Array and Area Models

Read the PDF document above and then have a look at some of the interactive models and examples that follow.  

This section contains activities and tools that lead from the array model to the area model.

Interactive Array Models

When the width and height are greater than 10 the model automatically partitions the array (see right).  Compare this to the area and grid models below.

This interactive model allows you to see the array and the traditional bus stop method.

Drag the sliders in the top left and bottom right to change the height and width of the array.

Multiplying positive and negative indices with double sided counter arrays

This representation models integers as opposites and multiplication as grouping.   See integers for more details of opposites.

Interactive Area Models

The area model can lead to a better conceptual understanding of the grid method.

Area model multiplying integers - Desmos

The model below represents the area model for multiplication and uses the same colours as Dienes Blocks and Algebra Tiles.  This helps students make the connections between number and algebra.

Multiply decimals using the grid and then drag the coloured tiles onto the grid model.

Multiply decimals using the grid and then drag the coloured tiles onto the grid model.

The area model can also be used for fractions.  Change the horizonal and vertical dividers using m and n.  Drag the orange and green sliders to shade the fractions.  Shade the product using the purple slider.

Interactive Algebraic Area Model

a(bx+c) - Desmos

Change a, b, c and x using the sliders above

Complete the square.

This model uses a zero pair to remove the square and then adds the constant term to complete the expanded form of the quadratic.