## Reflection: Complex Tasks Border Tiles: Seeing Structure in Algebraic Expressions - Section 3: Investigation

This piece of student work shows a misconception on the part of the student about how to incorporate a variable into the problem. At first I thought this student was disengaged and not trying, but when I looked closer at his work, I realized that he was trying to put an x in that would make the expression come out to 36. With the expression 10x - x, if x was equal to 4, then the expression would equal 36 (which is the correct number of tiles around the border).  A conversation around this misconception is a good way to talk about the value of even using a variable in a problem like this. In fact, a student in class was sort of hinting at this idea when he asked why we had to bring algebra into the problem when we could just count the tiles around the border.  We were able to talk about a different sized garden plot that would be much larger, where algebra would help us to find the number of tiles.  You could also use this problem to talk about the value of being a "translator" of algebra - in a sense, learning a new language.

Many students in this class had trouble incorporating the variable. One way I addressed it was to keep saying, well if one side of the garden has a length of 10, and we're calling that side x, how we can describe this side that has two tiles taken out, in relationship to x.  This seemed to help.  Students got as far as writing the expressions, but we will have to discuss how they are all related in the next lesson. We were not able to cover all the material in a one hour block.

Complex Tasks: Looking at Student Work

# Border Tiles: Seeing Structure in Algebraic Expressions

Unit 2: Multiple Representations: Situations, Tables, Graphs, and Equations
Lesson 1 of 17

## Big Idea: Don't count! Students find different approaches for counting tiles around a garden and then write rules that represent their methods.

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Standards:
Subject(s):
Math, algebraic expression, Algebra, Graphing (Algebra), combining like terms, distributive property, Algebraic expressions, equation
60 minutes

### Amanda Hathaway

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