Partial Product Finder is a free website that allows multiplication combinations to be represented as a rectangle, or array, with dimensions that match the combination. This helps students develop the flexibility and conceptual understanding required to build fluency with basic facts and strategies for multiplication of larger numbers. Students can create arrays up to 50 by 50.

Students type in two numbers to multiply and the site creates an area model.

For example, here’s a 15 by 15 array:

Students can then move the sliders (up/down on the right side & left/right across the bottom) to partition the area and create partial products. You can break the array up into as many sections as you want.

Here’s the 15 by 15 array divided up into 4 sections:

Here it is again divided up into 25 sections:

Note that the finder creates an equation that uses parentheses to describe the partial products.

One thing I like is that the partial product does not actually give the partial products. I think this encourages students to partition the area into partial products that they know.

The site is a good way for students to develop strategies for breaking down larger multiplication problems that engages their reasoning and number sense and doesn’t rely on rote memorization.

Using area models and partial products as a way to represent multiplication shows up on the TABE 11/12. This site provides some excellent practice to help students understand how to use the representation.

Area models are also excellent visual models that can help support students develop a conceptual understanding when they learn algebra.

Working problems through on this site can make working multiplication more engaging and meaningful.

Please let us know in the comments how you use the site with your students.