Solving Real-World Problems with Algebra (Addition & Subtraction)

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Objective

SWBAT solve real-world and mathematical problems arithmetically and by writing and solving algebraic equations.

Big Idea

Equations can model real-world problems in an abstract way by using numbers and symbols to make meaning of and define problems.

Think About It

7 minutes

Students work in pairs on the three parts to the Think About It problem.  After 3 minutes of work time, I ask students how they'd solve this problem.  I then have them share out the equation that represents this situation.  

Here, students may say that 81.30 - 51.40 = x can be the equation.  This represents the step we'd take to solve, but it's important here that students start with the equation that represents the situation.  Jamal starts with $81.30 and he spends an unknown amount of money, so I am looking for 81.30 - x = 51.40.

I frame the lesson by telling students that we are going to put together everything that we have learned in this unit- we are going to translate equations that represent real-world scenarios and then solve them to determine the value of the unknown within the context of the problem.  This lesson focuses on equations with addition and subtraction.

Guided Examples

15 minutes

Because this lesson puts together all of the skills students have mastered throughout the unit, there is not new material to be introduced before they start to work in pairs.  Instead of an Intro to New Material section, I facilitate a few guided practice problems.  The questions I use most often while guiding students are:  

  • What do we start with?
  • What happens next?
  • What's our unknown?

I want students to really make sense of the problems, and to understand what's happening in each. All of these problems also present an opportunity to talk about the reasonableness of an answer.  

Students also have access to a Visual Anchor as they work.  This visual anchor is lengthy, so I copy it on colored paper and pass it out to all students as a resource. 

Partner Practice

20 minutes

Students work in pairs on the Partner Practice problems.  As they work, I circulate around the classroom.  I am looking for:

  • Are students annotating the text?
  • Are students choosing the correct operation and order of terms?
  • Are students determining the correct answer?
  • Are students checking their work?

 

I'm asking:

  • How did you determine the operation in the problem?
  • What did you start with?
  • Then what happens?
  • What's your unknown?
  • Why did you order your terms as you did?
  • How did you determine your solution?
  • How did you know your solution was reasonable?
  • How could you check your work?

 

After 15 minutes of partner work time, I bring the class together to discuss problem 6.  I ask students what common mistake they think is made on this problem.  Once we name that students might accidentally subtract here, making the Heat the higher-scoring team, I ask students how many of them did indeed subtract to find their solution.  I ask them how checking the reasonableness of their solution could have helped here. 

 

Independent Practice

15 minutes

Students work on the Independent Practice problem set.

Problem 1 makes use of large numbers.  I am looking to be sure students come off to the side and show the needed computation.

Problem 3 can be challenging, because it involves fractions.  My students get fraction review work fairly often, so they are able to solve here.  You might consider moving this problem to later in the problem set, so that students are more confident with the process of writing and solving equations with whole numbers before presenting them with fraction problems. 

Problems 6 and 7 require students to access prior knowledge about finding perimeter of polygons.  You can include a similar problem in the guided practice, if students are not fluent with the idea of finding perimeter.  I don't mention perimeter at all before students start to work - I want them to work at making sense of the problems and persist in finding a path to the solution.

Closing and Exit Ticket

5 minutes

After independent work time, I bring the class together to discuss problem 7 from the Independent Practice set.  I ask students what equation they used to represent the perimeter of the square.  Although this lesson is centered around addition and subtraction equations, there are students who will chose to represent the situation with multiplication and division.  This is a nice way to preview what the next lesson will center around.

Students complete the Exit Ticket independently to close the lesson.  This Exit Ticket Sample shows what student work could look like.