Explore, Discover, Inquire: An Attempt at Inquiry Based Learning

I love the idea of inquiry based learning. I found this incredible graphic here to describe 10 reasons why teachers should be using inquiry-based learning in the classroom.

Phenomenal, right? Why would you NOT want to use inquiry-based learning in the classroom?

Let's be real for a second. There are just times when students cannot simply inquire their way through something. For example, the Quadratic Formula. I'm sorry, but no 15 year old is going to have enough grit or perseverance to ever come up with that bad boy.

I am very selective with when I use inquiry in my classroom, cautiously only choosing content that students have plenty of background knowledge with so that they have an entry point to their exploration. I never want to have so much self guided inquiry that students shut down, give up, or feel like they have no idea how to begin. For 10th grade Geometry, finding the area of a polygon is the perfect opportunity for students to find success with an inquiry-based activity. Prior to this unit, students have had instruction on trigonometry, Pythagorean theorem, special right triangles, interior angle sum of polygons, and area of quadrilaterals, triangles, and trapezoids. With all the tools in their toolbox they need, students were ready to start exploring how to find the area of regular polygons!

In groups of 4, students were given a regular hexagon with a side length of 6. Of course I used my favorite dry erase mats. 

They were instructed to work together, using whatever mathematical tools necessary, to find the area of the hexagon. Here are some of the creative ways they split up their hexagons...

After students found the area (which by the way, almost every group was able to!), each group presented their strategy to the class.

After each group presented, we asked the class the following questions: 

1. How does this method compare with your method? What's similar? What's different?

2. If you had to find the area of another hexagon, would you change your method and do this one instead? Why or why not?

3. If you had to find the area of a heptagon, would this method still work? What about a octagon?

It was an awesome day and will lead beautifully into a more formal strategy for finding the area of any polygon as well as the formula using the apothem and perimeter. You could literally have checked each box from the graphic organizer above today. All the things happened. When inquiry is done right, it's a magnificent tool. 

Kudos to my student teacher, Ms. Schmidt for all the set up for this activity. She's half way through her student teaching and totally rocking it like a seasoned pro. I am so excited to see where her career takes her. If this is the beginning, I can't even imagine what's next!

Traffic Light Class Activity

There's always certain topics that make me a little nervous to teach. Big topics. Those topics that you know your students need to understand, not just to be successful on this chapter or this year, but for all math every year after this year. It's a big responsibility to be the first teacher to expose them to a new idea, solving strategy, etc. It's sort of like laying the foundation on a house that you know others will need to build upon and the pressure to build a strong foundation can sometimes feel overwhelming. 

One of these topics for me this year is completing the square. I am especially anxious every year to teach this because it's a topic that I didn't understand at all when I was in school. It wasn't until college when I fully understood why we complete the square, when we complete the square or mathematically what the heck we're doing when we "randomly" add this "magic number" to both sides of the quadratic equation. I want to make sure that my students aren't just memorizing a bunch of steps but rather understanding the entire process with the end goal the focus of every step. 

After some good teaching days we were ready to practice but it was apparent that the level at which students were grasping this new idea was dramatically widespread. I needed an activity that would allow them to practice at a level that they felt comfortable, but would also challenge them to keep working on harder problem types. BOOM! Traffic Light Activity. Here it was...

The idea behind this activity is to create a variety of problems at different difficulty levels. Student choose the level they want to work at with the flexibility to change as needed. The cards are placed in my favorite pouches and spread all over the front of the room. It's organized chaos.

For this activity, green cards were worth 1 point and included completing the square problems where a=1 and the answers were nice rational numbers. Yellow cards were worth 2 points and included problems where there was a GCF involved (a is NOT 1) but still had rational solutions. Red cards were more challenging problems that sometimes had a GCF, but did NOT have rational answers, requiring them to simplify their answers in radical form. 

Students were told they needed to complete 8 points worth of work and they could be done for the day. Students got to choose how they wanted to earn their 8 points, with a mixture of easy, medium, and hard problems types. You could do more easy problems, or less hard problems. The choice is yours! The nice thing about a number like 8 is that you can't just do all green (there were only 5) so it forced students to at least try one or two of the harder ones to achieve 8 total. 

Many students got a little excited at the idea of the less work option, but when they realized they weren't quite ready and needed to go down a level, they just walked up to the front of the room and tried a level easier. There is lots of flexibility to allow students the ability to self asses where they are at, and change as needed with the goal of working up to the red cards. 

I wrote the answers on the back of the cards so that students could self check as we go. Our class culture involves almost daily conversations about how the answers are not the only end goal. Understanding how to arrive at the correct solution and being able to articulate a variety of solving methods with regards to efficiency, visualization, connections to previous concepts etc. is the bigger goal. When the answers aren't secret, students don't obsess over copying them with out doing the work. They know that I look for evidence of student thinking, not just answers.

There are so many ways to incorporate a traffic light activity in math content! This semester I have a student teacher again (TALK ABOUT A BLESSING) and she was so helpful in creating all these problem types. Seriously, can I have a student teacher like her every semester!? I am so lucky to have won the student teacher jackpot this semester! Boise State sure produces some top notch future educators.