Putting It All Together - Problem Solving Day

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SWBAT solve rate problems by applying various tests of proportionality

Big Idea

Let's put aside new concepts and solve problems using all that we have learned over the last couple of weeks.


10 minutes

The purpose of this lesson is to get students to work on several problems that require them to apply what we have worked on over the past 2 weeks.  Before we begin, however, we will review some of the essential questions that we have explored in the lessons of this unit.  

The main questions are:

1) How can we determine if two quantities are in a proportional relationship?

We explored three ways:  scale factor between rates, scale factor between terms of rates, and the unit rate

2) What is the constant of proportionality?

This is the unit rate or m = y/x

3) How do we write an equation of a proportional relationship?


4) What does the graph of a proportional relationship look like?

The graph is of a straight line that passes through the origin.

5) What coordinates represent the unit rate of a proportional relationship graphed on the coordinate plane?

The coordinates are (1, r)

My students keep their notes in a binder that stays in the classroom.  Students can access lessons to help answer the questions and see sample problem types.  I want this review to be quick however so that most of the time can be saved for problem solving and student grading.  

I have a few anchor charts for these questions.  If I feel like the class will need a lot of time, I can just have them refer to the relevant posters.


Problem Solving

25 minutes

This problem solving task will be done independently.  Many of these problems mirror problems that will be on the assessment the next day of class, so this will serve as a way for students to see how prepared they are AND for students to have a study guide.

While students are working, I will be walking the room observing how various students are answering questions.  This will let me know what issues to bring up when we go over the answers.

 I will treat this lesson mostly like a test environment since questions will be answered later in the lesson. That being said, I will have to be armed with plenty of encouraging thoughts and statements for students who are frustrated and/or struggling.  I will perhaps provide some help of the following sort.  See problem 1 as an example- Did you use a table?  Are your values in the table matching the description of the pay?  What are the units that should be in the graph? I may even say "Enter values for 0 to 4 hours of work.".

Similar questions would apply to question 2.

The help I give, or the questions that I ask, are just meant to get students to start thinking about things they should be doing to be successful.

One other note.  I will insist that students only use pencils for this.  I know everyone expects the math teacher to insist on pencils, but I don't.  I often let my students use pen as well, though I prefer that they use erasable ink.  Also, if they make mistakes in permanent ink, I tell them they can't expect to receive a brand new packet of materials.  Today I want pencil and will have plenty on hand so that when we check the work, the correction will be done in red ink - red pens provided by me!





Partner Grading

15 minutes

Once nearly everyone is finished, students will swap papers with their neighbors.  (It's okay if you decide for students to grade their own work.)  I will provide red ink pens and we will go through each problem.  Perhaps this seems obvious, but it will be helpful to have the answer key finished before the lesson, so that during this part of the lesson the teacher is not wasting time working problems out. This will save time for questions.  

For the purpose of this assessment, problems 1-3 are each worth 2 points: 1 for a correct answer and 1 for a correct explanation.

Problem 4 has 6 values to find so it is worth 6 points.  

Problem 5 is worth 2 points: correct answer with correct explanation

Problem 6a is 2 points.

Problem 6b gets 1 point.

Problem 6c gets 1 point.

Problem 6d gets 1 point.

Problem 6e gets 1 point.

Problem 6f gets 1 point.


By my count that is 21 total points.  The point system does not need to be perfect here, it is just a way for students to gauge their progress.  Students who score 16 or more correct answers (scores above 75%) are considered to be at least proficient.  

Students should be encouraged to review this assignment in the evening in preparation for the assessment on the next day.