Relooking at a Balance to Explain Algebraic Equations

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Math trends come and go, but the thing to always keep in mind is; “Did that activity make a connection for my students?”

My first field trip for my students comes on the second week of school, and it’s called the 24 Hour Experience.  We take this trip twice, splitting our class of 8th graders to make things more manageable for the nature of the trip.  We bus our students out to a local state park, where we infuse education, culture, sports, team building and socialization in one big package.  The morning is the academic time, where each core class (math, language arts, science and geography) has a particular activity related specifically to the park.  After lunch, our students take a three hour canoe ride, hike to the fire tower and experience a different view of their geography.  We then focus on team building activities before the students split into groups and cook their own dinner.  Around dusk, we venture out on the hiking trails for an all night hike.  It can be a quite intensive activity for our students, and we have be very fortunate to not have any mishaps on the trip.

When I joined the 8th grade team and was informed of the nature of the trip, I had to decide what type of activity I would do at the park.  Since the focus for 8th grade math is Algebra, I tried to find an activity that I could always reference back to throughout the year.  Illuminations gave me the spark of “Geology Rocks” and I use this activity still.  Since many of my students are still transitioning from concrete to abstract learning, I went to the wood shop and assembled a few crude balances to use.

Using counter-balances they can find at the site, students need to measure the weight of four unknown objects.  These become single step algebraic equations that students are familiar with and know how to solve.  Using this background knowledge, they then transition to the Illuminations activity involving two step equations.  Many students still have to draw diagrams of the formal algebraic equations, but that is a logical scaffolding piece at this time.

Since we are using natural materials (pebbles found around the river), when we return to the classroom I have students share their data.  Conversations about why there are different values and what they represent lead to many different teachable moments.  I also have students find a mean value to the weight of a pebble, incorporating data analysis with the lesson.

Strengths of using the balance approach for equations are numerous.  The fact that it can be recreated as a physical model helps your tactile learners.  Using diagrams to translate equations into pictures addresses visual learner’s needs.  It also allows students to form connections when you have negative values for either x or the constant.  They have more confidence and willingness to attempt problems because they have an understanding conceptually of the equation.  The most important strength I have found is longevity.  I have talked with students three years later and they can remember the activity and why we did it.  Many of them admit that they still tackle “new hard” problems by first visualizing the scale model and some still create the drawing.

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