Open Inquiry in Math?

In reflecting about this year of inquiry, I have been all over the map!  I initially felt that focusing on math inquiry would be an interesting way to steer my thinking.  There are so many topics that naturally lend themselves to literacy, I am always adapting them to math.  Then, I thought an easier route would be social studies and science inquiry, which really lend themselves to a more open inquiry approach... not easy at all!  Now I am to the conclusion that I perhaps have been a little too reflective!  Sometimes I dig myself into a hole of thought and have trouble executing a plan for fear of failing. So, I am going to continue with plans for integrating inquiry into math through the end of the year and focus on successes and challenges there.

Our last inquiry work with Michelle was around open inquiry, which is by far the most demanding in some ways because it requires me to be so flexible with plans.  It all depends on where kids are at in the process of learning.  Jamie and I are taking this approach to our current unit on Colorado History.  I don't think this is an approach that can be used in math.  An open inquiry approach in math would do little to lay the foundation that kids need in order to execute sound math thinking.  Am I wrong?  My current approach in math is curricular inquiry, where students participate in inquiry around a specific foundational topic.  Right now, that topic is perimeter and area.

Chalk Talk

As I shared in my last post, students have been thinking about math thinking and created chalk-talk posters for each of the Standards for Mathematical Thinking indicating what each standard meant to them and/or an example of how they have demonstrated that standard.  We then used sticky notes to indicate which of the cognitive thinking strategies we need in order to successfully demonstrate each standard.  The posters are now hanging in the classroom under the thinking strategies.  My next step is to physically connect each standard to its corresponding thinking strategy using yarn.  I am going to use the topic of perimeter and area to challenge students to think about how they think to solve problems.

Hallway Polygons

I am planning this week using the most logical approach.... searching 'perimeter area' on Pinterest.  I found some great inquiry activities, but do these activities lend themselves to true curricular inquiry?  Will students be discovering the meaning of each by engaging in activities that really push their thinking.  Here is what I have so far:

• Students will make 'hallway polygons' using the 1 x 1ft. tiles on the floor and painter's tape.  This is Tony's favorite!  In the past I have made these polygons and had students use red, 1 ft. strips of paper to measure the perimeter and green 1ft. square sheets to measure area.  I am thinking that I will make one and have student make 6 or 7 more for the rest of the class to measure.  I found that this is a great way for kids to 'walk' the perimeter and get very kinesthetic with the concept.
• Using Google Maps and the ruler tool to find perimeter and area.  Students find the perimeter of our school, the US, the Pentagon, the state of Colorado, Lake Superior.  This will be a great way to really problem solve the perimeter and area of irregular shapes and integrate tech. 
• Find the area of your footprint using graph paper.  Straight out of Everyday Math, this is another great one for looking a irregular shapes and solving problems.
• Measuring Penny, a read aloud about measurement that also has an activity where students have to design a dog house and a dog run to maximize area for the dog to have space to run around.
• Students will make a visual representation of the meaning of perimeter and area to hang on the wall.  The visual can be anything (tool, example, non-example, picture) to cement the meaning of each in the reader's mind.

My inquiry questions for my students:

• How does what we measure influence how we measure?
• How do we find areas of rectangles?
• How do we find perimeters of rectangles?
• How can we find rectangles’ lengths if we know their areas and widths?
• How is area connected to multiplication?
• Why does area matter?  Why does perimeter matter?
• Who uses perimeter and area in their lives besides fourth grade math students and their teacher?

How does this relate the Standards for Mathematical Practice?  I am going to ask students to identify which of the standards they are using when the compute area and perimeter.  According to my scope and sequence, they should focus on:

1. Make sense of problems and persevere in solving them.
4. Model with mathematics.
5. Use appropriate tools strategically.
6. Attend to precision.