Parallel Lines and Transversals
Lesson 5 of 8
Objective: SWBAT explore relationships between parallel lines and transversal to identify and calculate missing angles.
Over the next week, students worked to master skills with parallel lines and transversals. Each day they would enter silently, according to the daily entrance routine, and complete a Do Now which would inform me about their progress in these skills. This was a concept many students struggled to understand and the priority for me on a daily basis was their ability to correctly identify the angles created when two parallel lines are cut by a transversal. Each do now is broken down below to show why I included the items in the Do Now and how they helped students’ progress toward mastery:
Keeping our work with equations sharp is a skill I always want to spiral through and review with students when we get ready to learn something new in this geometry unit because I know it is a skill some struggle to master even late in the year. Algebra and the ability to solve equations such as the ones included in this assignment is a fluency issue. Students who “forget” or do not keep up with these skills find it very difficult to get through problems involving new information, such as the identification of angles created by parallel lines and transversals. In other words, I know I want to spend most of my time this week familiarizing students with the new vocabulary in the class notes section, so I need to make sure they practice solving equations at the beginning of this series so that they have “room” in their brains to concentrate on new terms.
After introducing the new terms to students the previous day, it is best to begin with these terms the following day. This is a sprint which students must complete in 3 minutes, including bubbling the answers. While students are waiting outside of the room to enter silently, I will advise them to use their class notes from the previous day to complete the sprint. Those who succeed in getting it done and get 80% or more correct will be awarded achievement points.
The following day, rather than have students select the correct answer from multiple choices, they will be asked to write the vocabulary term which describes the angle. Again, students will be advised to use their class notes from the first day of this series (Day 152) to correctly write the terms. This will be a partner do now. This means students will be able to work quietly with partners to identify all the angles by name. Since students were given notes with the angle names included, they are responsible for copying down the names on their Do Now and spelling them correctly. The first three pairs to bring me their answers completed and spelled correctly will earn achievement points and will be asked to write their answers on the board. To save time and be efficient, I break up the Do Now into three sections and I have these three pairs each take a section to complete on the board.
This assignment includes ALL of the terms we’ve learned in the past few weeks, relevant to angle geometry. Students are advised to use their class notes from the first day of this series (Day 152) and are asked to complete this do now independently. It is important for us to be aware of what each student knows independently since the quiz will take place the next day. Students are reminded that the quiz will include questions about angles formed by parallel lines and transversals, as well as vertical angles, complementary/supplementary angles, and angles about a point.
On the first day of this series, after we have reviewed answers to the Do Now, students will receive their Class Notes. This sheet is to be used all week since we will be adding notes and drawings each day. The document is split into two sheets for a couple of reasons:
- If a student is absent on the first day of this series they are given a copy of the filled out notes (page 2)
- If a student loses the notes, they are given a copy of the filled out notes (page 2)
- If a student has graphomotor impairments or other speech and language difficulties, they are given a copy of the filled out notes (page 2)
On that first day I only worried about introducing students to the new terms and getting them to use these terms to identify angles. Using the picture included in the notes I was able to ask the following essential questions that first day. Students were asked to respond in a complete sentence, using appropriate vocabulary terms to answer:
- Angles 2 and 6 are corresponding. Name another pair of corresponding angles.
- How many total pairs of corresponding angles are there?
- Angles 3 and 6 are consecutive. Name another pair of consecutive angles.
- How many total pairs of consecutive angles are there?
I complete the same line of questioning for all other terms included I the notes
The next day, I changed the picture. I drew parallel lines cut by a transversal on the board, but instead, rotated this image 90 degrees to challenge students a different way. Once again, I ran through the same line of essential questions, once again asking students to answer in the same manner.
The third day we kick it up a notch by including algebra. I begin with the following drawing on the SMARTBoard, asking one of the questions included in the essential questions list above:
- Angles h and d are corresponding. Name another pair of corresponding angles.
- What do we know about corresponding angles? They’re equal to each other
- What if I told you the measure of this angle was 3x + 2 and the measure of the other angle was 47 degrees? Would you be able to put together an equation to solve for x?
At this point I look out for massive confusion. This tends to happen, as I’ve noticed from past lessons throughout the year, when I take something concrete like equivalent numbers and change it up to an abstract representation in algebraic form. Some students have a hard time making that leap, from concrete to abstract. It is important to notice these students so that I may pull them into a smaller group to work with me during class work.
On the fourth day, I use this section of class to play a quick round of angles bingo. Since students spent time working independently during the Do Now on this day, and since the quiz the next day will include past angle relationships, this activity is a great way to review in the least stressful way possible.
Class Work, Closing, HW
Each day, students had at least 15 minutes to work in pairs and complete the attached classwork sheets. Each day I also made sure I was working with a small group of students who needed additional one on one help. Once there were 5 minutes left in class I would begin to ask different students to copy the drawings and work on the board for us to review during the closing. The following strategies were the most successful when helping students with these new angle relationships:
- Use of tracing paper. I had extra sheets of tracing paper whenever I was working with my small groups. Those who were having a difficult time noticing all the equivalent angles in the diagrams would be given tracing paper and asked to trace one angle and then lay the paper over all other angles to identify the equivalent ones.
- Use of a protractor. Using the protractor was a bit of a feat for some students and not as idea as the tracing paper. Some needed a review of how to measure angles using a protractor, but once they got the hang of it they were able to measure all the angles in their diagrams to check their solutions to the class work items.
Each of these strategies also helped students continue making connections beyond parallel lines and transversals, reviewing all the other relationships we’ve explored. The tracing paper helped immensely to seal the gap for that group still struggling with concepts such as vertical angles. I had students draw two intersecting lines with the use of a straight edge and then use the tracing paper to verify that the vertical angles were equivalent.
Quiz Day + HW
On the final day of this series students enter silently according to the daily entrance routine and begin taking their Quiz right away. It should only take about 30 minutes, but students are able to take up the entire class if necessary.
The previous day, students were also given a list of vocab list to expect on the quiz. All class work and homework given over the last few days should be completed and is allowed for use during the quiz. This is an open note assessment.
Next week we will be exploring concepts in surface area and volume of 3D figures. To prepare for these concepts, students will once again be given an equations task for HW so that they can keep their algebraic skills sharp.