Maximum size: 30 x 30
= 5 x 5
= 25


Allow rectangle re-sizing
Number of active sliders

Share a Link

Those you share this with will see the current array and settings. They will not be able to change the options above.

Copy Link
- copied to clipboard


Make a new rectangle

Change the size of the rectangle by entering whole numbers (up to 30) in the boxes. Then press the MAKE button.

Drag the sliders

Drag the slider handles to divide the rectangle into smaller parts.

View partial products

Watch how the equation changes depending on the position of the sliders.

Show or hide answers

Toggle these buttons to show or hide the results of the equation.

The following are only found in the Educator Version:

Go to Options to change settings

Change the settings of the Partial Product Finder in the Options panel.

To Open the Options panel, select the Options tab or go there now.

Share the current rectangle and settings

To share the current rectangle and its settings, find Copy Link in the Options panel. go there now.

Note: the Options panel is not available in the shared version, so students can't change the settings.


Partial Product Finder allows multiplication combinations to be represented as a rectangle, or array, with dimensions that match the combination. The sides of the rectangle can then be divided into parts to reveal partial products that make up the total product. This helps students develop the flexibility and conceptual understanding required to build fluency with basic facts and strategies for multiplication of larger numbers.

Go to the educator version to create your own arrays.

We Welcome Your Feedback

Help us guide the ongoing development of this app by sharing your reactions or suggestions.

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Partial Product Finder is brought to you by The Math Learning Center, a nonprofit organization serving the education community since 1976. Visit us at, where you can learn more about our organization, the Bridges in Mathematics PK–5 curriculum we publish, and the many free math education resources we provide, including a robust suite of free virtual manipulatives for use online or as downloadable apps for a variety of operating systems, including Apple iOS and Google Chrome.

Version 1.0.16
Please use portrait view