## Reflection: Staircase of Complexity Rectangular Gardens - Section 3: Rectangular Gardens

In all of today's classes, students reminded me that my favorite thing to hear is, "Wow, this is easy!" as they get to work on #'s 4-6 on the back of this assignment.  That's exactly what must happen here for this assignment to be successful.  The more students have the conceptual understanding necessary to feel confident working on these first few problems, the more perplexed they'll be when they get to the ones that don't work out so nicely!

Even more, that act of saying, "this is easy!" builds a kid up and makes them feel like they're humming along, only to run up against a problem like #10, where they're asked to draw a garden with P=20 and A=26.  If they've felt successful up to that point, they'll be more willing to try and figure out what's going on, and then eventually to have the confidence to say, "Wait, something is not right here..."

Contrast that with a student building on weaker foundations, who can't quite tell the difference between their own inability to solve a problem and a problem that is actually impossible to solve.  The depth of understanding that I want students to achieve is inaccessible to such a student.

When I hear student excitement about this assignment, my anticipation builds for tomorrow's lesson, in which students will see another representation of the rectangle situation, as their doubts about the more difficult problems are justified.

"This is EASY!"
Staircase of Complexity: "This is EASY!"

# Rectangular Gardens

Lesson 1 of 21

## Big Idea: Just when students are at their most confident that they've got this task down, there will be a little twist to propel us into this new unit.

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43 minutes

### James Dunseith

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