## Reflection: Staircase of Complexity Kitchen Tiles - Section 2: Investigation

My students struggled with this task!  With that said, I found it to be very engaging for them and I ended up breaking the content into two class periods.  The first class we worked almost entirely on part a. of the task. I assigned part b. for homework and we discussed it in depth the next day (with some review of part a. as well).

Here's where students struggled with Part a.

Students had no trouble at all identifying a pattern or recognizing what was happening in the diagrams.  They struggled with the part of Fred's expression that includes the (b - 1).  All students could see where the + 10 was coming from.  Most students could also articulate why the diagrams were adding for shaded tiles each time. What students had a lot of trouble recognizing was the link between the diagram number and what multiple of 4 was added to the border.   Before I teach this lesson again, I would probably show students more example of functions or In/Out tables that included this same kind of pattern (that is, having the change be directly related to the In value itself).  Another activity that would be nice to do with students who struggle with this content is in the TERC EMPower Algebra curriculum (Seeking Patterns, Building Rules) called Banquet Tables.

I actually think it was helpful for students to look at and try part b. even if they did not have a full understanding of the expression in part a.  Once they see that five inner tiles will lead to + 12 shaded tiles, they may have an easier time understanding where the multiples of 4 tiles are going in the diagrams. Again, students may need some guidance connecting this to the (b - 1) piece of the task.

Scaffolding the Lesson
Staircase of Complexity: Scaffolding the Lesson

# Kitchen Tiles

Unit 2: Multiple Representations: Situations, Tables, Graphs, and Equations
Lesson 4 of 17

## Big Idea: Students explain the reasoning of others and make use of structure as they make sense of the form of an expression as it relates to a real world context.

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60 minutes

### Amanda Hathaway

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