Creating Equations to Solve Problems

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SWBAT use linear equations to represent and solve problems.

Big Idea

Mathematically proficient use mathematics to represent a problem situation and check their solutions for accuracy.

Warm Up

8 minutes

I plan to start class by giving students a few minutes to solve these warmup problems on their own. While students are working, I will monitor their progress and watch out for students that are lacking fundamental skills.  I will ask my students to justify each step in their solution process.  I may also ask students to post their answers on the board, if I am concerned about the errors that students are making as they solve. 

As students complete the warm-up, I will also look to see how many students are plugging their solutions back into the original equation.  In raising this issue, I will remind students of MP6 and the importance of habits that support precision. At the same time, part of being precise is determining if your answer makes sense.  This approach to precision is going to be a major focus of today's class and classes to come.


5 minutes

After the Warm Up, I will distribute the opening task. I will give students a few minutes to look through the question and work.  Then, I will use a Non-Verbal Cue (thumbs up or down) to determine how many students think that the answer is correct.  Once I have a sense of the level of students' confidence, I will have students do a Think-Pair-Share to discuss this.  

While they work I will listen to student conversations. After, I will have one or two students share out their answers with the whole class.  I hope that students will volunteer the idea that if they multiply Kaiden's age by 3 and Leah's age by 5 they will get the same answer of 30 (MP2).  This shows that the solution is correct.

as we conclude this opener, I will explain to students that they are going to be solving problems like this one today. But, a large emphasis of the class will be put on how to check your solutions to make sure that they make sense in the context of the problem.


20 minutes

For today's practice, I developed a series of questions that will allow students to construct equations to solve problems:


I have also attached a graphic organizer that I use with my students which has been very helpful in the past.  The organizer serves a few purposes:

  1. Slow students down - Students need to take their time in constructing a let statement which will represent the unknowns in the problem.  This setup is the most important part of the process and needs to be emphasized.
  2. Organization - student's work should be organized in some way and this graphic organizer gets them in the habit.  It is amazing to me that once students have used this for a few days and the organizer is taken away they still have their work setup in a way similar to this.
  3. Emphasis on checking -The check should not just be something that you do if there is time. Students need to actively determine how to make sure that their answer makes sense in the context of the problem.  

Using this document, I will do the first example with students so that they can see how the graphic organizer is used.  I will require that all of my students use the graphic organizer for the first few days. After that, if they no longer want it they don't need to take it.  But, I will provide one for any students who want to continue to use it.  

After introducing the organizer, I plan to let students work with their partners on the remaining exercises and continue to emphasize the setup and the check.




7 minutes

This Ticket Out the Door will help you to determine if students are able to construct the let statement and solve the problem.  The scaffold of telling students the unknowns has been taken away and students need to construct the two expressions on their own.  This formative assessment will offer valuable feedback as you prepare the next lesson on using equations to solve problems.