MODELING ALGEBRAIC EXPRESSIONS

Examples 1 -4 : Use a bar model to represent the following expressions.

Example 1 :

7 + x

Solution :

Example 2 :

z/3

Solution :

Example 3 :

t - 2

Solution :

Example 4 :

4y

Solution :

Example 5 :

Katrina and Andrew started the day with the same amount of money. Katrina spent 5 dollars on lunch. Andrew spent 3 dollars on lunch and 2 dollars on a snack after school. Do Katrina and Andrew have the same amount of money left ?

Solution :

Let x be the money that Katrina and Andrew had at the beginning. 

Step 1 :

Write an algebraic expression to represent the money Katrina has left.

x - 5

Represent the expression with a model.

Step 2 :

Write an algebraic expression to represent the money Andrew has left.

x - 3 - 2

Represent the expression with a model.

Step 3 :

Compare the models.

The models are equivalent, so the expressions are equivalent.

Andrew and Katrina have the same amount of money left.

Example 6 :

On a math quiz, Tina scored 3 points more than Julia. Juan scored 2 points more than Julia and earned 2 points in extra credit. Write an expression and draw a bar model to represent Tina’s score and Juan’s score. Did Tina and Juan make the same grade on the quiz ? Explain.

Solution :

Let y be the points scored by Julia.

Step 1 :

Write an algebraic expression to represent the points scored by Tina.

y + 3

Represent the expression with a model.

Step 2 :

Write an algebraic expression to represent the points scored by Juan.

y + 2 + 2

Represent the expression with a model.

Step 3 :

Compare the models.

The models are not equivalent, so the expressions are not equivalent.

Hence, Tina and Juan did not make the same grade on the quiz.

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