Students are supported in making 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 supported to develop multiplicative thinking through exploring the relationships between word problems, equations and arrays; between multiplication and division; and between factors, multiples and 'remainders'.
  • In the three 'arrays: word problem' objects, students are provided with a word problem, which they convert into a number sentence then solve. For example, 'When 21 is divided by a number the answer is 4 remainder 1. What is the number?' becomes 4 x ? + 1 = 21 or 21 ˜ 4 = ? rem 1. Students are supported as they create either a multiplication or a division number sentence. An array is used as a visual model for the number sentence to show if the correct number has been found.
  • Printouts are available for all learning objects.

Learning objects

 Arrays picture.

Arrays: factor families
Students make equal rows and columns to explore how numbers can be broken up into factors. For example, the number 24 can be expressed as 12 ? 2 or 2 ? 12, and it can be divided equally using its factors 12 and 2. Students identify a missing factor to complete a factor family. Students solve four expressions: two multiplication and two division statements for each activity.

 Arrays picture.

Arrays: solving word problems from 10 to 30
This object requires the application of knowledge of multiplication facts whose products range between 10 and 30.

 Arrays picture.

Arrays: solving word problems from 30 to 50
This object requires the application of knowledge of multiplication facts whose products range between 30 and 50.

 Arrays picture.

Arrays: solving word problems from 34 to 65
This object requires the application of knowledge of multiplication facts whose products range between 34 and 65.

 Arrays picture.

Arrays: explore factors
Students explore how numbers can be broken up with factors. For example, the number 9 can be expressed as 9 ? 1 or 3 ? 3. Students select a set of 9 numbers between 1 and 50 and then identify the factors of a number in the set by choosing a statement that describes how many factors the number has. Once all nine numbers are completed, a printout of work is available.