Tower Task: Exploring Explicit Formulas

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Objective

SWBAT define a situation both recursively and explicitly and explain the relationship between the formulas.

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.

Do Now

3 minutes

Slide 1: As students are entering the room they can begin working on this error analysis question.  I like to use error analysis as a way to have students attend to MP3 on critiquing another student’s work.  Finding errors or proving that a solution is correct forces students to a deeper level of understanding than simply carrying out a process or procedure.

Opening

5 minutes

Pass out the tower task worksheet or display it on the projector for students to read and begin going through the problem solving process.  Because this is at the beginning of the year, I like to take some time to model the habit of taking time to understand the problem.  The first thing I do is ask students to read the problem a second time.  Students often rush through reading a math problem and basically skim for key words, numbers, etc.  Having students slow down and process is a crucial step in solving any problem.  Next, I ask students to talk with their partners to decide how they will define a 5-block tall tower or a 10-block tall tower.  During this time I pass out 25, 1-inch cubes to each pair of students.  The number 25 is chosen strategically so that students can build towers 1-5 but then will have to abstractly determine how to find the remaining towers.  Once students are finished with their discussions about how to define the height of the tower, I do not have groups share out and I do not discuss the definition.  It is important to the problem solving process that students understand the problem and work through it (MP1).

Investigation

25 minutes

Closure

5 minutes

Slide 3: Before students leave I want to make sure they are starting to develop an understanding of the difference between recursive and explicit formulas.  This understanding will be crucial as we move forward in the functions unit.  Students can certainly cite specific examples from the problem that they just solved but I want to make sure that their definition shows some generalized understanding of the difference between the two types of equations.