This document provides instructions for using a pan balance applet to help students understand numerical expressions and equality. The applet allows students to enter expressions into red and blue pans and see if they balance when equal. It is meant to show students that equality is a relationship, not an operation. The instructions describe how to enter expressions, move the cursor, and see results and errors. It also provides tips for analysis and use of the applet in the classroom.

1. Pan Balance
• Use this tool to strengthen understanding and computation of numerical expressions and equality. In
understanding equality, one of the first things students must realize is that equality is a relationship,
not an operation. Many students view "=" as "find the answer." For these students, it is difficult to
understand equations such as 11 = 4 + 7 or 3 × 5 = 17 – 2.
• Click the PAN BALANCE title to access applet
• Reviewed by Hoai Le and Kelly LeCoq

3. Using the Applet
• Begin by clicking in either the red or blue pan. Enter an expression using either the keyboard or the keypad at
the bottom of the work area.
• Special keypad buttons:
• Home will move the cursor to the beginning of the expression.
• End will move the cursor to the end of the expression.
• ← will move the cursor one character to the left.
• → will move the cursor one character to the right.
• Notes on entering expressions:
• Using the keyboard, multiplication should be entered using *.
• Using the keyboard, division should be entered using /.
• x2 and x3 are used to indicate squaring and cubing a number. They must be entered using the keypad. Each
operation can be used only once.
• A number in front of parentheses is recognized as multiplication. For example: 3(4 + 8) is calculated as
3×(4 + 8).
• The result of your expression will be shown above the selected pan. Invalid entries are indicated with a
message.
• When you are finished entering an expression in one pan, click on the other pan to enter an expression. The
pans will move up and down depending on which expression is greater. When the expressions are equivalent,
the pans will balance and the full equation will be entered into the Balanced Equations table.
• At any point, you can click the Reset Balance button to remove the expressions from the pans. You can also
click the Reset Table button to remove all equations from the table.

4. Analysis
Strengths Weaknesses
*Simplicity *More explanation
*Differentiation-content needed to encourage
level can vary understanding
*Interactive *Need focused
instruction
*Allows for visual
representation of equality *No formative
*Easily accessible assessment available

5. Evaluation of Applet

6. A Problem-Based Task
• Task:
• Connection to the standards and/or big ideas:

7. Questions to Ask to Assess and
Advance Student Thinking
• Launch (Task Set-Up):
• Explore (During Task Implementation):
• Summarize (As students share findings,
strategies, reasoning, etc.):