**Modeling algebraic expressions :**

An algebraic expression is an expression that contains one or more variables and may also contain operation symbols, such as + or -

Algebraic expressions can also be represented with models. A rectangular bar can represent a variable, and a square bar can represent a unit.

**Example 1 : **

Use a bar model to represent the expression given below.

"7 + x"

**Solution :**

**Example 2 : **

Use a bar model to represent the expression given below.

"z / 3"

**Solution :**

**Example 3 : **

Use a bar model to represent the expression given below.

"t - 2"

**Solution :**

**Example 4 : **

Use a bar model to represent the expression given below.

"4y"

**Solution :**

**Example 5 : **

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

**Solution :**

**Let "x" be the money that Katriana and Andrew had at the beginning. **

**Step 1 :**

Write an algebraic expression to represent the money Katriana 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 Katriana 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.

After having gone through the stuff given above, we hope that the students would have understood "How to model algebraic expressions".

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