Super Practice with Angles and Algebra
Lesson 14 of 16
Objective: Students practice algebraic methods to determine angles to reach fluency with modeling and computation.
Setting the Pace
The lesson is the second in a two part practice series, so students are already familiar with the pace, goals and opportunities. I still find it helpful to recenter them at the start of a class session. Staying organized is a challenge for any middle school student. So this part of the lesson is the generally the same as the previous practice session.
The one difference is that studemts are able to take out the tracking sheets that they have already started. I ask them to check-off step 3, 4 and 5 (which they worked on in the previous lesson and took home for homework):
In general, this lesson is driven by independence. But, I start the process by outlining the expectations and opportunities of this type of practice session. My coteacher helped me design the Checklist. The numbers 27 and 28 refer to the topic numbers we gave to our angle study this year.
There are lots of choices for students to make during this practice session. Since this can feel overwhelming, the Checklist helps students keep track of their choices. They mark down which mild, medium or spicy problems they have done. This way, when we conference later, they can share the problems they have covered. Then, I can suggest the best course of action based on the results of their assessment.
For this lesson, students simply focus on steps 1 and 2 of the process. Later, I will explain how we have designed our conferencing and feedback system, which is covered in steps 3, 4 and 5.
Mild, Medium or Spicy
Even though this topic is much tougher than the last practice session, we still offer differentiation to challenge all of our learners. The model is based open meeting the needs of the individual student.
Students solve as many problems as they can at a level that reflects their comfort level. They can start with the introductory mild problems and then work their way up to medium and spicy. They can start at medium and then go up or down from there. They can even go right for spicy and then work on other problems if they have time. I tell them that the assessment is at the medium level, but that mild will help them warm up and spicy will push them beyond the difficulty level of the assessment. Our students understand the value of this independent practice and know that we are there to support them. They take these independent choices seriously and try to make the best plan for the 30 minutes allotted towards this practice.
The mild problems are all listed on this Powerpoint: Topic 28 mild
These problems help students work with angle basics. Each of the accompanying videos simply works through the examples. The videos don't discuss any detail or theory. They simply guide students through algorithms they have already worked with or inferred from class discussion. Students use the videos in different ways, but the ultimate goal is to have them at least check their reasoning and work as they go. The video format gives them immediate feedback with respect to accuracy and process. It also helps students who are struggling.
The video represents my standard response to the "how do I this?" question. Students listen to my first response on the video. Then, they their hand. This way, if they have a question, I already know that something about my standard explanation isn't working for them. This saves me time and helps me work with alternate approaches even before they begin to ask their specific question.
I often post the videos in place of a worksheet. This saves paper and also simplifies the process. Students start the video, pause it to try the question on their own and then work through the brief video lesson to check their work.
I should also mention that many of the angle calculations will not match the diagram in any way. For example, in the second question, students will calculate the angle value at 3.5 degrees and see a diagram that looks more like 60 degrees. I do this to reinforce the idea that the diagrams are not to scale.
Here are the videos:
- Supplementary Angles with Algebra Mild 1
- Vertical Angles and Algebra - Mild 2
- Adjacent Angles and Algebra - Mild 3
I placed the most problems in this category as they were doing well with the angle measures and algebra around this topic. There is no worksheet file for the medium problems. I posted the problems in a series of videos for the students to review:
- Angles Medium 1
- Vertical Angles Medium 2
- Supplementary Angles and Algebra Medium 3
- Angle Question Medium 4
- Angles Medium 5
- Proving Parallel Lines Medium 6
- Using Algebra to Find Parallel Lines Medium 7
Technology Note: I posted the videos as a smaller file size to lower latency issues and help student navigate the problems and solutions quickly.
These problems are by far the most difficult, but they are also the most rewarding for students. They know that these problems are challenging and are proud to attempt them. I only created two for this section, because I wanted them to have time to also work on the medium problems during class.
Here is the worksheet:
Here are the videos:
Instructor's Note: There is a calculation error in the end of the second video. However, I decided to leave that in the video to challenge students, "see if you can find my error in the second video." This tends to generate some buzz around the problem and encourage them to carefully review the video for the problem.
The Teacher's Role
There is so much to facilitate and discuss during this lesson. It is exciting to navigate the wide variety of precise feedback generated during these lessons. They have just finished the previous practice session and spent a day reviewing the results. This means I had a chance to conference with almost every student and now I have a chance to follow up on that conference work.
- "Did you have a chance to review the follow up problems?"
- "Did you go back and finish all the medium problems from our last session?"
- "Would you like to meet with me during lunch to try some more problems around transversals?"
Even if all students were doing well on the last topic, I like to discuss the topic they are currently working through. Here are some basic guidelines (which is the same from the last session):
At first, it is challenging to understand the role of a teacher in a classroom supported by video, answers and tremendous choice. However, I find that these lessons simply offer new opportunities and teaching moments. Nothing is lost in using video. Instead, you will find that you gain time to work with small groups and individuals in ways that were previously not possible. Here are some suggestions to make the most of this lesson:
First, always resort back to the lesson checklist that was given at the start of the lesson. As you circulate, ask students to see the sheet and then ask them low inference questions, like "I notice that you started on Spicy. How far have you gotten?" You could also make suggestions based on their work so far, "I see that you have finished half of the mild problems. Do you think you are ready to move up to medium now? You could always go back to mild later if you like?" By using the checklist, you will find that you have directed conversations all period long.
If a student is struggling with a problem, ask them to see their notes and talk about what they did and did not understand from the video. If they don't have a response, I gently remind them to review the video before talking to me.
Then, when a student raises their hand and you confirm that they already tried watching the video and taking notes, you can begin to teach them with other strategies (other than the ones presented in the video.)
The Exit Ticket
There isn't time for a formal summary. Instead we ask students to take a minute and discuss the problems they chose to do and to mark down their problem on their tracking sheet. Then we give them about 15 minutes to try a problem based on the work from class.
We collect these exit tickets and use them to guide the feedback we offer on the next day.
For this particular exit ticket session, I gave them a problem on the current topic and the one before (to give them another attempt at the previous topic). I like to see if my feedback is helping.