My all time favorite budget compass. I'm pretty sure this is cheaper at target, but it's not on their website.

An abandoned cactus. I've been wanting one for my desk, but not sure I wanted to spend the money.

I also found a pile of folders full of some of my favorite activities from Algebra I and Geometry. I haven't taught these classes for about 5 years, so I was excited to stumble upon these resources.

This first resource from my box that I decided to look at is a problem set used during chapter 1 in Geometry. The objective for this problem set is to find missing angle measures by using a protractor and deductive reasoning. It is a review activity since it combines rules from several sections of the textbook. I only have a few opening questions for my reflection on this activity:

1. Why did I keep this activity?

2. Why is this activity better than problems from the textbook?

3. What aspects of this activity (if any) can be replicated for other topics?

To begin this activity I handed each student a piece of computer paper. We folded the paper into eights and numbered each box. This is an easy go-to strategy when you don't have time to format a worksheet for responses, and students like the folding.

Next step is to take one of these problem cards, and go over the problem together on the whiteboard.

Sometimes we won't number the boxes, and instead you identify a problem by its color. Below is the orange problem.

As I am modeling how to do the problem on the whiteboard, I am also setting up the rules and/or procedures for the activity. Remember, the objective is to find all angle measures. For this particular activity the first rule is to measure as few of the angles as possible. While I write the first rule on the whiteboard, I will pause and give students time to discuss which angles don't necessarily need to be measured, and why this is true. Then I'll measure an angle suggested by students, and show them how to record the answer in the appropriate box. I will also model for them how to show work when needed, and we will write this down as a rule for the activity. We will finish this problem together, during which students will have individual think time, pair time, and then whole class discussion.

Part of the grade for this activity is an explanation grade. At any point during the activity, I can come to your table and ask any group member to explain the strategy for how they found the angle measures that were not measured with a protractor. You can only get full credit on the assignment if you have explained an answer correctly. It can be time consuming to check in with every student, so I usually do an activity like this on a block day, which for my school is 90 minutes.

I kept this activity because students were visibly successful. It encouraged conversation around the mathematics, and the majority of students were eager to have their turn explaining their thinking. Students were engaged throughout the activity.

This activity was better than solving problems from the textbook because students had to apply several of the rules for angle relationships at a time. They had to pick a path for solving the problem. Not all students had to have the same starting point. This was interesting because they could verify answers with each other and still have a chance to talk about the strategy used for finding missing angles. The format of the activity helped students work together because they could not move on to the next problem set until everyone at the table was finished. (When finished, you swap problem sets with another group).

This activity can definitely be replicated for other topics. It will be important to pick a set of problems that are worth talking about, but not too challenging if the teacher needs to be free to hear student explanations. What I hope to remember in the future is that the value of this activity (and any of its replicates) is that it provides a structure for students to justify their reasoning.

A few closing thoughts and questions:

-quicker students can get frustrated when they have to wait on classmates to move on. How can I make the activity more meaningful for them? Is this a reason not to use this type of activity?

-One set of cards isn't always enough. Sometimes I make two sets of the cards so that groups aren't waiting on a problem set.

-What other types of activities encourage conversation? (I know many of these, but this is a question I should always be asking myself.)

In the next folder I found a stack of papers with the following four words printed.

I don't know the name for these, but I had students fold them into fourths and hold the correct side up to give the appropriate name for a pair of angles that I showed on the board. For the future I might try using this strategy with Plickers. Check out Pam Wilson's fantastic blogpost on Plickers for more info.

I like the idea of letting them measure what angles they want, but telling them to try to measure as few as possible.

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