MODELING EQUIVALENT EXPRESSIONS WORKSHEET

Problem  1 :

Consider the two expressions 3(x + 2) and 3x + 6 and answer the following questions.  

Questions :

(i)  Model each expression using algebra tiles. 

(ii) How many x tiles and 1 tiles does the expression 3(x+2) have ? 

(iii) How many x tiles and 1 tiles does the expression 3x+6 have ? 

(iv) Is the expression 3(x + 2) equivalent to 3x + 6 ? Explain.

Problem  2 :

Consider the two expressions 2(x + 3) and 2x + 3 and answer the following questions.  

Questions :

(i)  Model each expression using algebra tiles. 

(ii) How many x tiles and 1 tiles does the expression 2(x+3) have ? 

(iii)  How many x tiles and 1 tiles does the expression 2x+3 have ? 

(iv) Is the expression 2(x + 3) equivalent to 2x + 3 ? Explain.

Detailed Answer Key

Problem 1 :

Consider the two expressions 3(x + 2) and 3x + 6 and answer the following questions.  

Question (i)

Model each expression using algebra tiles. 

Answer :

Question (ii)

How many x tiles and 1 tiles does the expression 3(x + 2) have ? 

Answer :

From the above model of 3(x + 2), we have three x tiles and six 1 tiles. 

Question (iii)

How many x tiles and 1 tiles does the expression 3x + 6 have ? 

Answer :

From the above model of 3x + 6, we have three x tiles and six 1 tiles. 

Question (iv)

Is the expression 3(x + 2) equivalent to 3x + 6? Explain.

Answer :

Yes; each expression is represented by three x tiles and six 1 tiles.

Problem 2 :

Consider the two expressions 2(x + 3) and 2x + 3 and answer the following questions.  

Question (i)

Model each expression using algebra tiles. 

Answer :

Question (ii)

How many x tiles and 1 tiles does the expression 2(x + 3) have ? 

Answer :

From the above model of 2(x + 3), we have two x tiles and six 1 tiles. 

Question (iii)

How many x tiles and 1 tiles does the expression 2x + 3 have ? 

Answer :

From the above model of 2x + 3, we have two x tiles and three 1 tiles. 

Question (iv)

Is the expression 2(x + 3) equivalent to 2x + 3 ? Explain.

Answer :

No; 2(x + 3) is represented by two x tiles and six 1 tiles. 2x + 3 is represented by two x tiles and three 1 tiles.

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