Exploring Angle Relationships Through Transformaitons Continued

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Objective

Students will be able to use transformations to connect angle relationships created by intersecting lines and parallel lines cut by a transversal.

Big Idea

Make connections and deepen understanding by appling transformations to angle relationships

Bellringer (Warm-Up)

15 minutes

I chose to use a strategy called “My Favorite No” during our bellringer today.  I took this strategy from a teacher channel video: When using this warm up strategy, you give one question on the board and paper supplies to answer the question.  As students finish you gather the papers and sort into two piles – yes (correct answer) or no (incorrect answer).  Then you pick your favorite no that has some really good correct parts but some common problem areas that many students usually have.  You put this favorite no under the document camera and ask students to analyze what is correct first and then what is incorrect.  I chose to ask students to graph the equation y = 1/4x – 2 because our activity today requires students to graph lines.  I printed graph paper from Mathbits and cut it into four small sheets to give to students:  I chose a favorite no that had a correct y-intercept and positive slope, but not the correct ¼ slope.  The paper also graphed a very short line segment, not a full line across the page.  I gave students time to “think-pair-share” around the questions what is correct about this graph, and then what needs to be corrected.  I wrote the questions on the board and students thought for about 30 seconds and then shared with a partner for 30 seconds and then shared with the class.   

Environment:

I always allow students to work in pairs that I have pre-assigned so they will have another student who is on the same level mathematically (homogeneously paired) to talk with and discuss the new concept. I begin class with a warm-up of some kind that is short but gets their minds thinking towards the activity of the day and then I give them the clear learning expectations for the day. After this, I begin the activity whole group but mostly allow students to work on their own within their pre-assigned group to complete a certain section of the activity. I even set a timer sometimes for how long they have to work.

Here is a short video from my strategy toolkit on how to make students resources for one another through cooperative groups:

Here is a short video about how I create cooperative groups 

Making Experts: While students are working within teams to complete a section of the activity, I am walking about the room formatively assessing their understanding by listening to their conversations, viewing their work, and by asking questions myself to see if students can clearly explain their thinking. While assessing learning, I am also making note of all the different correct approaches that students are taking to complete the work. I ask students to present their thinking during our whole class discussion time (consolidating student thinking) so that the class may listen to multiple methods of completing the work. If struggling students are having difficulties, then I spend even more time with these groups to "create" question the student partnership in such a way that they begin to think about the task in a productive way and begin to understand enough to generate solutions on their own. Here is a short video further explaining how I give feedback to move learning forward and make experts:

Consolidating Thinking (Mini Wrap Up Time)
At the end of the designated time, I call the class together and ask students to come to the front of the room and either present their work by writing on the white board or present by putting their papers under the document camera. This time of sharing out helps students to consolidate their learning as we move through the lesson and is usually why I do not spend a long period of time at the end of class wrapping the entire lesson. We hold mini wrap up sessions as we move through the lesson. If you would like to watch a short video explaining my classroom environment for this lesson and all my lessons, clip below.

 


Continuing the Activity

25 minutes

I reminded the students of why we began this lesson the day before.  This activity will require students to apply transformations (we listed the three transformations on the board: translation, rotation, reflection) to find and understand relationships between angles when line intersect. I let them know that I would be reviewing all theirs graphs from the previous day as they worked, just to ensure everyone was working with correct diagrams.  I gave everyone tracing paper because I expected them to use the paper to literally compare the sizes of each angle in the pair and then think about the movement it took for the tracing paper to accurately compare angle sizes. If you would like to watch a video on clarifying and sharing learning intentions and criteria for success with students click here.

The focus of class time today was around giving students time to work with their partners to complete the questions that follow graphing on page one. The goal was for students to realize that a rotation of 180 degrees about the point of intersection would map one vertical angle onto the other and thus prove the two angles are congruent. A reflection is also a method of mapping angle one onto angle three but the line of reflection is not currently present.  For students who wanted to map using a reflection, I found it helpful to have them copy both angles onto tracing paper and then fold the paper to map one angle on top of the other.  The crease line created by the folding is the line of reflection and students could clearly see the line and sketch it onto the graph by laying the tracing paper on top of the graph after folding.  Students made a quick connection to linear pairs because they already understood that a straight angle has a measure of 180 degrees.  I had to review the meaning of the vocabulary words supplementary and complimentary, but the concept was easily grasped. 

Wrapping Up the Lesson + Homework

10 minutes

After the students presented their thinking under the document camera during our mini-wrap up time, they spent the rest of the class working on the homework page.


Math Standards

This class period focused onunderstanding and proving why angle relationships along intersecting lines exists.  Therefore, the math standard addressed in this lesson is 8.G.A.2 Understand that a two-dimensional figure is congruent to another if the second can be obtained from the first by
a sequence of rotations, reflections, and translations; given two congruent figures, describe a sequence that exhibits the congruence between them.
 Working in small groups, receiving feedback from both their partner and from me as they worked with many different
representations of the equation (algebraic, numeric, graphic) and using different tools from rulers to tracing paper to calculators really utilized the following math practice standards:  MP3 & MP5.