Don't be PARTIAL with Partial Products!

I simply adore following Donna Boucher on Math Coach's Corner. She's low-key my role model. I wanna be like her when I grow up!

Check her out: Math Coach's Corner


Recently she wrote a blog about how the new 3rd grade concept of two-by-one multiplication includes a critical strategy called partial products.

She nails it! But can you humor me as I add a representational component from the TEK (standard)?

Let me restate it:

"Use strategies and algorithms, including the standard algorithm, to multiply a two-digit number by a one-digit number. Strategies may include mental math, partial products, and the commutative, associative and distributive properties."

One of the critical components of students understanding algorithms, is the foundation of concrete and representational models. How powerful in the problem 14 x 6 is teaching them that 14 decomposes into 10 and 4 and they should multiply each component by(or compose equal groups of) 6.  

When students can draw, shade and label their model, how much more can they justify their product as well as peer-teach!?

So go read her blog...digest it and don't forget to add the models. It's a strategy that helps bridge the gap in connecting to the algorithm. And honestly, when the standard says "strategies may include...commutative, associative and distributive properties.", this representational model helps students internalize the commutative and distributive property without them ever knowing they are using them. They may not need to know those terms, for example:

(10 x 6) + (4 x 6) = (4 x 6) + (10 x 6) and students will often write them both ways on accident. But that opens the door for discussion about whether the product will be the same.

Exit Ticket:
Using the model, write a number sentence that would help you solve the product of 14 x 6.