Solving and Proving Multi-Step Equations with One Variable

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SWBAT... 1. Solve multi-step equations with one unknown AND create a valid argument proving their solution.

Big Idea

Students work on solving complex equations in 1-variable and continue to hone the skill of proving their solution and backing up those proofs with evidence!

Entry Ticket

15 minutes

For this entry ticket, I put the following problems on the white board or project on the Smart Board or hand out copies of the Entry Ticket: Solving and Proving Multi-step Equations resource to students at the beginning of class. I choose these particular problems because I want students to review the concepts covered in last class AND the problems are at the heart of the skills needed to be successful in today's lesson. 

I have students work on two problems with fractional coefficients because I have found this is a type of problem students typically struggle with. In addition, the last question not only involves dealing with a fraction, but the answer is a fraction. 

Entry Ticket

Solve AND Prove (check your work!)

1.   2X = 14 

2.   -5Y  = -20

3.   10/11(X) = 60

4.    3/4(D) = 17



Direct Instruction and Active-Note-taking

20 minutes

During this section, students take two-column notes as a way to actively engage in the math content. 

There is a sample set of Class Notes as a resource in this section. Teachers can use the notes as a guide to write on the board. I find that students tend to like taking notes off the white board, one problem at a time, as opposed to having notes already written and projected on a SmartBoard.

I also use the typed notes as a resource for students who are absent (more more info, see the strategy video on Student Absences and Missing Work). The notes are scaffolded, with all the steps written out for the first problem and gradually decreasing support.  I use this strategy to increase student independence as instruction proceeds. The handout can be given to all students or used to Differentiate Instruction.

Collaborative Practice: Jigsaw Expert Groups

20 minutes

During this time students complete a Jigsaw Activity. For the first section of class, students form groups based on ability. In this lesson, I often have a group or two work on one-step equations, and other groups working on multi-step equations. The setup in this exercise allows students of all ability levels to access math practice 6 (MP.6) because they collaborate on the problems, encouraging students to attend to precision to understand BOTH the underlying concepts and the details of the steps involved in solving the problems.

During this time I am checking in with the different groups and like to think of myself as a facilitator. I tend to ask guiding questions, but avoid giving answers to groups as a way to help frame and continue the rich academic conversations for the groups.

I typically use a resource like Kuta software for the problem sets. Sometimes I will also assign problems from the textbook. If teachers have a class where there is access to technology, students can work on an online assignment using a resource like Delta Math to complete the questions online. 

Collaborative Practice: Jigsaw Mixed Groups

20 minutes

After completing the Expert Group work, students are organized into mixed groups. I like to use a funny or catchy phrase to assign groups (for example, Let's Go Red Sox, making four mixed groups - 1. Let's group, 2. Go group, 3. Red group, and 4. Sox group). 

In the mixed groups students are asked to go throught the worksheet as a group, taking the time for peers to ask and answer questions of each other. Note, students are still working on the Jigsaw Activity from the previous section.

During this time, I make rounds checking in and providing cues to keep each group on track. Once groups are finished I take a few minutes to have the class reflect and engage in some meta-level thinking. This can be as easy as asking students what the big picture task is and where we are in the process. This is also a great opportunity to ask students to reflect on what they have done well and what they need to work on to be successful for the remainder of the class. 



Exit Ticket: Proving a Solution through Writing

15 minutes

To conclude the lesson I have students complete one problem in an Idea Organizer, asking them to write out their thinking as they work. As part of the solution, I encourage students to prove their answer, or in other words use language to show that their answer solves the equation. In this lesson I give students an equation where they have to combine like terms because students tend to have difficulty with this type of problem and I want to assess their level of understanding to be able to adjust future instruction accordingly. 

I like to wrap up the lesson with a written response because it allows students time to process the main ideas from the lesson, and also helps them organize their thoughts. By writing out their reasoning, students not only have to be able to get the answer, but they have to express their thinking abstractly and quantitatively (Mathematical Practice 2).

Note: There is an example of Student Work for this assignment as a resource in this section.

Homework: Delta Math Assignment

For homework I assign a problem set on Delta Math. I typically have students complete ten problems in a row, with a penalty of one for an incorrect response. In other words, if students complete the first 8 problems correctly, but then get the 9th incorrect, then they have credit for 7 in a row and need to complete 3 more problems in a row to get full credit for the assignment. 

For a great overview video on Delta Math and how to set up an account (it is free!), click here: Delta Math Overview Video