##
* *Reflection: Advanced Students
Pulling It All Together: Parallel Lines Unit Review - Section 4: Practice Before the Test

Question #6 came with a hint for students to assign an angle measure to one of the bisected angles. This surprised a lot of the students, who were then even more surprised when they all came to the same answer regardless of the starting angle measure they chose.

A good number of my students were really intrigued (not all, unfortunately, but a lot!). We tried varying the measure of the vertex angle A and then looked for patterns in the resulting internal angle U. It was a great use of repeated reasoning (**MP8**)! Eventually students were able to generalize and to arrive at a formula predicting the measure for angle U in terms of the starting angle A.

*Advanced Students: Problem 6 is Interesting!*

# Pulling It All Together: Parallel Lines Unit Review

Lesson 4 of 5

## Objective: SWBAT apply their knowledge of the parallel line concepts to a unit review problem set.

## Big Idea: Time to pull it all together! Students work cooperatively, applying their knowledge of parallel lines in preparation for the unit test.

*90 minutes*

#### Discussion of the Homework

*15 min*

I ask that the students work in their **groups**, comparing answers and discussing the homework problems. As the students converse, I walk around the room, listening to their discussions with an ear toward common difficulties. When it appears that all of the groups have covered the entire assignment, I ask if there are any questions or issues on it that anyone would like to discuss, and we go over these as a class (**MP3**).

#### Resources

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#### More on Constructions

*30 min*

The set of construction problems includes 2 new constructions, i.e. constructing a perpendicular line from a point both on and off a line segment. The other constructions are either straight-forward review or are variations on familiar constructions (**MP5**).

I allow the students to complete problems 1 through 3, working in their groups as I circulate around the room. When everyone is ready, I demonstrate numbers 4 and 5, asking the students to prompt me with the steps as I go. I do this by asking now familiar questions: *where is the only non-random point? what do I accomplish when I swing an arc from this point*?

After problems 4 and 5, I allow the students to again work in their groups to complete the problem set. When it appears that most have finished, I ask for volunteers to display their constructions using a document camera, and we highlight any different methods or approaches that were used (**MP3**).

#### Resources

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I hand out the Review of Logic assignment. Students work in their groups to discuss and complete it and then we discuss it as a class. I have chosen this question because it serves not only to review logic statements, but also reinforces their knowledge of the classifications of triangles, another topic in this unit.

#### Resources

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#### Practice Before the Test

*30 min*

The Review Before the Test includes practice on all of the numerical concepts included in this unit, as well as proofs. The students work in their groups, discussing the problems and comparing answers. (**MP1, MP2, MP3**)

This problem set helps the students review both the geometric and the algebraic concepts included in this unit, and it requires that they pay close attention to the structure of the diagrams, including the use of some auxiliary lines (**MP7**). I am guessing that most of my students will be able to finish the majority of these problems in the allotted class time.

#### Resources

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In the final 5 minutes of the class, I summarize the concepts included on the unit test, listing them on the board as we discuss them:

- angle pairs and parallel lines: supplementary, vertical, alternate interior, corresponding, and same-side interior angles
- sum of the angles of a triangle and the exterior angle theorem
- constructions
- logic statements

I also ask the students to complete the Review Before the Test for homework if they have any problems left to do.

#### Resources

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