Writing and Solving Equations Part 2

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SWBAT: • Write an algebraic equation that fits a given situation. • Solve one-step and two-step equations.

Big Idea

How can you write an equation to represent the cost, c, of renting a bike for h hours? How much would it cost to rent a bike for 3 hours from each shop? Students work with one and two-step equations.

Do Now

7 minutes

See my Do Now in my Strategy folder that explains my beginning of class routines.

Often, I create do nows that have problems that connect to the task that students will be working on that day.  Today I want students to use substitution to determine which student is correct.  Terriana commits a common mistake.  She substituted the 5 for x and thought that the problem was now 63 – 55, rather than 63 – 5 x 11.  Here students have to apply their knowledge of order of operations. 

I ask for students to share their thinking.  If they take Karina’s side, I plead Terriana’s case.  I want students to be able to explain to me that when there’s a variable right next to a number they are being multiplied together. Students are engaging in MP3: Construct viable arguments and critique the reasoning of others.


7 minutes

Students work independently on problem 1 and 2.  I want students to practice writing an expression and using substitution to find an answer.  I ask students to share their expressions and answer to problem 2.  Some students may create m = b – 1.99 – 6.50 or m= b – 6.50 – 1.99.  Other students may write m = b – (1.99 + 6.50) or m = b – 8.49.  I ask students if b – 1.99 + 6.50 would also work.  I want students to use their knowledge of the order of operations to recognize that it is not equivalent to the other expressions.  Students are engaging in MP3: Construct viable arguments and critique the reasoning of others.

Writing and Solving Equations

26 minutes


  • I use the data from the previous lesson’s ticket to go to Create Homogeneous Groups of 3-4 students.
  • I give each group a Group Work Rubric to track individual and group behavior.
  • I Post A Key so that groups can get up and check their work as they finish each page.  I have groups check in with me when they finish a page, so I can make sure they are on track.

Today I want students to be able to work with one and two-step expressions and equations.  We work on Part A together.  I have a volunteer read the situation out loud.  I ask, “What is going on?”, “What do we know?” and “What does each variable represent?”  It may be easier for some students to break down each part of the equation and then put them together.  For example, students may be able to come up with 3a and 2b by re-reading the problem.  I ask the students what we need to do with 3a and 2b if we want to find the total cost.  I call on students to share their ideas.  Students are applying the skills they have developed over the last few lessons to more complicated problems.  I ask if c = 3a + 2b is equivalent to c = 2b + 3a.  For problem two, I show the strategy of re-writing the equation and substituting 6 and 3 for the corresponding variable.  Then we use the order of operations to find the answer.  I ask students how many bundles of broccoli Sebastian and Gabe bought.  Students participate in a Think Write Pair Share

Students move into their groups.  As students work, I walk around and monitor student progress.  Students are engaging in MP2: Reason abstractly and quantitatively and MP4: Model with mathematics.  Students may get confused about situations that involve an additional fee on top of an hourly charge. A common mistake is to confuse these values and multiply the number of hours by the additional fee.  In these situations, I have students go back and re-read the information.  If necessary, I ask students to show how much it would cost for a certain number of hours /etc.  This usually helps students to understand what operations they are using and in what order.

If students are struggling, I may ask them the following questions:

  • What is going on in the situation?
  • What do you know?
  • What does each variable stand for?
  • What operation is going on between the value and the variables?  How do you know?
  • How can you prove that your value for the variable(s) works?
  • Are there any other values for the variable(s) that would also work?  Why or why not?

If students are correctly working through the examples, they can move onto the challenge questions.

Closure and Ticket to Go

10 minutes

I ask students to turn to Part C.  I ask students to share their thinking about the equation.  For problem 2, I present my work showing that I divided $26.30 by $0.30 and declare that Juan downloaded 87.67 songs.  I want students to realize that I did not factor in the $20 membership fee.  With the fee, Juan only downloaded 21 songs.  Then I ask for a student to show and explain how they calculated Markelly’s cost for problem 3.  Students are engaging in MP3: Construct viable arguments and critique the reasoning of others.

I pass out the Ticket to Go and the HW Writing and Solving Equations.