Super Practice with Angle Values

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Objective

SWBAT pursue mastery with problems involving complementary, supplementary, vertical and other angle combinations.

Big Idea

Students can use targeted practice to identify misconceptions and grow in mathematics.

Setting the Pace

5 minutes

This lesson is driven by independence, but we start the process by outlining the expectations and opportunities of this type of practice session. My co-teacher helped me design a tracking sheet for students:

Super Practice Checklist - Topics 27-28

The numbers 27 and 28 refer to the topic numbers we gave to our angle study this year. We designed this sheet to help students keep track of this practice work.

In this lesson, there are lots of choices for students.  This sheet helps students manage the choices and it removes that stress from the activity. As they work students mark down which mild, medium or spicy problems they have done. This way, when I conference with them later, they can share the problems they have covered and 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. I will explain how we (my co-teacher and I) have designed a successful (although sometimes hectic) conferencing and feedback system, which is covered in steps 3, 4 and 5.

Mild Medium or Spicy

30 minutes

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.

Mild

10 minutes

This section has the most problems, which are all listed on this pdf (again created by my co-teacher, as she is both hardworking and brilliant):

TOPIC 27 - Parallel Lines and Transversals Mild Practice

This pdf includes the largest number of problems between the mild, medium and spicy, but they go the quickest and have the least amount of distractions. These problems help students work with angle basics. Each of the videos simply work through the examples. The videos don't discuss any detail or theory, they simply guide students through algorithms they have already worked with and 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:

• Did I get that right?
• How does my solution compare to the one in the video?

At this date in time, the video represents my standard response to the "how do I this?" question. Students listen to my first response and then raise their hand. This way if they have a question I already know that something about my standard type of explanation isn't working for them. Carefully preparing or selecting video resources saves me time and helps me work with alternate approaches even before students begin to ask specific questions.

Here are the videos for the Mild Problems:

Medium

10 minutes

This section only has three problems, but they are designed to push student thinking on each of the angles we have discussed. For example, you will notice that the vertical angle question really forces students to think about what constitutes a vertical angle (other than have a simple diagram with two intersecting lines).

Here are the problems: topic 27 medium.docx

As mentioned in the previous section, the videos are meant to help students check their work, reasoning and guide them in when they have questions. If they find that the videos aren't helping them, then we talk in class. I ask that they check the videos first as this allows me to help as many students as possible with their individual questions.

Here are the videos for the medium problems:

Circle Wedges - Topic 27.mp4

Vertical Split - Topic 27.mp4

Transversals for topic 27.mp4

Spicy

10 minutes

Students know that spicy represents the toughest challenge we offer on the topic. We use feedback on these questions to guide future super practice sessions. If they find that the questions are too difficult, we ask them why and then adjust the scaffolding. If they find that the questions are too easy, we rethink and research our choices until we know we have redesigned a tougher question set.

Here are the problems: Spicy topic 27.docx

Here are the videos:

Supplementary Wedges.mp4

Vertical Angles Spicy 3.mp4

The Teacher's Role

30 minutes

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

15 minutes

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.

Here is the exit ticket: Exit Ticket 27