Interactive Multiplication Array: Visualize Times Tables

Discover how multiplication works by arranging colorful shapes into visual arrays. Perfect for understanding multiplication as “groups of” objects, this tool helps students see patterns and make connections between different multiplication facts.

Controlling the Multiplication Square

In the default manual mode, you can simply click anywhere on the grid, and the shapes will arrange themselves to show the product. Alternatively, you can use the buttons:

Numbered Buttons: Click any of the numbered buttons along the axes to show the corresponding times table.
Random: Displays a random product.
Arrow: Moves to the next value in the current times table sequence.
×: Clears all shapes from the grid.

Multiplication Arrays

This activity uses shapes with two colors to correctly represent multiplication arrays. For example, the product 2×6 represents two groups of six. Using two colors ensures that each group of six is clearly distinct. The default shape is circles for clarity, but you are free to choose fish or cards using the shape style selector.

Modifying the Grid’s Appearance

You can change various aspects of the multiplication square’s interface:

Show Products: Click this to show all the products in the background, like a traditional multiplication square.
Show Headers: Toggles the visibility of the numbered buttons along the axes.
Numbering Direction: Switches between numbering the shapes vertically or horizontally.
Side Shapes: Determines if unused shapes are visible off-screen or hidden completely.

Shape Numbering

By default, every shape is numbered. You can change this using the number style control:

None: Hides all numbers on the shapes.
All: Shows a number on every shape.
Last: Shows a number only on the final shape, which represents the answer.
Sequence: Displays the multiples (e.g., 3, 6, 9…), described in more detail below.

Numbering Direction

The arrangement of numbered shapes in the grid can be set to either horizontal or vertical. This setting also affects the sequence when the next button is pressed.

Automatic Mode

To start the automatic mode, press the play button. This reveals the timer slider, which controls the speed. The activity will then cycle through the multiplication facts automatically, which is a great tool for classroom recitation.

Learning Concepts

This activity reinforces the concept of multiplication as repeated addition and demonstrates how multiplication is a faster way to count ordered objects.

It is also an excellent tool for showing that multiplication is commutative. Students can clearly see that 4 × 3 and 3 × 4 are just different orientations of the same 12 shapes. You can also use the grid to show why square numbers are named as such and why they always lie along the diagonal.

Multiples of a Number

To view the multiples of a number, it’s best to change the shape style to balls or cards for clarity. Then, set the number display type to sequence. The grid will now display multiples in a sequence, either horizontally or vertically depending on the numbering direction.

For foundational skills, there is also the Addition and Subtraction Facts activity.
The Number Explorer uses animated shapes to teach about division, prime numbers, and more.