Balances

Illustration from ,Coming To Know Number,  G. Wheatley, 1999

Balance Scales

Classroom students are accustomed to doing addition and subtraction algorithims in a vertical method or a horizontal method.  This is perceived as a operational procedure and lacks purposeful math operations.  When students see 5 + 6 = __, they recognize this as "put in the answer".  This is lacking in depth to their math experience.  It is more of a rote activity.  The optimum way for the students to grasp math ideas is in a setting where they can make sense of their activities instead of just following sets of rules.

Balance scales have been proven to be interesting and worthwhile to enable students to learn addition and subtraction.  Balance is an innate experience.  Children know that balance is needed to walk, ride a scooter, ride a bike, walk on a balance beam on the playground and especially when sharing.  We have to be sure that there is a balance of portions so it is fair to all.

If a teacher uses the balance scales, there is no operational sign, and no mechanical responses.  It provides a visual image that commands a childs mind to think about what is there and what is missing.  The student must examine the scales and process how to act.  If your classroom has a pan balance, it is useful for students to manipulate blocks on both sides to create balance.  This is not mandatory.

Any variety of problem and operation can be achieved on the balance scales.  For our purposes, we will show examples that can be used with older first and second graders.  When we start to put combinations of numbers together (addition) or deconstruction of numbers (subtraction) the balance scales are a meaningful example.

Illustration from, Coming To Know Number, G. Wheatley, 1999

The balances scale at the top of the page illustrates an addition operation. (e.g. 7 = 3 + __ ).  The 3 and the 4 can be be reversed.  This is the communicative property of addition.  That is for third grade.  We could pose the question, "What could we put with 3 to balance 7?  The larger numbers can be on the left or on the right.   As the example at the top of the page, we can pose this scale activity as an addition or subtraction problem. 


The balances scale above can be considered an addition operation. (e.g. 7 = 3 + __ ).  The 3 and the 4 can be be reversed.  This is the communicative property of addition.  That is for third grade.  We could pose the question, "What could we put with 3 to balance 7?  The larger numbers can be on the left or on the right.

I have used the balance scales to teach elementary math in grades first through fifth.  As soon as we start to put combinations of numbers together to find sums and differences, I found that the scales brought out a very attentive and engaging classroom.  What was this, what did it mean, what are we supposed to do?  What are we looking at?  It is a set of balance scales.  They are balanced.  We do have some clues.  What are the clues?  What do we see on the left side of the scales?  What is on the right side?  Is there a value missing?  How can we identify that value?  Students have a visual method of learning.  They have been learning in a similar way with tens frames.  Let them continue this strategy to "move the dots around" mentally or bring out the frames physically to continue looking at numbers collectively.

As the students get more familiar, let them tackle this activity with a partner.  The strength in this lesson is for the student to explain their solution and proof to the class.  If students do not agree, the real learning begins.  This interactive approach increases strategy methods learned from each other.  The students defend their findings and take responsibility for their own perceptions.

Source material:  Coming to Know Number, Grayson Wheatley, 1999