## Reflection: Diverse Entry Points "The Answer" vs. "The Problem" - Section 3: Problems Without Words

It's amazing how emotional some of my kids will get about some dots on a page.

In one of my classes, some students found this so frustrating that they were very angry at me during class.  Now, in the long view, I know that being frustrated is an important step toward feeling the thrill of discovery.  But in the immediate term there's a thin line between healthy frustration and disengagement.  I saw a few students disengage today, and when I saw that, I knew that I had to make some adjustments on the fly.

First, I asked everyone to flip over their papers and write questions on the back of the page.  I told them to start simple, and then to ask harder questions as they went along.  After a few minutes, I asked them to read their questions, and this helped us start to define vocabulary.  With a few words defined - cluster, row, and group in this case - I asked them to write a few more questions that used these words.

After a few more minutes, we framed the main question by using those three vocabulary words.  "How many CLUSTERS are in the GROUP with 5 dots in the bottom ROW?"

Then I said that I was going to steal and share a few ideas from some students in the class.  I pointed to one student who'd pointed out that each group begins with a line of dots and ends with a "pyramid".  I drew these starting and ending points on the board.  Then, I pointed out another student who'd started by very simply placing one dot in the second row.  I asked if anyone else had drawn this, and some hands shot up.

"After we draw this diagram, what can we do next?" I ask.  I got two different answers.  One student told me to add another dot, and another told me to move that one dot.  What's brilliant is that these two students described the two moves necessary to systematically find all the possible clusters.  Add one dot at a time, and move it to all possible locations.  If I was writing an algorithm, that's what it would say!

These moves were just enough to make sure that our frustration stayed productive, and it was exciting to see how kids continued by implementing their plans.

Diverse Entry Points: Scaffolds for Frustration

# "The Answer" vs. "The Problem"

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

## 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