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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A Week of Equation Exploration

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My fifth graders started to explore equations this week.  They’ve created number models and solved for the unknown, but most of their experience has been using one method.  They tend to substitute a number in for x and then check their answers.  If it doesn’t work then they guess a different number.  This guess-and-check type of of strategy has worked well in the past with 1-2 operations and with x on one side of the equation, but this unit that I’m teaching starts moving students towards using a more formal substitution method.

So, in an effort to improve students awareness of equations I decided to use a few specific activities.  My intention was to give students an opportunity to see equations in many different settings.  I started off the week with a few Nearpod review questions related to order of operations.  The class worked in groups of 2-3 to solve the problems.  Students definitely needed a review on this topic because it seems like forever since they’ve completed problems like this.

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The next day students used SolveMe mobiles.  I drew a balance on the board and the class completed a few different examples.   Students worked in groups to find out what each shape represents.  This class used these types of mobiles earlier in the year with a certain degree of success.  This particular math unit will put the reasoning behind these mobiles into a better context.

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How much is the triangle worth?

Students were given homework that night related to equations.  After checking it over I noticed that students needed additional practice with the properties of numbers.  Specifically, students were struggling a bit to identify the correct property.  Students completed a few different problems involved with properties the next morning.

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I reviewed the terms with the class and connected them to what happens when a variable is substituted for a number.  Students were making progress.  They were continuing to use the guess-and-check substitution method and checking their work to see if they’re correct.

Next week, students will start to investigate inequalities.  This is one of my favorite lessons as students observe that there can be multiple answers for an equation.  While some students are  stoked to learn about this, others get confused.  At this point, many students have been conditioned to look at equations as problems that have one solution.  Having multiples solutions, or solutions with a specific range of numbers isn’t usually the norm at the fifth grade level.

While looking for a few new ideas I came across Always, Sometimes, Never.

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I’ve heard of ASN, but haven’t had a chance to try it out in the classroom.  I paired up students and modeled one of the solutions.  Students were off to the races to think about statements and label them as always, sometimes, or never true.  The discussions about numbers were fantastic.  I went to each group and asked questions to help direct students towards possible solutions.  While this was going on I could tell that students continued to have questions.  These questions impacted whether a statement was sometimes, always, or never true.

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The discussion that stemmed from the above questions provided an opportunity for students to discuss their understanding of numbers.  Overall, this discussion, along with the previous activities will help set the stage for students as we continue to discover and solve equations.

Next week, students will  use the distributive property to solve equations.  They will also delve deeper into a study on inequalities and how they’re represented outside of the classroom.