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.

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

5 minutes

The Warm Up prompt for the lesson asks students to recall the different types of geometric properties. We used these categories to frame the scope of the course at the beginning of the unit. Students will remember 'shape' and 'size'. In this unit, we will go in a different direction by studying the property of 'dimension'.

I display the prompt using the slideshow for the lesson. The lesson opener follows our Team Warm-up routine, with students writing their answers in their Learning Journals.

**Goal-Setting**

Following the warm-up, I display the Agenda and Learning Targets. Today is the first day of the new unit.

30 minutes

As I pass out the Unit PreTest, I remind students of the purpose of Pre-Tests in this course. Students will revise their answers to pre-test questions and turn them in as part of their Learning Portfolios at the end of the unit.

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.

**Portfolio Problems**

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

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.

Since these problems invite students to draw right on the paper, I expect most students to make a start. Most will probably not be accurate, however. One goal of this unit is to help students visualize geometric figures and their intersections more accurately by giving them knowledge to inform their 'inner eye'. (Those who do make an accurate answer probably have strong spacial visualization ability. It is interesting to note who they are and find out what sort of interests or jobs they have.)

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.

Displaying the Standards for Mathematical Practice, I ask the class to tell me which standards they think came into play as they were working on the problem. Students will certainly think of **MP1**, but the meaning of **MP7** is probably not clear at this point. I tell students that in this unit we will learn what 'structure' means and how they can use the structure of a geometric figure to understand a problem.

In the time remaining, 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 Dazzling Duals and Underwater Mortgage are provided. (NEED TO UPDATE WITH SOLUTIONS)

15 minutes

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.

4 minutes

**Individual Size-Up**

The lesson close follows our Individual Size-Up Routine. The Lesson Close prompt asks students to write their personal learning goal for the unit.

**Homework**

For homework, I assign problems #6-8 of Homework Set 1. These problems review topics from the previous unit. Following the unit quiz--and before new material has been covered in the unit--is when I try to assign problems for review.

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