Equations and Rules

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My fifth grade crew is making progress.  Last week we explored equations and learned about the distributive property.  My district has an institute day and MLK day, so it ended up being a three day week for the students.  Over the weekend I came across Greta’s amazing blog and found some great ideas that I could use immediately.  If you haven’t had a chance to check out her blog, stop, and get over there.  I actually used her Desmos activity this morning.

Today was our first day back and equations was on the agenda.  The day started off with a brief review of the distributive property and equations.  We then dove into a different activity related to creating rules for situations.

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The students understood the question and the situation.  A few even commented that this could happen outside of school.  You think?  So, after reading about the situation students moved to the questioning portion.

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From here, students wanted to put together 19 hexagonal tables and count them all up.  Some students started to think out-loud about creating some type of rule so the class didn’t have to connect all of the hexagons together.  After more discussion and many, I mean MANY attempts at creating a rule, we moved back to the drawing board.  Shortly after the attempt session, I brought the class to looking at different strategies.

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I brought out the hexagon pattern blocks and put them together.  The class then filled out the table and graph.  We noticed and wondered about why the graph went up the exact same amount every time, except for the first n.  The class knew that four was an important number as that’s how much the # of guests went up each time.  The trouble came when solving for just n on the table as the rule couldn’t be n + 4.

Students met in groups and discussed the topic of creating a rule for this situation.  They needed the rule for the next groups of questions.

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Some students were successful and came up with a rule that worked.  Many students started to notice that their rules were different.

A few arguments came around this, but what was interesting was that the rules worked.  Students observed that the rules could look different, but simplified, they were the same.

The last part of this task asked students to create an expression to represent the number of tables needed.

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This was more challenging.  Even if students were able to create a rule for the first part, this caused headaches.  Students had to look at the rule that they created and find a way to rearrange it to match a different expression.  Some students were successful with this, others not.  I had all the students turn this sheet in and briefly looked over the results.  I was excited to see that about a quarter of the class had everything correct the first time.  This means that the class will be exploring this topic further as students get a second attempt tomorrow.

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