7th Grade Math : Unit #1 - Introduction to Mathematical Investigations : Lesson #6

Let's Put Our Hard Work to the Test!

Objective: SWBAT draw heavily on the Mathematical Practices to solve problems involving proportional reasoning.
Standards: 7.RP.A.2 7.RP.A.2a 7.RP.A.3 MP1 MP2 MP3 MP4 MP5 MP6 MP7 MP8
Subject(s): Math
60 minutes
1 (Pre-Lesson) Opening Notes for you! - 1 minutes

Opening Side Bar Notes:

This is the final day of the lesson!  Students should now draw on the Mathematical Practices with comfort and ease. Students should have a view of the norms of the classroom and have established routines set in place.  With this Introductory Unit, your students should know which questioning you will ask to help engage with a certain Mathematical Practice.  The goal of this lesson is to culminate the week’s learning target.  The lesson began as a buildup, you introduced the Mathematical Practices, the students created a resource to refer to throughout the year, students were given a review objective to practice the Mathematical Practices for the first time, students practiced the Mathematical Practices given a grade level standard and critiqued the dialogue of other students to help improve their own mathematical dialogue, and now we put it to the test!

Students will be given a proportional reasoning pre-assessment.  You will find that the first unit of this course is proportional reasoning.  This is a great Segway into the first lesson of the course.  Students will draw heavily on the eight Mathematical Practices in order to complete the pre-assessment.  Students will be given the opportunity to grapple through the questions on their own, as well as communicate with their peers.  The pre-assessment is comprised of 5 questions.  If the students are drawing on all Mathematical Practices, this will take an entire class period.  The pre-assessment will be broken up into 2 sections.  Students will have 20 minutes for Individual Think Time, and 20 minutes for pair up time.  Students will need to answer each question correctly, explain their thinking in writing, show the work that shows the strategies they used, and write down information that they gained during their pair up time.  You will close the lesson with a brief discussion over how they used the Mathematical Practices, any problems that the students found drawing on the practices, and where the students will be going next. 

2 Student Activity Part 1 - 20 minutes

Student Activity:  Students will enter the room and sit in their I.T.T seats. Instruct students that they will be taking a pre-assessment that has problems involving proportional reasoning.  You may want to give brief examples of proportional reasoning to your students before handing them the pre-assessment.  I will give my students an overview of the week, and empower their thinking through positive affirmation.  Saying things such as “You became detectives and showed your investigative skills in solving math mysteries. Let’s put those skills to the test again by solving the mysteries that will be handed out to you today.  Don’t worry, in your bag of tricks you have 8 helpful tools to aid you in solving the mysteries ahead.”  

Once you have opened your lesson, pass out the pre-assessment to each student. Students should draw heavily on MP1, 2, 3, 4, 5, and 6. Students may draw on MP 7 and 8 as well. I will give my students 20 minutes of individual investigative time.  I will remind students to look for clues within the question, highlight important vocabulary, find things in the problem that they already know, and eliminate answers that do not make sense according to what the problem is asking.  Please draw to the Open-Ended Questions to help guide student thinking. Reminder, dim lights and low classical music really helps build an environment of focus.  

Mathematical Practice Number one is giving the "blues"

I have nominated MP 1 as the mathematical practice to get the bang for our buck.  I feel if students are truly persevering, they are using all other mathematical practices to do so.  This is the one practice that is giving my students the most frustration.  They are border line angry with me.  During this lesson, because it was a pre-test, students were quiet, yet quiet does not mean thinking.  There was an understanding because of it being a pre-assessment that I was not going to help them.  However, I could see the students giving up.  I could see them saying to themselves, "I don't get this."  I observed the majority of my students staring off, tapping their pencils, putting their heads down, etc.  When these things occurred I addressed the class and reminded them "MP1!"  "You can do it!" "Think!" "Don't Give Up!"  That is our motto, "We will not give up!"  It is hard not to give in to their frustrations, however it is paramount that you persevere too. 

3 Student Activity Part 2 - 20 minutes

Once the 20 minutes of I.T.T time expires, transition your students into P.U.T time.  Lights will go up, and students will begin to engage in rich mathematical discussions.  As you found in the first four days of this unit, it is imperative to walk the room engaging in the student discussions.  If you use open-ended questions, this will help guide student thinking and not give students the answers that they will crave. 

4 Closing - 10 minutes

Closing before you collect the pre-assessment from each student take 5 minutes to discuss how they feel about using these practices.  Are they comfortable? Why?  What are some issues students may still have?  Why?  What clarifications do students need in order to draw upon these practices and feel successful using them?  Student discussions may include using an example problem from the assessment and explaining which Mathematical Practices they used to solve the problem and give proof on how they used the practice. 

Collect the pre-assessments from each student.  Take the weekend to assess their work, offer rich feedback, and use the data to help with your best practices moving forward into the proportional reasoning lesson.