Preview and Goal-Setting

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SWBAT use problem-solving strategies to begin to understand a problem. Students will understand that solving problems in the real world is a process that requires time and creativity.

Big Idea

Students learn what will be expected of them in this course as they are encouraged to persevere in making sense of a pair of novel problems.

Lesson Opener

8 minutes

Team Warm-up

Today I am teaching my students class procedures for beginning and ending a lesson.  As I display the Warm-Up  prompt for the lesson, I explain my procedures for a team warm-up and for Awarding Preparedness by checking for homework and required materials each day.   I point out that today I will be checking to see that each student has brought their planner, and I ask students to put their planners where I can see them before they begin on the warm-up problem.   Then, I give students 3 minutes to discuss the warm-up question and ask them to come up with a High Quality Answer, which I describe with the help of the slideshow for the lesson.

At the end of the time limit, I randomly select a student to be the scribe for each team by rolling a die. The student whose seat number 1-4 comes up represents their team by writing the team's answer on the board.

As the scribes are writing their teams' answers on the board, I ask the class to judge which are high-quality answers.

The warm-up question: What is Geometry? also gives me a chance to see what the class took away from the What is Geometry? activity of the previous lesson. 

Displaying the Agenda and Learning Goals, I tell the class that the purpose of today's lesson is to preview the current unit, beginning with a pre-test.


Unit Preview and Portfolio Problems

25 minutes

Unit Pre-Test

As I pass out the Unit Pre-Test, I explain the purpose of Pre-Tests in this course.  Some students will be uncomfortable, because they are being asked to take a test where they cannot be expected to know many of the answers.  I assure students that pre-test scores do not get entered in the grade-book, but they do let the student, as well as me, know where they stand at the beginning of the course.  I tell students that they will revise their answers to pre-test questions and turn them in as part of their Learning Portfolios at the end of the unit.  They will learn more about learning portfolios next week.

I give instructions and ask students to begin.  I encourage them to answer the questions they think they know first, then make educated guesses for the rest. 

As students work, I hand out a ball-bearing compass and a ruler to each student.  I issue each student a compass for the entire year.  (The ruler might be useful on the problems they will be solving next.)

Portfolio Problems

As students complete the pre-test (5-10 minutes), I collect it while distributing Porfolio Problem 1 for the unit.  

I explain how I use portfolio problems in my units in this video.

Once most students have finished the pre-test, I display instructions for the portfolio problems.  I circulate through the classroom, answering questions and offering encouragement.  If students have trouble starting, I ask them to try one of the problem-solving strategies listed in the instructions.  I encourage students to work alone at first.  They will have time to share ideas later, but it is important for every student to learn how to make a start on an unfamiliar problem on their own.  My goal is for every student to be engaged in working on each portfolio problem for 5 minutes.  As students work on the first problem, I distribute Portfolio Problem 2.

As I walk around, I also take note of students whose work can be used as exemplars for others.  I am not looking for a complete or even a correct solution, especially if I suspect that the student will not be able to explain how they arrived at their answer.  Instead, I am looking for work that offers a good idea or effective stratetegy that others can emulate while feeling that it is something they could have thought of on their own.  In particular, I am looking for students who realize that their compass can be used for comparing and reproducing distances.

At the end of the time limit (or earlier, if most students appear to be 'dead in the water') I call the class's attention.  I ask how students feel about these problems.  Some will be uncomfortable, if they have not been challenged with a novel problem before.  Others may not want to stop working.  Displaying the Standards for Mathematical Practice, I explain that knowing how to make a start on a completely unfamiliar problem is an important skill that takes time to develop (MP1).  In this course, we will use timed exercises like this to develop that skill.  They should use this time to familiarize themselves with the problem and ask clarifying questions.  I assure them that they will be learning concepts and skills in the coming lessons that will help them to solve these problems, and I will give them some more time to work in class.  But, students will also be expected to put in time outside of class.  It takes time and effort to develop the ability to apply what you learn in a math class to problems such as you might encounter in the real world (MP4).  If you are not willing to put forth that effort, however, you have already answered the question that students like to ask: "when are we ever going to use this?"

If there is time, I ask students to share their ideas for solving the problem with their team-mates.  Or, I may ask the class to look at promising student work to help them get a start.

Today, I only expect students to make a beginning.  Nevertheless, the solutions to Where's My Package? and Placing a Call are provided.


Unit Syllabus

I display instructions as I pass out the Unit Syllabus and Unit Learning Portfolio.  I give students 5 minutes to read over the learning goals, write the date of the unit test in their planners, and write a personal learning goal for the unit.  I emphasize that the goal should be about "understanding" or "being able to do" something specific, something related to the unit goals in which the student has a personal interest.  The goal should not be about getting a certain grade or turning in assignments.






Team-Building Activity

20 minutes

The purpose of this activity, based on a classic research article on cooperative learning from the 70's, is to show students that they can perform better when they collaborate with others than alone.

I plan this activity as an alternative to beginning-of-the-year administrative tasks, such as issuing textbooks.  If I do not use it during this lesson, it can be a sponge to fill time during another interrupted lesson.

I begin by distributing the Lost On Mars handout.  I ask a volunteer to read the short narrative.  I then tell students that they have just 5 minutes to decide which items they will bring with them, working alone.  At the end of the activity, they will have a chance to compare their answers to the answers of NASA experts.  As students work, I display a digital count-down timer on the front board and call out times every minute.  I encourage them to make decisions within the time limit.

Next, I have students form pinwheels for working with their cooperative learning teams.  I tell students that they will have just 10 minutes to come to an agreement on how to prioritize the items on the list.  I coach students that they will have to compromise.  If they fail to reach an agreement within the time limit, they will receive a lower score when we compare their answers to the experts'.

As the teams work, I circulate.  It is fun to watch the team dynamics.  If it seems like a team is in a gridlock, I ask them to imagine that they will be able to take the first 10 items on their list.  Otherwise, the exact order does not really matter. 

At the end of the time limit, I display the Lost On Mars expert answers (based on the responses of actual NASA experts).  I explicitly demonstrate how students can find their score (otherwise, many will struggle and not have time to finish).  I point out the calculators that are in pouches on the classroom wall and get them started calculating their individual scores.  I ask students who finish to calculate the score for their team's answers. 

Teams nearly always perform better than most (but not all) individual students.

Lesson Close and Homework

1 minutes

Generally, there will not be time for a lesson close in this lesson. 


I distribute the homework.  Displaying a slide, I assign the first three problems in Homework Set 1.   These problems review algebra skills.  While students are learning the concepts of a new unit, I typically assign review problems for homework.  Also, these problems help students "brush off the rust" after summer vacation and prepare them for baseline and diagnostic testing that is usually scheduled during the first two weeks of the semester.

I also remind students to return their signed course syllabus, together with their parental consent form, on Monday.  Monday is also the day on which I expect students to have all their materials.