A twenty hour module on Maths for first year students at Liceo Scientifico

SARDEGNA SPEAKS ENGLISH LINEA DI INTERVENTO 1

realizzaziOnE DI Progetti per l’apprendimento dell’inglese ATTRAVERSO LA METODOLOGIA CLIL

Liceo Scientifico “Europa Unita” – Porto Torres

CLIL Maths Module 1 TEST Cloze

Fill the blanks inserting ONE correct word: Binomial squared The square of a binomial is a ____________ in which there are no ____________

terms. It is composed of the ____________ of the first

monomial plus the ____________ product of the ____________ monomial and the second one ____________ the second monomial raised to the ____________ power. Therefore the ____________ of how to square a ____________ is the following: “ (a + b)2 = a2 + 2ab + b2 “ , in other words the result of a ____________ binomial is a trinomial.

A cura dei Proff. Luigi Cennamo e Maria Grazia Pichereddu © 2010

SARDEGNA SPEAKS ENGLISH LINEA DI INTERVENTO 1

realizzaziOnE DI Progetti per l’apprendimento dell’inglese ATTRAVERSO LA METODOLOGIA CLIL

Liceo Scientifico “Europa Unita” – Porto Torres

CLIL Maths Module 1 TEST Multiple choice Choose the correct answer to the following questions : What does this expression represent (a+b) (a-b)?

Product of sum and difference of two terms The sum of two monomials A squared binomial A trinomial Which of the four is the formula of a squared binomial? (a+b2)2 a2 - 2ab + b2 a2 - b 2 a2 + b 2 Which of the four is the solution to (a+b) (a-b)? a2 - 2ab + b2 a2 - b 2 a2 + b 2 a2 + b2+ab Which of these is the area of a square? (a+b)2 a+ b2 ab a2 + b 2 Which of these is the area of a rectangle? a2 + 2ab + b2 (a+2b)2 a2 - b 2 a(a+3)

A cura dei Proff. Luigi Cennamo e Maria Grazia Pichereddu © 2010

SARDEGNA SPEAKS ENGLISH LINEA DI INTERVENTO 1

realizzaziOnE DI Progetti per l’apprendimento dell’inglese ATTRAVERSO LA METODOLOGIA CLIL

Liceo Scientifico “Europa Unita” – Porto Torres

CLIL Maths Module 1 TEST

Matching exercize Match the words in the left column to their correct definition: (put the corresponding letter in the right column next to the definition)

A.

Binomial

The value of a surface

B.

Algebra

The set of points of a plane within a closed line

C.

Power

A measure or number repeated twice

D.

Area

Algebraic sum of two monomials

E.

Trinomial

Geometrical figure whose 4 sides have got the same length

F.

Rectangle

Algebraic expression in which there are no additions or subtractions

G.

Square

Algebraic sum of three monomials

H.

Double

You can raise a number to it

I.

Monomial

Geometrical figure whose area is “ab”

J.

Closed Surface

An area of Maths where numbers are represented by letters

A cura dei Proff. Luigi Cennamo e Maria Grazia Pichereddu © 2010

SARDEGNA SPEAKS ENGLISH LINEA DI INTERVENTO 1

realizzaziOnE DI Progetti per l’apprendimento dell’inglese ATTRAVERSO LA METODOLOGIA CLIL

Liceo Scientifico “Europa Unita” – Porto Torres

CLIL Maths Module 1 TEST - Solution Cloze

Fill the blanks inserting ONE correct word: Binomial squared The square of a binomial is a polynomial in which there are no like terms. It is composed of the square of the first monomial plus the double product of the first monomial and the second one plus the second monomial raised to the second power. Therefore the formula of how to square a binomial is the following: “ (a + b)2 = a2 + 2ab + b2 “ , in other words the result of squared binomial is a trinomial.

A cura dei Proff. Luigi Cennamo e Maria Grazia Pichereddu © 2010

a

SARDEGNA SPEAKS ENGLISH LINEA DI INTERVENTO 1

realizzaziOnE DI Progetti per l’apprendimento dell’inglese ATTRAVERSO LA METODOLOGIA CLIL

Liceo Scientifico “Europa Unita” – Porto Torres

CLIL Maths Module 1 TEST - Solution Multiple choice Choose the correct answer to the following questions : What does this expression represent (a+b) (a-b)?

Product of sum and difference of two terms The sum of two monomials A squared binomial A trinomial Which of the four is the formula of a squared binomial? (a+b2)2 a2 - 2ab + b2 a2 - b 2 a2 + b 2 Which of the four is the solution to (a+b) (a-b)? a2 - 2ab + b2 a2 - b 2 a2 + b 2 a2 + b2+ab Which of these is the area of a square? (a+b)2 a+ b2 ab a2 + b 2 Which of these is the area of a rectangle? a2 + 2ab + b2 (a+2b)2 a2 - b 2 a(a+3)

A cura dei Proff. Luigi Cennamo e Maria Grazia Pichereddu © 2010

SARDEGNA SPEAKS ENGLISH LINEA DI INTERVENTO 1

realizzaziOnE DI Progetti per l’apprendimento dell’inglese ATTRAVERSO LA METODOLOGIA CLIL

Liceo Scientifico “Europa Unita” – Porto Torres

CLIL Maths Module 1 TEST

Matching exercize Match the words in the left column to their correct definition (put the corresponding letter in the right column next to the definition)

A.

Binomial

Algebraic sum of two monomials

B.

Algebra

An area of Maths where numbers are represented by letters

C.

Power

You can raise a number to it

D.

Area

The value of a surface

E.

Trinomial

Algebraic sum of three monomials

F.

Rectangle

Geometrical figure whose area is “ab”

G.

Square

Geometrical figure whose 4 sides have got the same length

H.

Double

A measure or number repeated twice

I.

Monomial

Algebraic expression in which there are no additions or subtractions

J.

Closed Surface

The set of points of a plane within a closed line

A cura dei Proff. Luigi Cennamo e Maria Grazia Pichereddu © 2010

SARDEGNA SPEAKS ENGLISH LINEA DI INTERVENTO 1

REALIZZAZIONE DI PROGETTI PER L’APPRENDIMENTO DELL’INGLESE ATTRAVERSO LA METODOLOGIA CLIL

Liceo Scientifico “Europa Unita” – Porto Torres

TEST (Module 1) Fill the blanks Complete the following Special Products:

1) x2 −b ⋅ x2 +b =..................−b2     2) 2+ 5 xy2  ⋅ −2+ 5 xy2  = 25....................4 9 3 4   3 4  16

   7 7 3 2 3   3) a +8...... ⋅ ......b - a  = − ................64b4 6 6  36      

4) 1-9...... ⋅ ......a5 +1 =1−81a10 2

 2 5 2 5) − + xy  = 25 x2y4..........................4 3 4 16 9     

2 4 1 2 6) 4x y  = ....................− x3y2...................

6  3    

3-

7) (.........+.........)2 =25a2..........................+4b2 2

8) ........-a4b3 =100− .........................a8b6

Cognome:…………………………… Nome:……………………… data:…………………… classe:…..…..

A cura dei Proff. Luigi Cennamo e Maria Grazia Pichereddu © 2010

SARDEGNA SPEAKS ENGLISH LINEA DI INTERVENTO 1

REALIZZAZIONE DI PROGETTI PER L’APPRENDIMENTO DELL’INGLESE ATTRAVERSO LA METODOLOGIA CLIL

Liceo Scientifico “Europa Unita” – Porto Torres

Multiple choice 1) Which of the following is the result of (3 − x )⋅ (x + 3)? x2 − 9

x2 + 9

x2 + x + 9

9 − x2

2) Which of the following produces as a result 36a2 −1 ?

2

(6a −1)

(1-6a) ⋅ (6a+1)

(1+6a) ⋅ (6a-1)

(2a+1) ⋅ (3a-1)

3 2

4 3 5 2

4 5

3) Which of the following is the result of  x2y +  ⋅  x2y −  ?

-

16 9 4 2 + x y 25 4

16 9 4 2 − x y 25 4

9 4 2 16 x y + 4 25

9 4 2 6 2 16 x y - x y+ 4 5 25

4) Which of the following produces as a result b6 − 8 2 7 2 3  3  a + b  ⋅ b − a  7   8 

7 2 7 2 3  3  a − b  ⋅ b + a  8   8 

49 4 a ?

64

 3 7 2 b − a  8 

7 2 7 2 3  3  a + b  ⋅ b − a  8   8 

1 2 5) Which of the following is the result of  x + 2y ? 2  4y2 +

1 2 x 4

1 2 x +2xy+4y2 4

1 2 x + xy+4y2 4

1 4 2 9 2 2 2 2 x y + y − x y ?

9 25 5

6) Which of the following produces as a result 1 2 3  1 2 3   x y + y ⋅  x y − y 3 5  3 5 

2  1 2 3  − x y − y    3 5 

1 2 x +2x2y2 +4y2 4

2 1 2 3  x y − y   3 5 

2 1 2 9 2 x y − y   9 5 

 4 3 5 5 2 7) Which of the following is the result of  a − b  ? 5 6  16 6 4 3 5 25 10 a − ab + b 25 3 36

16 9 4 3 5 25 25 a − ab + b 25 3 36

16 6 25 10 a + a 25 36

16 9 25 25 a + b 25 36

8) Which of the following produces as a result b2 + 8ab + 16a2 ?

2

(8a + b)

2

(-4a − b)

2

(4a − b)

(8a + b)⋅ (2a + b)

Cognome:…………………………… Nome:……………………… data:…………………… classe:…..…..

A cura dei Proff. Luigi Cennamo e Maria Grazia Pichereddu © 2010

SARDEGNA SPEAKS ENGLISH LINEA DI INTERVENTO 1

REALIZZAZIONE DI PROGETTI PER L’APPRENDIMENTO DELL’INGLESE ATTRAVERSO LA METODOLOGIA CLIL

Liceo Scientifico “Europa Unita” – Porto Torres

Solve and Draw Solve the following exercises:

1) (−3x+5y)⋅ (−3x−5y)=_______________________________________________ 2)

6 3 4  6 3 4  a b −1,3⋅ 1,3+ a b  =__________________________________________ 5   5

3)

3 2 2  x+ y =______________________________________________________ 4 9 

4)

2  3 2 2 −2,5a + b  =____________________________________________________  7 

Draw the figure corresponding to the following formulas:

1

a 2 - b2

2

a 2 + b2

3

a2 + ab + b2

4 a2 + 2ab + b2

Cognome:…………………………… Nome:……………………… data:…………………… classe:…..…..

A cura dei Proff. Luigi Cennamo e Maria Grazia Pichereddu © 2010

SARDEGNA SPEAKS ENGLISH LINEA DI INTERVENTO 1

realizzaziOnE DI Progetti per l’apprendimento dell’inglese ATTRAVERSO LA METODOLOGIA CLIL

Liceo Scientifico “Europa Unita” – Porto Torres

CLIL Maths Module 2 TEST Cloze

Fill the blanks inserting ONE correct word: Binomial cube A

binomial

represented

______________ by

a

______________

to

the

third

______________

power

composed

can of

be

eight

which fit together in a binomial pattern,

representing the cube of two ______________, (a + b).

Each side of the cube has the same dimensions and pattern, and represents

the

______________

of

(a

+

b).

The

______________ of a binomial cube is the ______________ term raised to the third power, plus the ______________ product of the first term ______________ and the second term, plus the triple product of the ______________ term squared and the first term, plus the second term raised to the third power.

A cura dei Proff. Luigi Cennamo e Maria Grazia Pichereddu © 2010

SARDEGNA SPEAKS ENGLISH LINEA DI INTERVENTO 1

realizzaziOnE DI Progetti per l’apprendimento dell’inglese ATTRAVERSO LA METODOLOGIA CLIL

Liceo Scientifico “Europa Unita” – Porto Torres

CLIL Maths Module 2 TEST Multiple choice Choose the correct answer to the following questions : How many monomials is the formula of the binomial cube composed of?

3 4 6 8 How many blocks is the cube expressed by a binomial cube formula composed of?

4 6 8 10 How many of the blocks in a binomial cube are cubes?

2 3 4 6 Which of these expressions is the formula of a binomial cube? a3+b3 a3+a2b+ab2+ b3 a3+3a2b+3ab2+ b3 a3-b3 Which of these is the area of one side of a cube?

3a2b 3ab b3 (a+b)2

A cura dei Proff. Luigi Cennamo e Maria Grazia Pichereddu © 2010

SARDEGNA SPEAKS ENGLISH LINEA DI INTERVENTO 1

realizzaziOnE DI Progetti per l’apprendimento dell’inglese ATTRAVERSO LA METODOLOGIA CLIL

Liceo Scientifico “Europa Unita” – Porto Torres

CLIL Maths Module 2 TEST

Matching exercize Match the words in the left column to their correct definition (put the corresponding letter in the right column next to the definition)

A.

Cube

Its formula is composed of four terms

B.

Sides

The product of length, width and height

C.

Block

Repeated three times

D.

Volume

Its formula is composed of six terms

E.

Triple

Repeated model or structure

F.

Pattern

Monomials with the same literal part

G.

The square of a trinomial

A cube has got six

H.

Binomial cube

Squares in a trinomial to the second power

I.

Three

Its volume is a3

J.

Like terms

Every piece composing a binomial cube

A cura dei Proff. Luigi Cennamo e Maria Grazia Pichereddu © 2010

SARDEGNA SPEAKS ENGLISH LINEA DI INTERVENTO 1

realizzaziOnE DI Progetti per l’apprendimento dell’inglese ATTRAVERSO LA METODOLOGIA CLIL

Liceo Scientifico “Europa Unita” – Porto Torres

CLIL Maths Module 2 TEST - Solution Cloze

Fill the blanks inserting ONE correct word: Binomial cube A binomial raised to the third power can be represented by a cube composed of eight blocks which fit together in a binomial pattern, representing the cube of two numbers, (a + b).

Each side of the cube has the same dimensions and pattern, and represents the square of (a + b). The formula of a binomial cube is the first term raised to the third power, plus the triple product of the first term squared and the second term, plus the triple product of the second term squared and the first term, plus the second term raised to the third power.

A cura dei Proff. Luigi Cennamo e Maria Grazia Pichereddu © 2010

SARDEGNA SPEAKS ENGLISH LINEA DI INTERVENTO 1

realizzaziOnE DI Progetti per l’apprendimento dell’inglese ATTRAVERSO LA METODOLOGIA CLIL

Liceo Scientifico “Europa Unita” – Porto Torres

CLIL Maths Module 2 TEST - Solution Multiple choice Choose the correct answer to the following questions : How many monomials is the formula of the binomial cube composed of?

3 4 6 8 How many blocks is the cube expressed by a binomial cube formula composed of?

4 6 8 10 How many of these pieces are cubes?

2 3 4 6 Which of these expressions is the formula of a binomial cube? a3+b3 a3+a2b+ab2+ b3 a3+3a2b+3ab2+ b3 a3-b3 Which of these is the area of one side of a cube?

3a2b 3ab b3 (a+b)2

A cura dei Proff. Luigi Cennamo e Maria Grazia Pichereddu © 2010

SARDEGNA SPEAKS ENGLISH LINEA DI INTERVENTO 1

realizzaziOnE DI Progetti per l’apprendimento dell’inglese ATTRAVERSO LA METODOLOGIA CLIL

Liceo Scientifico “Europa Unita” – Porto Torres

CLIL Maths Module 2 TEST - Solution

Matching exercize Match the words in the left column to their correct definition (put the corresponding letter in the right column next to the definition)

A.

Cube

Its volume is a3

B.

Sides

A cube has got six

C.

Block

Every piece composing a binomial cube

D.

Volume

The product of length, width and height

E.

Triple

Repeated three times

F.

Pattern

Repeated model or structure

G.

The square of a trinomial

Its formula is composed of six terms

H.

Binomial cube

Its formula is composed of four terms

I.

Three

Squares in a trinomial to the second power

J.

Like terms

Monomials with the same literal part

A cura dei Proff. Luigi Cennamo e Maria Grazia Pichereddu © 2010

SARDEGNA SPEAKS ENGLISH LINEA DI INTERVENTO 1

REALIZZAZIONE DI PROGETTI PER L’APPRENDIMENTO DELL’INGLESE ATTRAVERSO LA METODOLOGIA CLIL

Liceo Scientifico “Europa Unita” – Porto Torres

TEST (Module 2) Fill the blanks Complete the following Special Products: 2

1) x-2y-1 = x2 +4y2...................................+4y 2)

 2 3 2 - xy2 + x2y+4y = .............4 x 4y2 +16y2................................    4  3 9

3)

1 3 5 2 2  3 2 3 2 0.6a -1.6b +0.16 = .................................-2a b + a - b   5

9

3

4) a-2 = a3...........+12a............

3

3  27 2 5) 0.6a b- ab =.............-2a5b3..................- a3b3 2  8    

3 1 1 3 6) -0.5x-0.25y = - x3.......................................y 8 64

Cognome:…………………………… Nome:……………………… data:…………………… classe:…..…..

A cura dei Proff. Luigi Cennamo e Maria Grazia Pichereddu © 2010

SARDEGNA SPEAKS ENGLISH LINEA DI INTERVENTO 1

REALIZZAZIONE DI PROGETTI PER L’APPRENDIMENTO DELL’INGLESE ATTRAVERSO LA METODOLOGIA CLIL

Liceo Scientifico “Europa Unita” – Porto Torres

Multiple choice 2

1) Which of the following is the result of (a − 2b + 3) ? a2 − 4b2 + 9 − 4ab + 3a − 6b

a2 + 4b2 + 9 − 4ab + 6a −12b

a2 + 4b2 + 9 − 2ab + 3a − 6b

a2 + 4b2 + 9

1 3

2) Which of the following produces as a result a9 − a6b2 + a3b4 −  2 1 3 3 a − b   3 

 3 1 2 3 −a − b   3 

 2 1 3 2 a − b   3 

1 6 b ?

27

 3 1 2 3 a − b   3 

3  1  3) Which of the following is the result of 2a+ b ?  2 

a2 − ab +

1 2 b 4

1 8a3 + b3 8

3 1 8a3 + 6a2b + ab2 + b3 2 8

3 1 8a3 − a2b + 6ab2 − b3 2 8

4) Which of the following produces as a result 25x 4 +  2 3 3 5 2 y − z 5x −  10 3 

9 25 2 50 2 y6 + z − 3x2 y 3 − x z + y 3z ?

100 9 3

 2 3 3 5 2 y + z 5x −  10 3 

2  3 3 5  2 -5x − y + z    10 3 

 2 3 3 5 2 y + z 5x +  10 3 

 2 1 2 2x − x −1 5) Which of the following is the result of   ?   2 4x4 +

1 2 1 x + 1 − x3 − 2x2 + x 4 2

4x4 +

1 2 x +1 4

4x4 +

1 2 1 x + 1 − x3 − 4x2 + x 4 2

4x4 − 2x3 −

15 2 x + x +1 4

6) Which of the following produces as a result 27x 3 − 9x 2 y 2 + xy 4 − 3  1 2 3x − y   3 

3  1 2 3x + y   3 

2  1 2 3x − y   3 

1 6 y ?

27

3  1 2 9x − y   9 

Cognome:…………………………… Nome:……………………… data:…………………… classe:…..…..

A cura dei Proff. Luigi Cennamo e Maria Grazia Pichereddu © 2010

SARDEGNA SPEAKS ENGLISH LINEA DI INTERVENTO 1

REALIZZAZIONE DI PROGETTI PER L’APPRENDIMENTO DELL’INGLESE ATTRAVERSO LA METODOLOGIA CLIL

Liceo Scientifico “Europa Unita” – Porto Torres

Solve Solve the following exercises:

2

1) (2a−b+3c) =____________________________________________________

2)

3 2 2 1  a+ a2b− ab =_____________________________________________ 2  2 3 2

3) 0.5x +0.3y −6 =______________________________________

(

2

3

)

4)

2 5  8  x2 −4x−  =__________________________________________________ 5 2

5)

3 1  2  x3 − y2 =____________________________________________________ 3  4

6)

 3 0.75a+0.6b = ___________________________________________  

7) 1.25x y −0.4xy

(

2

2

3

)=

____________________________________

3

3 2 8) (−a −b ) =_______________________________________________________ Cognome:…………………………… Nome:……………………… data:…………………… classe:…..…..

A cura dei Proff. Luigi Cennamo e Maria Grazia Pichereddu © 2010

SARDEGNA SPEAKS ENGLISH LINEA DI INTERVENTO 1

REALIZZAZIONE DI PROGETTI PER L’APPRENDIMENTO DELL’INGLESE ATTRAVERSO LA METODOLOGIA CLIL

Liceo Scientifico “Europa Unita” – Porto Torres

FINAL TEST Fill the blanks Complete the following Special Products:     1) 2+ 5 xy2  ⋅ −2+ 5 xy2  = ....................4 3 4   3 4  16

2) 1-8...... ⋅ ......b5 +1 =1−64b10 2  3) −0.6+1.25xy2  = 25 x2y4..........................4   16 9   

4) 4x 0.16y 5)

3-

2

2  

4 =....................− x3y2...................

3

 2 3 2 - xy2 + x2y+4y = .............4 x 4y2 +16y2................................    4  3 9

3 1 1 3 6) -0.5x-0.25y = - x3.......................................y 8 64 3

 27 2 2 7) a b-1.5ab =.............-2a5b3..................- a3b3  8 3     

Cognome:…………………………… Nome:……………………… data:…………………… classe:…..…..

A cura dei Proff. Luigi Cennamo e Maria Grazia Pichereddu © 2010

SARDEGNA SPEAKS ENGLISH LINEA DI INTERVENTO 1

REALIZZAZIONE DI PROGETTI PER L’APPRENDIMENTO DELL’INGLESE ATTRAVERSO LA METODOLOGIA CLIL

Liceo Scientifico “Europa Unita” – Porto Torres

Multiple choice Choose the correct answer to the following questions :

3 2

4 3 5 2

4 5

1) Which of the following is the result of  x2y +  ⋅  x2y −  ?

-

16 9 4 2 + x y 25 4

16 9 4 2 − x y 25 4

9 4 2 16 x y + 4 25

9 4 2 6 2 16 x y - x y+ 4 5 25

2) Which of the following produces as a result b6 − 8 2 7 2 3  3  a + b  ⋅ b − a  7   8 

7 2 7 2 3  3  a − b  ⋅ b + a  8   8 

49 4 a ?

64 7 2 7 2 3  3  a + b  ⋅ b − a  8   8 

 3 7 2 b − a  8 

 4 3 5 5 2 3) Which of the following is the result of  a − b  ? 5 6  16 6 4 3 5 25 10 a − ab + b 25 3 36

16 9 4 3 5 25 25 a − ab + b 25 3 36

16 6 25 10 a + a 25 36

16 9 25 25 a + b 25 36

4) Which of the following produces as a result b2 + 8ab + 16a2 ?

2

(8a + b)

2

(-4a − b)

2

(8a + b)⋅ (2a + b)

(4a − b)

 2 1 2 5) Which of the following is the result of 2x − x −1 ?   2 4x4 +

1 2 1 x + 1 − x3 − 2x2 + x 4 2

4x4 +

1 2 x +1 4

4x4 +

1 2 1 x + 1 − x3 − 4x2 + x 4 2

4x4 − 2x3 −

15 2 x + x +1 4

2

6) Which of the following is the result of (a − 2b + 3) ? a2 − 4b2 + 9 − 4ab + 3a − 6b

a2 + 4b2 + 9 − 4ab + 6a −12b

a2 + 4b2 + 9 − 2ab + 3a − 6b

a2 + 4b2 + 9

Cognome:…………………………… Nome:……………………… data:…………………… classe:…..…..

A cura dei Proff. Luigi Cennamo e Maria Grazia Pichereddu © 2010

SARDEGNA SPEAKS ENGLISH LINEA DI INTERVENTO 1

REALIZZAZIONE DI PROGETTI PER L’APPRENDIMENTO DELL’INGLESE ATTRAVERSO LA METODOLOGIA CLIL

Liceo Scientifico “Europa Unita” – Porto Torres

7) Which of the following produces as a result 25x 4 +  2 3 3 5 2 y − z 5x −  10 3 

9 25 2 50 2 y6 + z − 3x2 y 3 − x z + y 3z ?

100 9 3

 2 3 3 5 2 y + z 5x −  10 3 

2  3 3 5  2 -5x − y + z    10 3 

 2 3 3 5 2 y + z 5x +  10 3 

3  1  8) Which of the following is the result of 3a− b ?  3 

1 9a2 − ab + b2 9

27a3 +

27a3 + 9a2b − ab2 +

1 3 b 27

1 3 b 27

27a3 − 9a2b + ab2 −

 

1 3 b 27

3 1  2 

9) Which of the following is the result of 2a+ b ? a2 − ab +

1 2 b 4

1 8a3 + b3 8

3 1 8a3 + 6a2b + ab2 + b3 2 8

3 1 8a3 − a2b + 6ab2 − b3 2 8 1 3

10) Which of the following produces as a result a9 − a6b2 + a3b4 −  2 1 3 3 a − b   3 

11)

 3 1 2 3 −a − b   3 

 2 1 3 2 a − b   3 

1 6 b ?

27

 3 1 2 3 a − b   3 

What does this expression represent (a+b) (a-b)?

The sum of two monomials A squared binomial Product of sum and difference of two terms A trinomial

12)

Which of the four is the solution to (a+b) (a-b)? a2 - b 2 a2 + b 2 a2 - 2ab + b2 a2 + b2+ab

Cognome:…………………………… Nome:……………………… data:…………………… classe:…..…..

A cura dei Proff. Luigi Cennamo e Maria Grazia Pichereddu © 2010

SARDEGNA SPEAKS ENGLISH LINEA DI INTERVENTO 1

REALIZZAZIONE DI PROGETTI PER L’APPRENDIMENTO DELL’INGLESE ATTRAVERSO LA METODOLOGIA CLIL

Liceo Scientifico “Europa Unita” – Porto Torres

13)

Which of these is the area of a square? (x+y)2 x+ y2 xy x2 + y2

14)

How many monomials is the formula of the binomial cube composed of?

3 4 6 8

15)

Which of these is the area of one side of a cube?

3a2b (a+b)2 3ab b3

Cloze Complete the following passages inserting ONE correct word: (a+b)2 The square of a _________________ is composed of the square of the first monomial plus the _________________ product of the first monomial and the second one plus the _________________ monomial raised to the second power. In other words the result of a _________________ binomial is a _________________.

Cognome:…………………………… Nome:……………………… data:…………………… classe:…..…..

A cura dei Proff. Luigi Cennamo e Maria Grazia Pichereddu © 2010

SARDEGNA SPEAKS ENGLISH LINEA DI INTERVENTO 1

REALIZZAZIONE DI PROGETTI PER L’APPRENDIMENTO DELL’INGLESE ATTRAVERSO LA METODOLOGIA CLIL

Liceo Scientifico “Europa Unita” – Porto Torres

(a+b)3

The _________________ of a binomial cube is the _________________ term raised to the _________________ power, plus the triple product of the first term squared and the second term plus the _________________ product of the second term squared and the first _________________, plus the second term raised to the third power.

Solve and Draw Solve the following exercises:

1)

6 3 4  6 3 4 a b −1 ,3 ⋅ 1 ,3+ a b  =_________________________________________   5 5    

 

6

 



2)  7 a3 +8b2  ⋅ 8b2 - 7 a3  = __________________________ 6



3)

2   2 3 2 −2,5a + b  =___________________________________________________ 7  

4)

3 2 2 1 2  a+ a b− ab =_______________________________________________ 2  2 3

5)

1 3 2 23  x − y  =_____________________________________________________ 3  4 3

3 2 6) (−2a −3b ) =_____________________________________________________ Cognome:…………………………… Nome:……………………… data:…………………… classe:…..…..

A cura dei Proff. Luigi Cennamo e Maria Grazia Pichereddu © 2010

SARDEGNA SPEAKS ENGLISH LINEA DI INTERVENTO 1

REALIZZAZIONE DI PROGETTI PER L’APPRENDIMENTO DELL’INGLESE ATTRAVERSO LA METODOLOGIA CLIL

Liceo Scientifico “Europa Unita” – Porto Torres

Draw the figure corresponding to the following formulas:

1

a 2 - b2

2 b2 + a2 + 2ab

Matching Match the words in the left column to their correct definition: (put the corresponding letter in the right column next to the definition) A.

Binomial

A measure or number repeated twice

B.

Binomial cube

Algebraic sum of three monomials

C.

Power

Monomials with the same literal part

D.

Volume

Algebraic expression in which there are no additions or subtractions

E.

Trinomial

Geometrical figure whose 4 sides have got the same length

F.

The square of a trinomial

Its formula is composed of six terms

G.

Square

Algebraic sum of two monomials

H.

Double

The product of length, width and height

I.

Monomial

You can raise a number to it

J.

Like terms

Its formula is composed of four terms

Cognome:…………………………… Nome:……………………… data:…………………… classe:…..…..

A cura dei Proff. Luigi Cennamo e Maria Grazia Pichereddu © 2010

SARDEGNA SPEAKS ENGLISH LINEA DI INTERVENTO 1

REALIZZAZIONE DI PROGETTI PER L’APPRENDIMENTO DELL’INGLESE ATTRAVERSO LA METODOLOGIA CLIL

Liceo Scientifico “Europa Unita” – Porto Torres

FINAL TEST SOLUTION Fill the blanks Complete the following Special Products:     1) 2+ 5 xy2  ⋅ −2+ 5 xy2  = 25 x2y4 − 4 9 3 4   3 4  16

2) 1-8b5 ⋅ 8b5 +1 =1−64b10 2  3) −0.6+1.25xy2  = 25 x2y4 − 5 xy2 + 4   16 3 9   

4) 4x 0.16y 5)

3-

2

2  

4 1 4 =16x6 − x3y2 + y 3 36

 3 2 2 - xy2 + x2 y +4y     4  3

=

9

4 16 2 2 x2 y 4 + x 4 y2 +16y2 - x 3 y 3 -6xy 3 + x y 16 9 3

3 1 3 2 3 1 3 6) -0.5x-0.25y = - x3 x yxy2 y 8 16 32 64 3

 8 9 27 2 2 7) a b-1.5ab = a6b3 -2a5b3+ a4b3 - a3b3  9 2 8 3     

Cognome:…………………………… Nome:……………………… data:…………………… classe:…..…..

A cura dei Proff. Luigi Cennamo e Maria Grazia Pichereddu © 2010

SARDEGNA SPEAKS ENGLISH LINEA DI INTERVENTO 1

REALIZZAZIONE DI PROGETTI PER L’APPRENDIMENTO DELL’INGLESE ATTRAVERSO LA METODOLOGIA CLIL

Liceo Scientifico “Europa Unita” – Porto Torres

Multiple choice Choose the correct answer to the following questions :

3 2

4 3 5 2

4 5

1) Which of the following is the result of  x2y +  ⋅  x2y −  ?

-

16 9 4 2 + x y 25 4

16 9 4 2 − x y 25 4

9 4 2 16 x y + 4 25

9 4 2 6 2 16 x y - x y+ 4 5 25

2) Which of the following produces as a result b6 − 8 2 7 2 3  3  a + b  ⋅ b − a  7   8 

7 2 7 2 3  3  a − b  ⋅ b + a  8   8 

49 4 a ?

64 7 2 7 2 3  3  a + b  ⋅ b − a  8   8 

 3 7 2 b − a  8 

 4 3 5 5 2 3) Which of the following is the result of  a − b  ? 5 6  16 6 4 3 5 25 10 a − ab + b 25 3 36

16 9 4 3 5 25 25 a − ab + b 25 3 36

16 6 25 10 a + a 25 36

16 9 25 25 a + b 25 36

4) Which of the following produces as a result b2 + 8ab + 16a2 ?

(8a + b)

2

(-4a − b)

2

(8a + b)⋅ (2a + b)

(4a − b)

2

 2 1 2 5) Which of the following is the result of 2x − x −1 ?   2 4x4 +

1 2 1 x + 1 − x3 − 2x2 + x 4 2

4x4 +

1 2 x +1 4

4x4 +

1 2 1 x + 1 − x3 − 4x2 + x 4 2

4x4 − 2x3 −

15 2 x + x +1 4

6) Which of the following is the result of (a − 2b + 3) ?

2

a2 − 4b2 + 9 − 4ab + 3a − 6b

a2 + 4b2 + 9 − 4ab + 6a −12b

a2 + 4b2 + 9 − 2ab + 3a − 6b

a2 + 4b2 + 9

Cognome:…………………………… Nome:……………………… data:…………………… classe:…..…..

A cura dei Proff. Luigi Cennamo e Maria Grazia Pichereddu © 2010

SARDEGNA SPEAKS ENGLISH LINEA DI INTERVENTO 1

REALIZZAZIONE DI PROGETTI PER L’APPRENDIMENTO DELL’INGLESE ATTRAVERSO LA METODOLOGIA CLIL

Liceo Scientifico “Europa Unita” – Porto Torres

7) Which of the following produces as a result 25x 4 +  2 3 3 5 2 y − z 5x −  10 3 

9 25 2 50 2 y6 + z − 3x 2 y 3 − x z + y 3z ?

100 9 3

 2 3 3 5 2 y + z 5x −  10 3 

2  3 3 5  2 -5x − y + z    10 3 

 2 3 3 5 2 y + z 5x +  10 3 

3  1  8) Which of the following is the result of 3a− b ?  3 

1 9a2 − ab + b2 9

27a3 +

27a3 + 9a2b − ab2 +

1 3 b 27

1 3 b 27

27a3 − 9a2b + ab2 −

1 3 b 27

3  1  9) Which of the following is the result of 2a+ b ?  2 

a2 − ab +

1 2 b 4

1 8a3 + b3 8

3 1 8a3 + 6a2b + ab2 + b3 2 8

3 1 8a3 − a2b + 6ab2 − b3 2 8 1 3

10) Which of the following produces as a result a9 − a6b2 + a3b4 −  2 1 3 3 a − b   3 

11)

 3 1 2 3 −a − b   3 

 2 1 3 2 a − b   3 

1 6 b ?

27

 3 1 2 3 a − b   3 

What does this expression represent (a+b) (a-b)?

The sum of two monomials A squared binomial Product of sum and difference of two terms A trinomial

12)

Which of the four is the solution to (a+b) (a-b)? a2 - b 2 a2 + b 2 a2 - 2ab + b2 a2 + b2+ab

Cognome:…………………………… Nome:……………………… data:…………………… classe:…..…..

A cura dei Proff. Luigi Cennamo e Maria Grazia Pichereddu © 2010

SARDEGNA SPEAKS ENGLISH LINEA DI INTERVENTO 1

REALIZZAZIONE DI PROGETTI PER L’APPRENDIMENTO DELL’INGLESE ATTRAVERSO LA METODOLOGIA CLIL

Liceo Scientifico “Europa Unita” – Porto Torres

13)

Which of these is the area of a square? (x+y)2 x+ y2 xy x2 + y2

14)

How many monomials is the formula of the binomial cube composed of?

3 4 6 8

15)

Which of these is the area of one side of a cube?

3a2b (a+b)2 3ab b3

Cloze Complete the following passages inserting ONE correct word: (a+b)2 The square of a binomial is composed of the square of the first monomial plus the double product of the first monomial and the second one plus the second monomial raised to the second power. In other words the result of

a squared

binomial is a trinomial.

Cognome:…………………………… Nome:……………………… data:…………………… classe:…..…..

A cura dei Proff. Luigi Cennamo e Maria Grazia Pichereddu © 2010

SARDEGNA SPEAKS ENGLISH LINEA DI INTERVENTO 1

REALIZZAZIONE DI PROGETTI PER L’APPRENDIMENTO DELL’INGLESE ATTRAVERSO LA METODOLOGIA CLIL

Liceo Scientifico “Europa Unita” – Porto Torres

(a+b)3 The formula of a binomial cube is the first term raised to the third power, plus the triple product of the first term squared and the second term plus the triple product of the second term squared and the first term, plus the second term raised to the third power.

Solve and Draw Solve the following exercises:

1)

6 3 4   6 3 4  36 6 8 16 a b −1,3 ⋅ 1,3+ a b = ab −    5 5 25 9     

 

6

 



2)  7 a3 +8b2  ⋅ 8b2 - 7 a3  = 64b4 - 49 a6 6



36

3)

2   2 25 6 10 3 2 4 4 3 2 −2,5a + b  = a − a b + b 7  4 7 49 

4)

3 2 2 1 2 9 2 4 4 2 1 2 2 32 2 32 3  a+ a b− ab = a + a b + a b +2ab− a b− a b 2  4 9 4 2 3 2 3

5)

1 3 2 23 1 9 1 6 2 1 3 4 8 6  x − y = x − xy + xy − y 3  64 8 3 27 4

3 2 9 6 2 3 4 6 6) (−2a −3b ) = −8a −36a b −54a b −27b 3

Cognome:…………………………… Nome:……………………… data:…………………… classe:…..…..

A cura dei Proff. Luigi Cennamo e Maria Grazia Pichereddu © 2010

SARDEGNA SPEAKS ENGLISH LINEA DI INTERVENTO 1

REALIZZAZIONE DI PROGETTI PER L’APPRENDIMENTO DELL’INGLESE ATTRAVERSO LA METODOLOGIA CLIL

Liceo Scientifico “Europa Unita” – Porto Torres

Draw the figure corresponding to the following formulas:

1

a2 - b2

2 b2 + a2 + 2ab

Matching Match the words in the left column to their correct definition: (put the corresponding letter in the right column next to the definition) A.

Binomial

A measure or number repeated twice

H

B.

Binomial cube

Algebraic sum of three monomials

E

C.

Power

Monomials with the same literal part

J

D.

Volume

Algebraic expression in which there are no additions or subtractions

I

E.

Trinomial

Geometrical figure whose 4 sides have got the same length

G

F.

The square of a trinomial

Its formula is composed of six terms

F

G.

Square

Algebraic sum of two monomials

A

H.

Double

The product of length, width and height

D

I.

Monomial

You can raise a number to it

C

J.

Like terms

Its formula is composed of four terms

B

Cognome:…………………………… Nome:……………………… data:…………………… classe:…..…..

A cura dei Proff. Luigi Cennamo e Maria Grazia Pichereddu © 2010