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
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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
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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
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