Solving One-Step Equations with Rational Numbers

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Objective

SWBAT solve one step equations that use addition, subtraction, and rational numbers by working with partners to solve and check their work.

Big Idea

Students work independently to solve one step equations using fractions and decimals, and then switch papers with other students to complete check steps.

Do Now

10 minutes

Students enter silently according to the Daily Entrance Routine. There are Do Nows at their desks. There is also a SMARTboard random name generator displayed on the board showing all student names in the class. I instruct students to take their seats quickly so that I can assign problems at the board. Students sit in anticipation and wait to see which name is generated. The name generator makes a beeping sound as it randomly searches through the list to select a name. As each name is selected, I assign those students to the board to complete problems 1 – 3 in the Do Now. These three students are instructed to solve their given problem as quickly as possible and then return to their seats to complete the rest. 

I begin reviewing the first problem by asking students to tell me what the last part of this numerical expression says:

–4(–9/16)

I try to pick a student whom I have noticed, from their work, making the mistake of reading this type of problem as “negative 4 minus 9/16” instead of “negative 4 times negative 9/16”. Since many students have been misreading this type of problem, I feel that this is a good opportunity to build community around the idea that many students misunderstand this type of question. Many of my students are struggling with the idea of asking questions during class with the excuse “other kids will laugh at me or call me stupid”. This questioning has to be done carefully; for example:

“I need a very brave volunteer who can read this part of the problem for me. It has to be a student who has the courage to possibly be wrong when reading it.” Then I pick a student. After the student states this part incorrectly, I follow up with, “thank you for your courage, now call on some more courage because this is not a subtraction problem. Are there any other brave students willing to admit that you also thought it was a subtraction problem?” As students raise their hand I commend them all for their honesty and courage and then explain the correct way to read and solve the rest of this problem.

The second problem is a check-in/spiraling topic that I want to make sure students stay sharp about (complex fractions). Many students are answering showing work and answering these types of problems correctly as well, so a correct answer and work for #2 builds them back up if they made a mistake on #1. The last problem reinforces the idea of showing neat work, step by step, by showing the operation being performed on both sides of the equation to isolate the variable:

–4 + y = –1

+4         +4     .

       y = 3

 

Check step 

–4 + y = –1

–4 + 3 = –1

–1 = –1

Homework Check

10 minutes

Homework answers are displayed on the board and student questions about the work are shared. This document is attached to this section and is uploaded on our class website (www.sites.google.com/site/7thgrmath). Students are responsible for checking the class website at home and come to class prepared with questions. Only 2 students in the grade do not have access to the internet at home, so these students are given paper copies of the answers in the morning during “Thinking Skills” (a daily homeroom class) so that they can be ready for this part of class as well.

The homework last night included work problems that required equations to solve. The strategy I use for these types of problems is the use of a verbal model that summarizes the word problem and helps students translate into an equation. I ask for student volunteers to remind us which lesson this week will help us translate verbal models into equations (Day 45 Lesson). Then I ask which subject teaches them to summarize information (Reading/Writing/ELA). I point out that this is an example of math and reading coming together as strategies to solve problems. I work closely with our reading teacher as well to use the same language used in reading class to remind students how to “summarize” information.

Task

20 minutes

Students are asked to organize their homework from last night into their binder and also clip in their do now into the appropriate section. I tell them that we are going to use partner chelpers again today. Based on difficulty in behavior yesterday with all three classes and this type of task, I inform students that the process of choosing their partner will be different today. Students will receive one of two different types of worksheets. When I hand them a worksheet I will say, “you are A” or “you are B”, and they are to write this letter (A or B) at the top of their paper. I have been struggling with the following of directions, so this is a way for me check that students are following directions and improve behavior management in my class. After receiving a sheet and writing the appropriate letter at the top of their paper, students are to work silently and independently on solving all of the equations on the left-hand side of the paper. Once they are finished they will raise their hand. I will come by their desk to approve their work, but I will not be checking answers. If their work is appropriate (they are showing the solutions step by step as discussed in class yesterday), I will ask the class if there are any other students who are finished and have the opposite sheet. Students may then choose a partner from the group of raised hands. These partners will complete the right-hand side of their partner’s sheet with appropriate check steps that use their partner’s answer to check. By completing the check step with someone else's answer to a problem that was completely different that their problem set, students focus on completing the check step without the bias of a previously known answer. Students will be able to communicate to their partner a critique of the work and answer using a check step as evidence (MP3). The partner will have the choice of challenging his partners information based on the correct completion of a check step. Pairs may choose different locations around the classroom to work, such as the booths along the side of the room.

If I am running out of time, or most of the class is still not behaving, I make the choice of partners myself, students lose the opportunity to move to a different location in the room, I bring the switched sheets to the partners I choose and everyone continues working silently on completing the check steps.  

Closing

10 minutes

Once there are 10 minutes left of class, I ask everyone to return to their seat. We take a vote on sheet A and B for the toughest problem to solve and/or check. I use a document camera to display a volunteer’s work and answer if they feel confident that they have done it correctly. This showcases excellent student work and by asking the class to evaluate said work, students engage in MP3.

I distribute homework, remind students that it will be graded, and that they also have a quiz tomorrow. These are the last two opportunities to boost their grade for the end of Quarter 1.