Algebraic Expressions and the Real-World

Students work in pairs on the Think About It problem.

After 3 minutes of work time, I ask students if they can write the same expression for each scenario.  I want students to articulate that they can't be the same expression.  James has more money than Martha so his expression has to show that he has more money than her, but Martha’s expression has to show that she has less money than him.  I then have students share out the expressions they've written for each scenario.

In this lesson, students will write expressions when given a real-world problem and write real-world problems when given an expression.

Throughout the Intro to New Material section (and the entire lesson), students will follow the following steps. I'll keep these steps up on the document camera as a Visual Anchor throughout the lesson. My plan is to guide students through the examples in this section.

Steps for Writing Simple Expressions

1. Read and annotate.
2. Use a variable to represent unknowns and digits/operations for different values.
3. Define the expression.
4. Identify what amount you are starting with.
5. Determine if any terms or operations are grouped (parentheses).
6. Determine if there is any multiplication or division performed on the starting amount.  Translate.
7. Determine if there is any addition or subtraction.  Translate.
8. Check by restating and comparing to the written expression.  

Students work in pairs on the Partner Practice problem set.  As students work, I circulate around the room and check in with every group.  I am looking for:

• Are scholars correctly identifying the variable?
• Are scholars correctly identifying the constant?
• Are scholars correctly translating the verbal expression into an algebraic expression?
• Are students writing verbal expressions that represent an expression?

I am asking:

• How did you know what the variable was?
• How did you know what the constant was?
• What did you start with?
• What does the expression mean?
• Was there any multiplication/division?
• Was there any addition/subtraction?
• Will the expression have the same answer if you changed the order of the terms?
• How did you know what operation to use?
• What does the constant, coefficient and the variable represent in the context of the problem?

After 10 minutes of partner work time, I have 3 students share out their responses for Problem E.  The class evaluates whether the scenarios shared match up with the expression 15 + m.  Students then complete the Check for Understanding problem independently.  I circulate and check student responses as they work.    

Students work on the Independent Practice problem set.  As I circulate, I have with me an answer key for the first 12 problems, so that I can quickly scan students' answers and check for misunderstandings.

As students are working on Problem 13, I am making sure that they are writing single variable expressions, and not equations with two variables (for example, the marbles Cheney has can be represented as 12 + r, rather than c = 12 + r)

After independent work time, I have students share with their partners the scenarios they've written for Problems 14-19.  This gives them the opportunity to receive feedback on their work, ask clarifying questions, and hear alternate responses for the problems. 

Students then independently work on the Exit Ticket to close the lesson.