Reflection: Student Ownership Squares in a Row Day 2 of 6 - Section 2: Exploration


This lesson as written feels far too teacher guided. When I taught this lesson a second time I did much less leading, telling, and showing and a lot more asking and listening. I decided not to suggest a table, but instead ask them to keep track of their work in an organized way that made sense to them. Some of them drew diagrams, some drew checkerboards, some used tables to keep track of the squares on the checkerboards. Several students kept track by drawing out the checkerboard and marking the center of each square and then noticed patterns in the dots marking the centers as the size of the squares changed and used that pattern to predict the number on a 6by6 checkerboard.

Rather than telling them the parts that were tricky I asked them:

  • "what's tricky about this?"
  • "I wonder if there is a simpler way."
  • "I wonder if we could find a way without having to count each one."

As I circulated and asked my kids what they were trying I looked for different representations and asked students to share with the class. If they didn't want to I asked if I could share their work with the class. I asked the class:

  • "how does this represent the different squares?"
  • "how can we use this representation to figure out how many there are?"
  • "why does it make sense?"
  • "how does this make it simpler?"
  • "how could we record this?"

I also asked them if they were noticing any patterns in the checkerboard squares that might help us predict the number of each sized squares or the number of squares on another size board. Not only did they come up with using the formula for area, buy my students came up with more ideas and questions than I could have anticipated. I think that the overscaffolding in my previous attempt limited my students creativity and autonomy. They were just waiting for me to guide them down my path rather than finding one of their own.


  Student Ownership: This lesson would be improved with a lot less scaffolding
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Squares in a Row Day 2 of 6

Unit 2: Writing expressions
Lesson 2 of 7

Objective: SWBAT utilize the structure of the checkerboard to calculate the number of different sized squares and keep track of data in a table.

Big Idea: Students will calculate the number of squares on a checkerboard without counting and will begin to notice patterns emerging in a data table.

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