Saturday, January 7, 2017

The MTBoS, Week 1: My Favorite Game

It's time for Week 1 of the 2016 Blogging Initiative. I'm hoping that this is being submitted in time -- I just barely found out that this is due Saturday at "the end of the day." It's already past midnight Eastern Time, but I'm hoping that before midnight Pacific Time still counts as on time, or I've already blown the challenge!

This week's idea comes from Julie Reulbach, a North Carolina high school teacher:

Called a “My Favorite,” it can be something that makes teaching a specific math topic work really well.  It does not have to be a lesson, but can be anything in teaching that you love!  It can also be something that you have blogged or tweeted about before.  Some ideas of favorites that have been shared are:
  • A lesson (or part of one) that went great
  • A game your students love to play
Reulbach lists more options here, but this is the "My Favorite" that I wish to post. I've mentioned My Favorite Game here on the blog a few times before. In the following description, this game is set up for a Geometry lesson on quadrilaterals, but it can be adapted to any lesson.

Oh, and I've noticed that based on the blogs I've glanced at so far, many teachers' "My Favorite" posts involve computer programs. I seem to be behind the times as my activity uses pencil and paper.

(Yes, I know that's the image for the 2016 initiative, but no image for 2017 was provided to us!)

The point of this lesson is to get the students thinking about the properties of special quadrilaterals without worrying about how to prove them. In other words, I want to get the students engaged and thinking about the quadrilateral properties so that they can make the conjectures.

We begin by dividing the class into groups -- say of three or four students. Each group is assigned a worksheet -- or the members can write down answers on a common blank sheet. Then my usual set of ten questions are assigned -- but there are some differences between this and the usual individual worksheets that I post.

First of all, let's look at the first two questions:

1. What is the teacher's __________?

2. What is the teacher's __________?

Beforehand, the teacher fills in the blanks with words -- I'd fill them in with age and weight. I have no problem with giving this much information to the students -- but many people, especially women, are highly sensitive to revealing such personal data. This is why I left blanks in the questions -- so that the teachers fill in the blanks with words that they are comfortable revealing in class.

The teacher asks the question, "What is my age?" (or whatever is in the first blank). The groups signal when they want to answer. The teacher calls upon the group that signaled first to answer -- and since this answer will almost certainly be wrong, the teacher then calls upon another group. When a group finally gives the correct answer, the teacher awards this group a point. (In case you're as curious as the students are about my age, I am currently 35 years old.)

Notice several things about this game so far. The first team to give a correct answer -- and the answers in my version of this activity are numerical so far -- is the one to get the point. And after the first two questions, two groups have one point each -- or possibly one team already has two points -- and the rest have none.

Certainly the groups without points so far are eager to earn one. And so they are faced with the next question in the activity:

3. True or false: the diagonals of a rectangle are always equal in length.

Recall that this activity is all about conjectures. The students have already spent time making conjectures (that is, educated guesses) about the teacher's age and weight -- now it's time to make a conjecture about geometry!

This question serves several purposes. First, the students in groups that are trailing in points -- the same students who would have complained about doing math after the long exam -- now suddenly want to answer a math question because they want to catch up to the leaders. Second, this question is a true-or-false question, so students who might have tuned out if given an open-ended question will want to try this one at least since there are only two possible answers. The students are likely to guess at the answer -- and they're encouraged to do so, because a conjecture is a guess! Third, the conjecture in question involves rectangles -- and students who tend to forget what a rhombus or trapezoid is will still remember what a rectangle is. The only problem word that might be a barrier to participation is diagonal -- so the teacher reminds them that the two diagonals of a rectangle run from a corner to the opposite corner.

In my activity, every third question (that is, the third, sixth, and ninth) is a true-or-false question. I use these to give the students more opportunities to earn points. The teacher allows every group to give an answer of true or false before revealing the answer, and every group that gives the correct answer earns a point. In this way, groups can earn points without worrying about being the fastest group to get the answer.

Of course, the answer to Question 3 here is true. Hopefully, most, if not all, of the groups were able to guess that the diagonals of a rectangle are equal, so that every group is on the scoreboard. Now we move on to the next questions.

4. The diagonals of a square always divide the square into four triangles of __________ size.

5. The diagonals of a kite are always __________.

Now these questions are open-ended, just like the first two questions (but there are no more personal questions -- from now on, all are geometric). So we return to having the groups compete, and only one group will receive the point.

Now we move on to our next true-or-false question:

6. True or false: consecutive angles in a parallelogram are always equal.

And the game continues in this fashion. At the end of this post is a worksheet containing all ten questions plus a Bonus Question.

I'll let the teachers decide what prizes to award the winning team -- or teams, since I prefer to give the reward to the top two groups.

Now returning to the present, let me say that when I first posted this activity last year for the 2016 Initiative, I was just a substitute teacher. Now that I'm a full-time middle school teacher, I had the opportunity to play this game in my class a month ago, on December 7th. Here's how it went, as I first recorded on my blog:

Now I decide to play this game today in all my classes. And you may ask, why today? Well, I actually played this game as a sub one year ago today -- and I did it for one very particular reason.

The answer to the first question "What is the teacher's age?" is 36. That's because today is -- you guessed it (or remembered from last year) -- my 36th birthday! And so I knew that if I was going to play a game which starts with my age, it might as well be on my birthday.

What lessons do I include in today's game? Well, just as in the version of the game I posted as a sub, I want to focus on geometry questions. As it turns out, the game fits the current seventh grade lesson like a glove. Yesterday, the students cut out triangles out of straw, and Illinois State even asks the students to make conjectures about the triangles they created. So it's easy to fit some of those right into the game.

Today is Wednesday -- always a scheduling adventure at our school. For once, we actually follow the same schedule as last week -- but again, it means that I don't see the seventh graders as much as the other grades. I try having them come up with Triangle Inequality as a conjecture. A few of them are able to get on the right track, especially after I give them the hint (or "lead them by the nose").

For eighth grade, I notice that the STEM project mentions the measures of angles that are vertical, adjacent, corresponding, and so on. So I play the game using these conjectures. One big problem is that some students can't use a protractor correctly, so many don't arrive at the conjecture that vertical angles have the same measure. (Actually, the seventh graders also had to conjecture Triangle Sum, but I don't even try to reach that conjecture, knowing that if the eighth graders won't use the protractor correctly, neither will the seventh graders.)

Meanwhile, for sixth grade, the animals project ultimately relates to guessing how much room animals need, so it fits into the game as well. They are learning about how to find the dimensions of a rectangle given its area -- that is, factoring.

I like this game as a sub because it gives the students something to do. But if I use it in the regular classroom, it might be better to do some preparation. Once again, I just took the STEM project and added my own "What is the teacher's age?" questions. But instead, I could have come up with some questions such as just measuring random given angles. If I award points in the game, then the students should be motivated to find them. Then after that I segue to finding specific angles such as vertical angles or those of a triangle. That should lead them to make the conjectures.

So as you can see, my game works best for discovery or conjecture lessons to begin a new unit. I found out the hard way that it doesn't always work well for review. Groups with smart yet talkative students end up dominating the game, while quiet students who need extra help fall behind. In this case, it may be helpful to award extra points for behavior. Therefore, this is "My Favorite" lesson for introducing a new topic.

For those who have come to read my 2017 Blogging Initiative post, thanks! I'd like to inform you that there's another active MTBoS challenge, Tina Cardone's "Day in the Life," and I'm participating in that challenge too! Here is a link to Cardone's website explaining what "Day in the Life" is:

As today's the 7th, here's a link to Brianne Beebe, the blogger whose monthly posting date is the 7th:

(And yes, Beebe is also participating in the 2017 Blogging Initiative!)

My own monthly posting date is the 18th, and here's a link to my December 18th post:

My next post will be on January 10th -- that's not my posting date, but it's our first day back from winter break and Cardone wants us to post on special days, too.

This week, Barnes and Noble is having another Educator Appreciation Week, which means discounts for us teachers. Since I teach both math and science, today I purchased a science book, STEM to Story: Enthralling and Effective Lesson Plans for Grades 5-8. It is published by 826 National and edited by Jennifer Craig. I hope I'll be able to find some ideas for science activities in this book.

Finally, I conclude this post with a math problem:

sin 97 degrees = cos theta

As cosine is sine shifted 90 degrees left, the answer is 7 degrees -- and today's date is the seventh.

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