November 18, 2007

Pan balance problems to teach algebraic reasoning

Today I have a "goodie" for you all: a free download of some pan balance (or scales) problems where children solve for the unknown:

Just right click on the link and "save" it to your own computer: Balance Problems (a PDF). This lesson is also included in my book Math Mammoth Multiplication 2 and in Math Mammoth Grade 4 Complete Worktext (A part).

The problems look kind of like this:

These can help children avoid the common misconception that equality or the equal sign "=' is an an operation. It is not; it is a relationship.

You see: many students view "=" as "find the answer operator", so that "3 + 4 = ?" means "Find what 3 + 4 is," and "3 + 4 = 7" means that when you add 3 and 4, you get 7. To students with this operator-view of equality, a sentence like "11 = 4 + 7" or "9 + 5 = 2 × 7;" makes no sense.

You might also find these resources useful:

Balance word problems from Math Kangaroo

Algebraic Reasoning Game - a weighing scales game that practices algebraic reasoning

Interactive Pan Balance with Shapes

Balance Beam Activity
A virtual balance that provides balance puzzles where student is to find the weights of various figures, practicing algebraic thinking. Includes three levels.

A Balanced Equation Model from Absorb Mathematics
An interactive animation illustrating solving the equation 4x + 6 = x - 3. Drag the green handles to balance each side. Click the arrow button to reset the animation. On the right side, you'll see links to similar animations of equation solving using a balance.
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