Connecting Place Value Disks to Partial Products
This Grade 4 Eureka Math skill teaches students to connect place value disk models directly to the written partial products algorithm for multiplication. The value of the disks in each column on the place value chart corresponds to a partial product in the written algorithm. For example, 3 times 21: the ones disks show 3 times 1 = 3 (3 ones), and the tens disks show 3 times 2 tens = 6 tens = 60. These values become the partial products in the written record: 3 and 60, summing to 63. This conceptual bridge is taught in Chapter 11 of Eureka Math Grade 4.
Key Concepts
The partial products algorithm is a written method to record the multiplication shown on a place value chart. The value of the disks in each place value column corresponds to a partial product in the algorithm.
Common Questions
How does a place value disk model connect to partial products?
Each column of disks on the place value chart corresponds to one partial product. The ones column value equals the partial product for the ones, the tens column for the tens, and so on.
How do you solve 3 times 21 using disk model and partial products?
Disk model: 3 groups of 2 tens = 6 tens (60); 3 groups of 1 one = 3 ones. Partial products: 3x1=3, 3x20=60. Sum: 3+60=63.
What does each row in the partial products written record represent?
Each row represents the product of the single-digit multiplier and one place value component of the larger number (ones, tens, hundreds, etc.).
Why use disks and partial products together?
The disks make the multiplication concrete and visible, while the partial products record it symbolically. Connecting both models helps students understand why each step in the algorithm works.
How does this model prepare students for the standard algorithm?
Once students see how each disk column value translates into a partial product row, they can understand how the standard algorithm combines and compresses those partial products using carrying.