Array Model and Partial Products

ND State Standard
4.NO.NBT.3 Apply place value understanding to round multi-digit whole numbers to any place.

4.NO.NBT.5 Multiply a whole number of up to four digits by a one-digit whole number and multiply two-digit numbers. Show and justify the calculation using equations, rectangular arrays, and models.

Let's investigate how to use the Area Model as a strategy for Multiplication.   The area method is a powerful method as we continue to move from the concrete to the more abstract versions and can be utilized with fractions, decimals, and even within algebra!

• Investigation 1 - Array Method (Area Method)

• Investigation 2 - Array Method (Area Method)

• Investigation 3- Array Method (Area Method) and Partial Products

• Investigation 4 - Partial Products

• Investigation 5 - Partial Products

First, provide an estimation for each situation.  

Then, solve each scenario listed below using the Array Method (Area Model) and Partial Products.  

Record yourself explaining your steps and showing how you solved, make sure to comment on your estimation and how you chose to round and then estimate.

• Two digit number  x two digit number

• Two digit number with a nine in the ones position x two digit even number with a nine in the tens position. 

• Three digit odd number x three digit even number

• Two-digit number with a five in the tens place x two-digit number with a zero in the ones place.

• Three-digit number with a seven in the hundreds place x three-digit number with a six in the tens place and zero in the ones place.

Box Method (Area Method) Notes

The Box Method, also known as the Area Method, uses place value and a visual representation to multiply numbers. It decomposes numbers into their place values, and each part is multiplied separately.

The grid visually represents how each part of the numbers interacts, helping learners understand how multiplication works with larger numbers.

Partial Products Method Notes

Unlike the Box Method (Area Method), the Partial Products Method doesn't rely on a visual grid, but it still emphasizes the importance of understanding place value and breaking down the multiplication process into simpler steps.

Both methods help learners understand the concept of multiplication by decomposing the numbers into manageable parts, making it easier to multiply larger numbers and reinforcing the understanding of place value.