Reflection: Advanced Students "The Answer" vs. "The Problem" - Section 3: Problems Without Words

 

I was surprised to see that in every class, there have been a handful of students who take a purely numerical approach to this problem, and notice that the number of groups in each family is equal to the sum of twice the previous total plus each of the groups before that.  See photo: You May Have Noticed.

It's cool how many kids discover this pattern in the numbers, but I've kept a poker face about this when students point it out.  I act like this is a curiosity that may or may not be a coincidence.  I ask them to prove it, visually.  The majority of my students will prefer to create some sorts of diagrams, and they need help talking about the patterns they see.

It's equally important to push those who think in terms of the numbers to try to visualize what is happening and why.  It's one thing to notice a complicated number pattern.  Much harder is to explain, by using the diagrams, why this pattern works.

Tomorrow, we'll look at another problem without words who solution also consists of Fibonacci numbers, without skipping any.

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"The Answer" vs. "The Problem"

Unit 6: Mini Unit: Patterns, Programs, and Math Without Words
Lesson 1 of 10

Objective: SWBAT use words to define problems for puzzles that lack words.

Big Idea: It's a challenge for many students to focus on solution pathways rather than solutions. This activity gives students the chance to define problems, rather than just looking for a solution.

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Subject(s):
Math, Patterns (Algebra), Algebra, problem solving
  43 minutes
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