Learning goals
- 23×14 means (20+3)(10+4), so there are four partial products.
- Every digit keeps its place-value weight inside the box.
- The same model later supports polynomial multiplication.
Partial Products Box
Why multi-digit multiplication works
Change the factors and let the area model reveal the partial products. The four boxes are the visible source of the standard algorithm.
What this game shows · Partial Products
Partial products turn 23 × 14 into four labeled rectangles. Each rectangle keeps its place-value weight, so the standard algorithm becomes a visible 2 × 2 area model.
- 2 × 2 box
- one row per place value of factor A, one column per place value of factor B.
- Partial product
- the product of one row label × one column label.
- Sum of boxes
- four rectangles summed = the full product.
Aligned with CCSS 4.NBT.B.5 (use place value strategies to multiply).
Partial products box
The box fills itself from place value, so the algorithm has a picture.
23 x 14 = 322
10 x 20 200 | 10 x 3 30 |
4 x 20 80 | 4 x 3 12 |
First factor
23
Second factor
14
Multiplication model
Who this demo helps, and where to practice next
Partial Products Box is built for students who can recite facts but need to understand the array, area, or partial-product structure. It gives the page a clear search purpose: learn the model, manipulate it, then continue into the matching grade-level practice.
Partial Products Box helps when a student can copy a procedure but cannot explain why it works. The demo slows the idea down into a visible model before sending the learner to guided missions.
How to play
- 1 Build the visual model first; do not start with the formula.
- 2 Name the rows, columns, or partial products out loud.
- 3 Use the topic hub for guided missions after the visual structure is stable.
Continue with guided practice
FAQ
Tap to expand Partial products, organized.
01 Why are there four products in a 2-digit times 2-digit problem? 4 rectangles
(20 + 3)(10 + 4) = 20×10 + 20×4 + 3×10 + 3×4. Each digit pair becomes one rectangle in the 2×2 grid.
02 How does the box prevent place-value mistakes? Place value safe
Every box keeps its true weight: the top-left is hundreds, the corner ones is just ones. Compared to the column algorithm, nothing collapses prematurely.
03 Why does the standard algorithm work? Algorithm = box
Because the partial-products box does. Cross-multiplying the digits in columns is just a compact reorganization of the same four rectangles.
04 Which grade is this game for? Grades 4–5
Grades 4–5, aligned with CCSS 4.NBT.B.5. Good bridge from the area model to the column algorithm.