Students are introduced to the shift from additive to multiplicative thinking. The use of the array model of equal rows and equal columns allows the exploration of factors and multiples, and the associated number properties that underlie effective multiplicative strategies.

Teacher notes

  • Students are introduced to the commutative property of multiplication. A dynamic array provides a visual model to support understanding of the multiplicative relationship between factors.
  • Pobble characters create the rows and columns for the students. Students make a prediction, test their prediction and then make adjustments, if necessary, based on feedback.

Learning objects

Pobble array picture.

Pobble arrays: find a factor
Students see a given number of pobbles and a set number of gates (columns), then have to predict how many rows are required. They check their prediction by seeing if it enables the Pobbles to line up correctly and march through the gates. This is the simplest of the three objects in the series. Audio instructions are provided.

Pobble array picture.

Pobble arrays: find two factors
Students see a given number of Pobbles and must firstly select the number of gates that will enable equal rows and equal columns, then predict how many rows are required. Audio instructions are provided.

Pobble array picture.

Pobble arrays: make multiples
Students are able to vary the number of Pobbles as well as select the number of gates (columns) and the number of rows to line up the Pobbles correctly into equal numbers of rows and columns. This is the most complex object in the series.