Writing Algebraic Equations to Represent Real-World Scenarios (One-Step)

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Objective

SWBAT write and solve one-step equations to represent real-world and mathematical problems.

Big Idea

Students will translate verbal expressions into algebraic equations to represent real-world problems starting by correctly identifying the variables and operations in the situation.

Think About It

7 minutes

Students work on their own to write an equation to represent the Wonka Bar problem (TAB).  After 2 minutes of work time, we come back together as a class.  I go through the following question sequence:

  • What do we know in this problem? 
  • Do you know how many candy bars you can buy?  So what do we call the part of an equation that is unknown? 
  • What should we use for the variable? Let's be sure to define the variable with our work.
  • Why can you represent this situation with an equation?  
  • How can you represent this situation an equation? 

sample of a completed TAB problem is here.

Frame the Lesson: Yesterday we were discussing how to represent verbal expressions with algebraic equations.  Today we are going to continue this work but with real-world scenarios.  We will translate them using equations so that we can make meaning of them, and eventually solve the equations.  We will use everything we learned yesterday.

 

Intro to New Material

15 minutes

Students have experience translating expressions and simple equations.  Today's lesson gives students practice with translating from real-world connections.  We walk through the problems in the INM section together. 

  • For the first example, Eleni is x years old. In thirteen years she will be twenty-four years old, first read and annotate the equation.
  • What does the x represent? 
  • What does the 24 represent? 
  • What variables/numbers/operations do we have? 
  • What does this equation represent? 
  • What are we starting with? 
  • What amount are you ending with? 
  • Are there any terms or operations that are grouped? 
  • Is there any division or multiplication performed on the starting amount? 
  • Is there any addition or subtraction performed on the starting amount? 
  • What do we need to include for this to be an equation?
  • So what is this equation? 
  • Check for reasonableness: Now that we have our equation, let’s make sure we know that the equation is correct. To do this, we will use substitution. Let’s look at the verbal expression. What would make the equation true? 
  • Great. Now, we have the equation x + 13 = 24. If we plug in 11, does it work? 

 

We talk through the next three problems, in the same way.  In problem number 2 it's important to make sure kids use .25, rather than 25.  It's a great place to ask kids why that's important 

After the 4th example, students help me to fill in the words in our notes.  The key is included in the Visual Anchor, which I leave up while students work.

 

 

Partner Practice

15 minutes

Students work in pairs on the Partner Practice problems.  

As they are working, I am circulating and looking for:

  • Are students selecting the correct operation?
  • Are students ordering the terms correctly in the equation?
  • Are students able to justify their equation using substitution of a value in the problem and their equation?

 

I ask pairs:

  • How do you know this is the correct equation to represent the problem?
  • Why did you select that variable?
  • How can you justify that your equation correctly represents the context?

 

Discussion and CFU

7 minutes

For the class discussion in this lesson, I allow students to decide which problems we talk about.  I pick one person who decides which problem from the Partner Practice we're going to look at first.  The partner of that person talks through how the pair came up with their equation.  I then pick a second pair to go through the same process for a second problem.

I like problem 4 for conversation.  There may be more than one equation that students have written to represent the scenario.  I like to talk about all of them, so that students have the chance to see multiple representations of the information.

Students can be given time to use reasoning to solve for the variables in some of the problems from partner practice.  I like to ask for the solution to Problem 9, because it gives students the chance to practice with multiplication of decimal numbers.  It also allows me to talk about being quick and fluent with mental math.

Before moving on to the independent practice, students complete the final check for understanding (found here, at the start of the Independent Practice problems).   

Independent Practice

15 minutes

Students work on the Independent Practice problems.  

As they are working, I am looking for and asking the same things as I did during the Partner Practice:  

  • Are students selecting the correct operation?
  • Are students ordering the terms correctly in the equation?
  • Are students able to justify their equation using substitution of a value in the problem and their equation?

 

I ask:

  • How do you know this is the correct equation to represent the problem?
  • Why did you select that variable?
  • How can you justify that your equation correctly represents the context?

 

Problem 3 is one to watch out for.  Students may try to express the relationship as 58 divided by one-third, rather than 58 divided by 3 (or some other form of this).

Closing and Exit Ticket

7 minutes

Before students begin work on their Exit Ticket, we discuss two problems from the independent work problem set.

For Problem 6, I have students 'clap out' their answers - I say a, b, c, d and students clap when I get to the letter of the answer choice they've picked.  This allows me to hear where students are with mastery of a relatively simple problem.  

We also discuss problem 10.  I pull a popscicle stick and have a student put his/her work up on the document camera.  The student explains how (s)he worked through the problem.  I then open it up for feedback from the class.

Students then complete their exit tickets to end class.  An Exit Ticket Sample from class is included here.