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.

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