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* *Reflection: Developing a Conceptual Understanding
Reviewing Intersections - Section 3: Extra Practice

*Demonstrating Concepts With a Fish Tank*

*Reviewing Intersections*

# Reviewing Intersections

Lesson 14 of 15

## Objective: SWBAT describe the intersections of geometric figures and use conjectures about intersections to justify a claim. Students will understand what it means for figures to intersect or be parallel.

#### Lesson Opener

*5 min*

The warm-up prompt for the lesson asks students to think of the homework problems that gave them trouble. Each team must agree on ONE problem, which the team scribe will write on the board. I display the prompt using the slide show for the lesson. The lesson opener follows our Team Warm-up routine.

**Goal-Setting**

Following the warm-up, I display the lesson agenda and learning targets. Today we will review Homework Set 2, and students will complete thier learning portfolios for the unit.

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We conduct homework review as a team activity, using the Team Review variation of our Homework Review routine. I display the instructions and get the class started.

The solutions to most of the problems are provided with the homework set, so we can focus on answering student's questions and evaluating their justifications (**MP3**). It is satisfactory for students to simply quote the conjecture that applies, but I encourage them to add context (**MP4**). For example, (problem 39.c) *The ends of the table legs are points, and any three points are coplanar, so all three legs of the table will rest on a level floor at the same time. * I encourage students to share and compare their answers. What makes a justification complete and accurate enough to receive full credit on the quiz?

I also check to see how students answered problem 34.b. Do students recognize that the intersection of two planes is always a line? (Students may have answered that the intersection is a line segment, an edge of the polyhedron.) I am trying to help students recognize that a line segment--be it the side of a polygon, the edge of a polyhedron, or whatever--is always a part of a line. The strategy of extending a segment into a line (similar to adding an auxiliary line to a figure) will come in handy later (**MP5**, **MP7**). I tell students plainly that I will ask a question just like this one on the unit quiz.

When we finish checking the work and answering questions, I explain how students are to complete their their Unit Learning Portfolios. For the second time in this unit, students will use homework to assess their own progress toward unit learning goals.

Students turned in their portfolio problems for me to review a week ago, and I returned them with comments during the week. Students should have refined their solutions and are now turning both DS Portfolio Problem 1 - Dazzling Duals and DS Portfolio Problem 2 - UnderwaterMortgage for a grade. The goal is for students to gain experience with problem-solving as a *process* (**MP1**).

Completed unit portfolios will be collected following the unit quiz. This gives students a chance to assemble their notes, homework, and pre-tests to use when studying.

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#### Extra Practice

*20 min*

I plan time in this lesson for students to get Extra Practice. Ideally, students will identify the areas they want to work on themselves, but I generally know which skills the class needs extra time on.

I ask students to start by working together to correct thier Unit Pre-Tests. They are responsible for turning in a near-perfect product as part of their learning portfolios. I check for understanding by asking students to explain why they answered as they did.

I make a few extra copies of the practice activities from earlier lessons and have them on hand. I expect to focus on describing the 2-dimensional cross-sections of 3-dimensional solids and using conjectures about intersections to justify a claim.

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The lesson close follows our Team Size-Up routine. The Lesson Close prompt asks students to reflect on what it means for geometric figures to intersect.

**Homework**

For homework, students are to complete their unit Learning Portfolios and use them to study for the Unit Quiz.

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- UNIT 1: Models and Constructions
- UNIT 2: Dimension and Structure
- UNIT 3: Congruence and Rigid Motions
- UNIT 4: Triangles and Congruence
- UNIT 5: Area Relationships
- UNIT 6: Scaling Up- Dilations, Similarity and Proportional Relationships
- UNIT 7: Introduction to Trigonometry
- UNIT 8: Volume of Cones, Pyramids, and Spheres

- LESSON 1: Previewing Dimension and Structure
- LESSON 2: Unto the 4th Dimension
- LESSON 3: New Directions
- LESSON 4: Angle Management
- LESSON 5: Triangle Construction Site
- LESSON 6: Diagonal Daze
- LESSON 7: Platonic Relationships
- LESSON 8: Reviewing Structure
- LESSON 9: Flatland Encounters
- LESSON 10: Intersection Derby
- LESSON 11: Mission Impossible
- LESSON 12: Intersection Logic
- LESSON 13: Cutting Planes
- LESSON 14: Reviewing Intersections
- LESSON 15: Dimension & Structure Unit Quiz