## Reflection: Problem-based Approaches Tower Task: Exploring Explicit Formulas - Section 4: Closure

I always enjoy teaching this lesson because students can use something concrete (wooden cubes) to actually build the towers and examine the pattern.  Students did a great job with finding the pattern.  Looking at page 2 of the student work, you can see that I provided additional scaffolds for some of my struggling learners.  Rather than leaving the question in paragraph form, I broke it down into a step-by-step approach that they could more easily follow.

This was, however, the first year that I did not have any groups of students come up with the explicit function by looking at the pattern and constructing the towers.  Students were very uncomfortable with the idea of generalizing the pattern for any height tower.

I was able to question students and guide them to determining how to write a generalized formula.  There are a few ways to think about the generalization.  The group that got the closest and helped to lead the class discussion noticed that the "legs" of the tower were always one block shorter than the tower height.  This eventually led to a student from another group coming up with x-1 for the length of each leg.  Once we had that algebraic representation most groups were able to come up with the explicit formula and check that it worked.

In the closing activity, I wanted to see if students were grasping the difference between recursive and explicit formulas.  From the attached student work you can see that students were more comfortable with describing the recursive formula than the explicit.  In either case, this ticket out showed me that we still had some work to do with understanding recursive and explicit formulas.

Problem-based Approaches: Closure Reflection

# Tower Task: Exploring Explicit Formulas

Unit 1: Functions
Lesson 3 of 18

## Big Idea: Manipulatives help students build a foundation for understanding abstract concepts. This lesson allows students to use manipulatives to gain a concrete understanding of the concept of a function.

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Standards:
Subject(s):
Math, Algebra, function, recursive, explicit, manipulative, 9th grade
38 minutes

### James Bialasik

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