Angle Relationships

    One of my favorite units is the angle relationships formed with parallel lines cut by a transversal.  There is so much vocabulary, so many rules to remember and so many ways to have the students engage with the content that it seems overwhelming.

    I always begin with the vocabulary.  Geometry has a lot of words and concepts that are new for students and this it difficult. Keep in mind that they are not only learning your vocabulary, but they are learning new words in ALL their subjects. And students need more than word and definitions, they need a way to connect with the new ideas and engage. 

    Vocabulary Game

    In each unit so far, we play a game with the new words using a partner game called the “slap game”.  The first time we played, I was careful to explain the rules and be clear that they were to only slap the cards, not each other. ; )  Sometimes, teenagers do not understand the fine distinctions.

    The number of cards vary, the first time there were 20 cards.  Students worked in pairs, the 20 cards were spread single file, face up on top of their desks.  Then I read the definition and the student who “slapped” the right answer first would get the point. Kids enjoyed this and it was a great formative assessment for me to see who needed more intervention with the vocabulary before we moved forward. 

    After using this type of game (it has since been renamed as the grab game) several times, I am convinced that it is helping students become more confident with the concepts. I have also revised the rules a bit. The basics are still the same.  In the most recent version, there are 18 cards, however there is more than 1 correct answer for each term.  This way all students have an opportunity to get a point—no more winners vs losers—all students can be winners. And I renamed it to get rid of the word “slap” which I did not personally like.  And now the students grab the right answer.

    If you want to try this activity in class, download here.

    Note: I cut all the pieces myself before class. I can cut each set in about 90 seconds. It would take students 20-30 minutes to cut anything. It is not a good use of instructional time and it is painful for me to watch the careful and slow trimming.

    Pass the Marker

    After using the game, students were more confident.  Most could look at a diagram and identify the most obvious relationships (corresponding angles, alternate exterior angles), but many were still confused by the two different types of interior angles (alternate interiot and same side interior). Some students were also mixed up about adjacent angles and linear pairs.

    I introduced the measures of angles and which pairs were congruent and supplementary, mindful that students were still not as confident about the words as I wanted. We played “pass the marker” to check answers on some of the diagrams.  This is another in the moment assessment to see how students are progressing.

    Students are given this diagram with the instructions that r and t are parallel, angle 4 = 71 and angle 15 = 87.  They are to find the measures of the remaining angles.  While they work at their desks, I write angles 1-16 on the board with space to write the measures. Then I fill in < 4 and <15.  When students have had some time to work, I pick up a whiteboard marker and hand it to a student who has been struggling.

    Picking the First Student

    I deliberately pick a student who has under performed because being chosen at the beginning is easier than later in the process. At this point, there are 14 angle measures to be filled in, so lots of room to have a right answer. Once the first student is finished, they have the power to chose the next student to the board. No one can opt out, no one is allowed to say no. They can get help, they can get a student to coach them, they can ask the class, but they cannot just refuse. I also have a rule that the same person cannot be chosen more than once. This eliminates the same person being “picked on” and allows me to assess more students.

    In each of these activities, I am assessing student learning and gathering information. What do I do with all this information? As a result of all the activities in class, I can determine if students need more practice in a certain concept and ready to move on.. If students do not understand the basics, it is a disaster to move on too early. They will shut down, give up, or just keep struggling.

    Group Poster

    After all this practice, I had students create a poster.

    I gave students the poster title, category title and the diagrams in a stack (everything was cut for them except the titles). Students were asked to first sort the diagrams into categories. They worked in groups of 3 or 4 and everyone had to agree where the diagrams were sorted. When they were confident about their answers, they could get poster paper and glue everything in place. Students asked to to check their answers and I did not.  If you want this activity, click here.

    Using Posters to Increase Understanding

    After the posters were completed, I collected them and we ended the period by checking answers on another problem.  The next day, students arrived and all the posters were on the bulletin board and ready for the next part of the activity. All the posters were numbered at random and students were instructed to do a gallery walk and examine each poster. For each, they were to decide if the poster had correctly identifiied the diagrams and if not, how they could be corrected.

    As students are talking to each other about the posters and writing their answers, I am listening to their answers. In fact, I am interested in what they know, what they are still confused by and how they explain their understanding. Do they use the correct vocabulary? Do they identify any errors? Can they articulate their thinking.

    Why Use Activities

    Using a variety of activities in the classroom serves several purposes. Students have several ways to engage with the material. Students talk with other students and discuss their confusion. They gain support from others and hear other confusions. Students use the content vocabulary and write about it as well. And most importantly, the level of anxiety is lowered every time the focus of the learning is taken from the teacher control and given to the students. During all this process, I gain insight into what students are confused by and how I can help them. And most importantly, students are active and we are having fun.

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