Erasmus+ arteducation.eu Upper secondary RO2 Shapes ict

1. Date: the 9th of March 2016
School: National Military Highschool " Dimitrie Cantemir" Breaza
Teacher: Lorena Ezaru
Subject: Mathematics
Theme: Shapes and Volumes
Title: The volume of rotational bodies
Type of lesson: Acquirement of knowledge
Time: 50 minutes
Competences:
-identifying and naming 2D shapes
-identifying shapes in familiar contexts
-exploring the environment to discover familiar shapes
-describing things according to their shapes
-using simple shapes in practical problem solving
-using different visual elements to create meaningful compositions
Aims:
1. The students will be familiarized with the construction of bodies by rotating a funct
ion round an axis.
2. The students will calculate the volume with the help of the aplication called " Calcu
lus" on smartphone.
Methods and procedures:
- heuristic conversation
-explanations
-demonstration
-exercise
-individual work
Teaching aids:
-flipchart
-calculator
-smartphone app
-projector

2. Forms of organisation: frontal, in groups
Arrangements: The optimal scenery necessary for the class is being ensured
Time: 1 min
Catching the attention:The students are asked if they love mathematics and if they always se
e the connection between mathematics and real life. Time: 1min
Refreshing knowledges: known geometrycal bodies such as the cone, the cylinder, the spher
e are being presented in ppt format. Time: 10 min
Announcing the aim and the objectives of the lesson: In today's lesson we will learn to const
ruct bodies by rotating different functions around the Ox axis, and then, with the help of the a
plication "Calculus" we will calculate the volume of the resulted body. Time: 1 min
Prezentation of the new content: With the help of the programme Geogebrahttp://www.geog
ebra.org/m/40798 , we will construct bodies whose volume we want to find.
We will choose the following functions:
f1(x)=2sin((x - 0.66) / 2) + 1.16
f2(x)=tg(x)
f3(x)=ln(x + 2) / ln(2) - 2^x + 2
f4(x)=sin(x)-cos(x)
f5(x)=-2x/(1+x^2)^2+(2(1+x^4)-8x^4)/(1+x^4)^2
f6(x)=2^(2*x-1)-x^2
f7(x)=asin(x^2-1)

3. f8(x)=x³ + x²
f9(x)=sqrt(x² + 6)
f10(x)=sqrt(x² + sin(x) - 6)
The students, in pairs, will discover step by step how to design the forms and what kin
d of functions are necessaries.
In the aplication Calculus the discovered functions are being introduced, to calculate t
he volume of the rotational bodies. Time: 30 min
Obtaining performance: The students are challenged to discover what kind of functions gene
rate ,by rotating ,a shape similar to a cup of champaign and a function which designs on the s
creen a heart.
f(x)=(sqrt(cos(x))*cos(400*x)+sqrt(abs(x))-0.4)*(4-x*x)^0.1
Time: 5 min
Feed back: The new notions are orally revised. The teacher is making the appreciations regar
ding the participation of students at the lesson and is marking the active students.
Time: 2 min