Partial Products

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When your child first learns to multiply two two-digit numbers, she will use the area model. This visual tool illustrates how to decompose numbers and find four different products. As her skills improve, she will move from this pictorial model into a concrete method called partial products.

Using partial products to solve forty-three times fifty-six, looks like this. She will start by multiplying tens times tens. Next, she will multiply tens times ones. Then, ones times tens and last, ones times ones.

These are called partial products. This is the product, or answer. Using partial products removes the pictorial step but places the same emphasis on the actual value of the numbers being multiplied.

By the end of fourth grade, your child will use the standard algorithm to multiply! This algorithm is used to develop an abstract level of understanding. If she jumps right to using the algorithm,
she will not develop the conceptual understanding of multiplying two-digit numbers.

The standard algorithm has fewer lines of work because your child has a greater understanding of what she’s multiplying! Your child knows the actual value of these products because she has a strong understanding of partial products.

And that’s good to know.


This video addresses Common Core Grade 4 Standard Number & Operations in Base Ten: Use place value understanding and properties of operations to perform multi-digit arithmetic.

(4.NBT.5) Multiply a whole number of up to four digits by a one-digit whole number, and multiply two two-digit numbers, using strategies based on place value and the properties of operations. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models.

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