Learning goals
- A multiplication fact is a rectangle of equal groups.
- Rows and columns can switch while the total stays the same.
- The array is the bridge from repeated addition to area models.
Array Builder
Rows, columns, multiplication
Change rows and columns and watch equal groups turn into a multiplication structure.
What this game shows · Multiplication as a Rectangle
Multiplication is a rectangle of equal rows. This game lets you change rows and columns and watch repeated addition fold into one fact: 4 × 6 is not a memorized answer, it is a 4-by-6 rectangle of 24 dots.
- Rows × columns
- an array of r rows × c columns holds r × c dots.
- Commutativity
- 4 × 6 = 6 × 4 — rotate the rectangle 90° and the count is the same.
- Distribution
- 7 × 8 = 7 × (5 + 3) = 35 + 21 = 56 — split the rectangle.
Aligned with CCSS 3.OA.A.1 (interpret products of whole numbers as equal groups).
Array builder
Rows and columns are two views of the same product.
4 x 6 = 24
Rows
4
Columns
6
Multiplication model
Who this demo helps, and where to practice next
Array Builder 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.
Array Builder 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 Arrays and multiplication, unpacked.
01 Why is multiplication an array? Equal groups
Because equal groups stack into a rectangle. 4 groups of 6 dots = 4 rows of 6 = 4 × 6. The array is what makes "groups of" visible.
02 Why does 4 × 6 = 6 × 4? Commutative
Rotate the rectangle 90 degrees and the rows become columns. The dot count never changes — that is commutativity in one image.
03 How can arrays make hard facts easier? Split & sum
Split the array. 7 × 8 = 7 × (5 + 3). The 7 × 5 sub-rectangle = 35; the 7 × 3 sub-rectangle = 21; together = 56. That is the distributive property.
04 Which grade is this game for? Grades 2–3
Grades 2–3, aligned with CCSS 3.OA.A.1. Direct ramp to area in Grade 3 and the area model in Grade 4.