21,43 0,00

2,6 55 21,15 0,05

3,1 65 20,97 0,16

3,6 75 20,83 0,29

4,2 85 20,24 1,28

4,7 95 20,21 1,34

K1= 20,7N/m

0

20

40

60

80

100

120

0 0,5 1 1,5 2 2,5 3 3,5 4 4,5 5

K1

80

Determining elastic constant k2

∆𝑙

(cm)

m

(g)

k2

(N/m)

�̅�

(N/m)

∆𝑘

(N/m)

𝜎

(N/m) 𝜀 =

𝜎

�̅� (%)

𝑘 = �̅� ± 𝜀

(N/m)

0,85 15 17,65

17,28

0,37

0,085 0,5% 17,28±0,5%

1,4 25 17,86 0,58

2,05 35 17,07 -0,21

2,6 45 17,31 0,03

3,2 55 17,19 -0,09

3,8 65 17,11 -0,17

4,4 75 17,05 -0,23

4,95 85 17,17 -0,11

5,55 95 17,12 -0,16

K2 = 17,1N/m

0

10

20

30

40

50

60

70

80

90

100

0 1 2 3 4 5 6

K2

81

Determining elastic constant grouped in parallel kp

∆𝑙

(cm)

m

(g)

k1

(N/m)

�̅�

(N/m)

∆𝑘

(N/m)

𝜎

(N/m) 𝜀 =

𝜎

�̅� (%)

𝑘 = �̅� ± 𝜀

(N/m)

0,4 15 37,50

37,98

-0,48

0,143 0,4% 37,98±0,4%

0,65 25 38,46 0,48

0,9 35 38,89 0,91

1,2 45 37,50 -0,48

1,45 55 37,93 -0,05

1,7 65 38,24 0,26

2 75 37,50 -0,48

2,25 85 37,78 -0,20

2,5 95 38,00 0,02

Kp = 37,9 N/m

0

10

20

30

40

50

60

70

80

90

100

0 0,5 1 1,5 2 2,5 3

K paralel

82

Determining elastic constant grouped in series ks

∆𝑙

(cm)

m

(g)

k1

(N/m)

�̅�

(N/m)

∆𝑘

(N/m)

𝜎

(N/m)

𝜀 =𝜎

�̅�

(%)

𝑘 = �̅� ± 𝜀

(N/m)

1,55 15 9,68

9,82

-0,15

0,066 0,7% 9,82±0,7%

2,6 25 9,62 -0,21

3,7 35 9,46 -0,36

4,6 45 9,78 -0,04

5,55 55 9,91 0,09

6,6 65 9,85 0,02

7,4 75 10,14 0,31

8,6 85 9,88 0,06

9,4 95 10,11 0,28

Ks = 9,9 N/m

0

10

20

30

40

50

60

70

80

90

100

0 1 2 3 4 5 6 7 8 9 10

K serie

83

k1 = 20,7N/n

k2 = 17,1N/m

kp = 37,9 N/m

ks = 9,9N/m

0

20

40

60

80

100

120

0 1 2 3 4 5 6 7 8 9 10

84

LESSON PLAN: Determining slip friction coefficient using mechanic energy

variation of a body/object theorem, - Teacher: Bucătaru Marius Daniel

School: C. N. „A. T. Laurian”, Botoşani

Subject: Physics

Grade: a IX-a

Learning unit: Mechanic energy. Theorem of mechanic energy

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 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

85

Learning unit

sequences Specific competences

4. Applying –

Transfer

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

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.

Give examples from personal

experience, of objects that have kinetic

and potential energy simultaneously.

Open and use simulations.

86

Teacher’s role Learning tasks

Students (individually in groups, with

the teacher)

https://phet.colorado.edu/ro/simulation/en

ergy-skate-park

https://phet.colorado.edu/ro/simulation/ra

mp-forces-and-motion

Guide students’ thinking to deduce

mathematical expression of the mechanic

energy variation theorem.

Deduce the mechanic energy variation

theorem by applying theorem of kinetic

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 theorem of mechanic energy variation

in an isolated physic system with the result

of deducing mechanic energy

conservation law.

Deduce energy conservation law for an

isolated physic system. .

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.

87

Teacher’s role Learning tasks

Students (individually in groups, with

the teacher)

Extends students’ activity (with

homework), asking them to make a paper

on „Determining the coefficient of slip

friction using the theorem of mechanic

energy variation.

Do the homework, give work

hypotheses, plan the experiment in

team and choose the necessary

materials for the experiment.

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

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

88

Sequence II. Exploration – Experiencing

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

Presents theoretical part

Evaluates the proposed hypotheses,

material resources, time, group tasks,

etc.

Asks students to do the experiment 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 observations of

the exploration stage, to analyze the values table.

Ask students to interpret the results and come to

conclusions

Analyze experimental data

and apply calculus relations

to calculate the two friction

coefficients.

Sequence IV Application – Transfer

Specific competences: 4. Testing conclusions and predictions 5. Impact of the new

knowledge and valorizing the results.

89

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

investigations regarding cognitive, esthetic,

communication, social competences

Present their results

(Annex 2)

Final evaluation specifying instruments (written test

or oral assessment). Projects, portfolio, etc.

Communicate final

conclusions

Expand activity outside the classroom proposing

solving problems.

Make homework

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;

(4) Gherbanovschi, C ; Gherbanovschi, N. Fizica, manual pentru clasa a IX-a, Ed.

Niculescu, Bucureşti 1999;

(5) Păcurari, O. (coord.), Învăţarea activă, Ghid pentru formatori, MEC-CNPP, 2001;

(6) Leahu, I., Didactica fizicii. Modele de proiectare curriculară, M.E.C.T./ P.I.R., Buc.

2006;

(7) Păcurari, O. (coord.), Învăţarea activă, Ghid pentru formatori, MEC-CNPP, 2001;

(8) Sarivan, L., coord., Predarea interactivă centrată pe elev, M.E.C.T./ P.I.R.,

Bucureşti 2005;

(9) Ursu, S ş.a., Lucrări practice de mecanică pentru clasa a IX-a, Ed. All, Bucureşti

1995.

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

90

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:

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 ∆𝐸𝐶𝐴→𝐵= 𝐿𝐺𝐴→𝐵

+ 𝐿𝐹𝑓𝐴→𝐵 ⟹

𝑚𝑣2

2= −𝑚𝑔ℎ − 𝜇1𝑚𝑔𝑙 cos 𝛼

∆𝐸𝐶𝐵→𝑆= 𝐿𝐺𝐵→𝑆

+ 𝐿𝐹𝑓𝐵→𝑆 ⟹ −

𝑚𝑣2

2= −𝜇2𝑚𝑔𝑠

We get:

ℎ = 𝜇1𝑑 + 𝜇2𝑠

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

{ℎ = 𝜇1𝑑 + 𝜇2𝑠

ℎ′ = 𝜇1𝑑′ + 𝜇2𝑠′ ⟹ {

𝜇1 =ℎ𝑠′−𝑠ℎ′

𝑑𝑠′−𝑠𝑑′

𝜇2 =ℎ𝑑′−𝑑ℎ′

𝑠𝑑′−𝑑𝑠′

91

For experimental determination we fill in the table:

( s is determined as an average of, at least, five measurements

h

(mm

)

l

(mm

)

𝑑=

√𝑙2

−ℎ

2

(mm

)

s (

mm

)

ds'-sd

’ (m

m2)

hs'-sh

’

(mm

2)

dh

'-h

d’

(mm

2)

𝜇1

𝜇2

Nr.

220 543 1

230 543 2

240 543 3

250 543 4

260 544 5

270 545 6

280 546 7

290 547 8

300 548 9

310 549 10

320 550

Error calculation:

𝜎 = √(∆𝜇)2

𝑁(𝑁 − 1)

𝜇1 𝜇1̅̅ ̅ ∆𝜇1 𝜎 𝜀 =𝜎

𝜇1̅̅ ̅ 𝜇1

= 𝜇1̅̅ ̅ ± 𝜀

92

Annex 2

Experimental results

h

(mm

)

l

(mm

) 𝑑

= √𝑙2 − ℎ2

(mm) s (

mm

)

ds'-sd

’ (m

m2)

hs'-sh

’

(mm

2)

dh

'-h

d’

(mm

2)

𝜇1

𝜇2

220 543 496,44 42 11609,27 4640 5966,06 0,400 0,514

230 543 491,88 65 11133,49 4410 6023,06 0,396 0,541

240 543 487,08 87 11155,7 4410 6084,31 0,395 0,545

250 543 482,03 109 11060,27 4410 5865,45 0,399 0,530

260 544 477,85 131 11092,5 4410 5929,40 0,398 0,535

270 545 473,42 153 11131,2 4410 5997,70 0,396 0,539

280 546 468,74 175 11645,54 4690 6070,67 0,403 0,521

290 547 463,80 198 12162,61 4980 6148,68 0,409 0,506

300 548 458,59 222 12224,39 4980 6232,17 0,407 0,510

310 549 453,10 246 12748,47 5290 6321,62 0,415 0,496

320 550 447,33 271

𝜇1 𝜇1̅̅ ̅ ∆𝜇1 𝜎 𝜀 =𝜎

𝜇1̅̅ ̅ 𝜇1 = 𝜇1̅̅ ̅ ± 𝜀

0,400

0,402

0,0021

0,0021

0,53%

0,402±0,53%

0,396 0,0057

0,395 0,0065

0,399 0,0031

0,398 0,0042

0,396 0,0056

0,403 -0,0009

0,409 -0,0076

0,407 -0,0056

0,415 -0,0131

𝜇2 𝜇2̅̅ ̅ ∆𝜇2 𝜎 𝜀 =𝜎

𝜇2̅̅ ̅ 𝜇2 = 𝜇2̅̅ ̅ ± 𝜀

0,514

0,524

0,0097

0,0053

1,02%

0,524±1%

0,541 -0,0173

0,545 -0,0218

0,530 -0,0067

0,535 -0,0109

0,539 -0,0152

0,521 0,0024

0,506 0,0181

0,510 0,0138

0,496 0,0278

93

Results obtained by graphic means

µ2 = 0,40

µ1 = 0,52

4000

4500

5000

5500

6000

6500

7000

10800 11000 11200 11400 11600 11800 12000 12200 12400 12600 12800 13000

94

LESSON PLAN: ”A Healthy Life Style”, Teacher: Olivia Gornea, Roxana Vatavu

”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

95

Didactic aids: flip chart, ball, marker, videoprojector,work sheets, glue,

Organization: individual, group, frontal

T

ime: 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, Leonard,Un stil de viaţăpentrumileniultrei,

EdituraViaţăşisănătate, Bucureşti, 1999.

The educationalsite: www.didactic.ro

ACTIVITY PLAN

96

97

98

ANNEX NO.1

Group ”__________________”

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?

99

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.

100

LESSON PLAN: Millikan’s Experiment, Teacher: Irina Zamfirescu

Subject: Physics

Form: the 10th

Lesson Topic: Millikan’s Experiment

Lesson Type: Mixed (teaching/ reinforcing/ revision/ assessment)

Viewed objectives/ skills for students:

O1. to get connected at AEL system (Educational Assistant in High schools);

O2. to participate at the teaching of a lesson using AEL;

O3. to solve multiple-choice tests launched through AEL;

O4. to define physical measurements specific to electrostatics (electrical charge,

Coulombiane interaction force, intensity of the electric field, potential energy of the

field- probation charge system, the potential of the field in a point, difference of

potential between two points of the field, electric capacity of an isolated conductor,

capacity of a condenser);

O5. to enumerate the parts of the Millikan device, mentioning the role of each of

them;

O6. to write the fundamental principle for the oil drop which is moving between the

armatures of the plain condenser;

O7. to formulate the conclusion of Millikan’s experiment;

O8. to solve problems containing data specific to Millikan’s experiment.

Units of Contents:

C1. The presentation of Millikan’s experiment using the computer; reaching

conclusions;

C2. Reinforcing the notions specific to the taught lesson;

C3. Revising some notions from the “Electrostatics” chapter;

C4. Assessing students’ knowledge of electrostatics;

C5. Homework assignment.

Didactic Strategies

- teaching methods: lecturing, heuristic conversation, demonstration, explanation,

problem solving, exercises.

- educational aids: computer network, AEL system, chalk, blackboard.

Procedure:

101

102

103

104

105

LESSON PLAN: Graphic design applications for Second degree equation

graphics, Teacher: Cardas Cerasela Daniela

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

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

106

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:

107

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

{

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;

108

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);

}

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++;

109

timer1.Start();

AddFunctionToLegend(f, color[col]);

}

else

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;

}

void CheckImput()

{

OK = true;

try

{ a= Convert.ToInt32(textBox1.Text);

b = Convert.ToInt32(textBox2.Text);

c = Convert.ToInt32(textBox3.Text);

}

catch

110

{

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++;

} }}

Moments of the application

111

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.

112

The virtual experiment Teacher: Daniela Biolan, Alina Biolan

The schools potential of accessing the internet, had eased learning in the virtual

environment mode.

There are situations when it’s more accessible to use a virtual experiment than a real

one. Virtual labs can be accessed via a portal or a local server and grant students to

run different experiments, just like in a classic laboratory, but in a safe, secure

environment, in order to observe, study, prove, control, and measure the results of a

natural phenomena.

Since the experiments are simulated on a computer, they can be repeated until are

fully understood. Digital resources from virtual laboratories are attractive and user

friendly, converting the class into an unique and enjoyable activity.

I used the platform http://escoala.edu.ro/labs/#, which arranges physics, chemistry

and biology experiments for high school level. Some of them are accessible to the

participants of The Excellency Center for middle school students. As a consequence,

I chose from the physics library, the experiment: „Determining the specific heat of an

object”.

The platform is accessible designed to students through the fact that it gives

specific theory

information of the

experiment, a

glossary of

definitions, the

periodic table of

elements, all

presented in

remarkable

graphics. The

task is expressed in

a simple form: „ Lay down on the work table the materials you need, to determine

the specific heat of a metallic object”.

113

Students are

managing they

own experiment,

and can even set

some of the

parameters. In

the situation

where the

materials are not

used properly the

experiment can’t

move further. The experiment is guided with audio and written comments which can

help the students when needed.

For this specific

measurement,

one student

concluded the

value for the

cx=727,82

J/KgK. This

equivalent is

false so this

message

appeared on

the screen:

„The value is wrong. Check all the data you filled and try again.”, so the student has

an immediate reflection of the error.

Also, if the answer is correct on every stage, they receive positive feed-back,

instantly: „The table is correctly completed” and „ Congratulations, you finalized the

experiment!”

114

The usage of the virtual experiments in teaching physics, allows studying the reality

in an ideal way by removing secondary aspects which in the real procedure, or in the

laboratory, the phenomena can be camouflaged or distorted.

The virtual experiment facilitates the clarification of physics laws through

completing the same experiment in all of it’s complexity. The measurements and the

calculus gives this application a highly practical character and offers a finality in

studying the phenomena or process. Making measurements in the virtual experiment

eliminates the boredom that can occur when simple simulations, much more

approximate, of the physics phenomena, are made on the computer screen.

Furthermore, a quantitative virtual experiment can be used by students at analyzing

the proper problem solving in a certain chapter.

Wisely using computer software in teaching is a modern academic activity, in

which the teacher’s monologue is replaced with useful and interesting debates in the

classroom and also with excellent individual work skills of obtaining and training their

own knowledge. This kind of applications are acknowledged as an alternative to real

experiment, but also a procedure for improving student understanding of abstract

concepts. It can raise student’s learning motivation and their interest to involve in a

scientific path. Obviously, the attractiveness of the lessons is enhanced. The best

choice of the teacher would be combining the real experiment with the virtual one.

Resources

Florin Ovidiu Călțun, Capitole de didactica fizicii, Editura Universității

„Alexandru Ioan Cuza”, Iași – 2006

Palicica Maria, Gavrilă Codruță, Ion Laurenția, Pedagogie,

Editura Mirton, Timișoara, 2007

115

Table of Contents

PRIMARY SCHOOL MIKLEUŠ, CROATIA ............................................................. 3

LESSON PLAN - Ivana Tržić .................................................................................. 3

GOETHESCHULE WETZLAR, GERMANY ........................................................... 10

Use of the EIS-Principle in teaching. Karsten Rauber ...................................... 10

L.KARAVELOV PRIMARY SCHOOL BURGAS, BULGARIA ............................... 17

LESSON PLAN 1 - Gergana Gineva .................................................................... 17

LESSON PLAN 2 Veska Krasteva ...................................................................... 20

ЧАСТНА ЦЕЛОДНЕВНА ДЕТСКА ГРАДИНА "ЦВЕТНИ ПЕСЪЧИНКИ ",

VARNA, BULGARIA .............................................................................................. 23

LESSON PLAN: Orientation into space, Numbers 1 - 4 - Tanya Ivanova, Stanka

Aleksandrova ........................................................................................................ 23

LESSON PLAN: THE NUMBERS; DIRECTIONS - Tanya Ivanova, Stanka

Aleksandrova ........................................................................................................ 24

LESSON PLAN: THE APPLE - Tanya Ivanova, Stanka Aleksandrova .............. 29

LESSON PLAN: Inside –Outside - Tanya Ivanova, Stanka Aleksandrova ....... 32

SILIFKE CUMHURIYET PRIMARY SCHOOL TURKEY ....................................... 36

LESSON PLAN: Collection Process in Natural Numbers, Rahmi Sari ............ 36

I.I.S.S. “ORESTE DEL PRETE” – SAVA (ITALY) ................................................. 38

LESSON PLAN: Arithmetic helps algebra and algebra helps Arithmetic,

Pichierri Cosimo ................................................................................................... 40

116

CENTRUL DE EXCELENȚĂ A TINERILOR CAPABILI DE PERFORMANȚĂ,

BOTOȘANI, ROMÂNIA .......................................................................................... 45

LESSON PLAN: Circle - Teacher: Daniela Nela Ionasc...................................... 45

LESSON PLAN: The Perimeter of a polygon (square, rectangle, triangle) -

Teacher: Prof. Dr. Geanina Tudose ..................................................................... 53

LESSON PLAN: Houses - Teacher: Maria Oniciuc ............................................. 55

LESSON PLAN: The reduction formulas to the first quadrant - Teacher: Trișcă

Teodor .................................................................................................................... 58

LESSON PLAN: The definite integral of a continuous function - Teacher:

Buzduga Nicolai .................................................................................................... 60

LESSON PLAN: Upstream Upper Intermediate - Teacher: Cătălina Melniciuc 66

WORKSHEETS FOR PHYSICS LESSONS - Teacher: Adriana Vatavu .............. 69

LESSON PLAN: Determining elastic constant of a spring Study of spring

grouping, - Teacher: Bucătaru Magda Mihaiela ................................................. 73

LESSON PLAN: Determining slip friction coefficient using mechanic energy

variation of a body/object theorem, - Teacher: Bucătaru Marius Daniel .......... 84

LESSON PLAN: ”A Healthy Life Style”, Teacher: Olivia Gornea, Roxana Vatavu

................................................................................................................................ 94

LESSON PLAN: Millikan’s Experiment, Teacher: Irina Zamfirescu ................ 100

LESSON PLAN: Graphic design applications for Second degree equation

graphics, Teacher: Cardas Cerasela Daniela ................................................... 105

The virtual experiment Teacher: Daniela Biolan, Alina Biolan ....................... 112

117

Editorial staff:

Adriana Vatavu – coordinator // Centrul de Excelenţă pentru Tinerii Capabili de

Performanţă Botoșani ROMÂNIA

Mighiu Rodica // Inspectoratul Școlar Județean Botoșani, România

Meike Stamer // Goetheschule WETZLAR, GERMANY

Gaetana Bernardetta Musardo // Istituto tecnico industriale-liceo scientifico delle

scienze applicate "Oreste Del Prete", SAVA (TA), ITALY

Slaven Mađarić// OSNOVNA ŠKOLA MIKLEUŠ, CROATIA

Ivaylo Binev// Основно училище "Любен Каравелов", Burgas, BULGARIA

Rahmi Sari, Silifke Cumhuriyet Ilkokulu, MERSİN, TURKEY

Tanya Ivanova, Stanka Aleksandrova Частна целодневна детска градина

"Цветни песъчинки "// Частна целодневна детска градина "Цветни песъчинки ",

Varna, BULGARIA

Magda Mihaiela Bucătaru // Centrul de Excelenţă pentru Tinerii Capabili de

Performanţă Botoșani, ROMÂNIA

Marius Daniel Bucătaru // Centrul de Excelenţă pentru Tinerii Capabili de

Performanţă Botoșani, ROMÂNIA

Irina Zamfirescu // Centrul de Excelenţă pentru Tinerii Capabili de Performanţă Iași,

ROMÂNIA

118