### 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.

These are fun puzzles! Years ago, my then-8yo daughter saw a similar puzzle in my older son's algebra book and was so thrilled at being able to solve some "teenager math" that she proudly made up a balance puzzle of her own. She is 17yo now---doesn't time fly?

I've printed out your worksheets for my current 8yo, who says, "I don't like math, but I love algebra." Go figure!
Anonymous said…
I was looking for a worksheet like this forever! THis is the best! I really enjoy doing algebra!
Anonymous said…
I haven't posted much of my own content here awhile

This is NOT original content but a copy of the balance problems from Mammoth Mathematics Multiplication 2 Book. Unless the author of this blog is the author of that title also...
Maria Miller said…
Hi Anita,
I am indeed the same person... Maria Miller, and this is my blog, and I'm the author of that said book. : )
Unknown said…
Thank-you very very much Maria!! I have improved a lot!!
Anonymous said…
Thank you. But, I am looking for the problems where the students are asked, " One Z weighs as much as ______ Xs?
Unknown said…
Thanks for this! I am editing it to fit my needs for 4th grade science but this is getting me started!
Anonymous said…
You've helped a lot my daughter(makayla) didn't know how to explain the pan balance to me and I've never seen it before now I have a clear understanding thanks a lot. crystal
crystal said…
You've helped a lot my daughter(makayla) didn't know how to explain the pan balance to me and I've never seen it before now I have a clear understanding thanks a lot. crystal
Very well explained.. now I can teach this one to my kids perfectly. Thanks a lot.