• ### Where are they now?

Can use group structure and stress or rhythmic counting to determine total and is beginning to efficiently count using ‘easy’ composite units (2s, 5s and 10s), using group structure and stress or rhythmic counting to determine total.
Is beginning to identify 10x patterns. The groups and their elements still need to be modeled to support calculations however, using for example grouped counters
(e.g. counters within a circle) or sticks of Unifix cubes.

• ### Where to next?

Uses arrays to make, model and explore equal groups (rows or columns) and determine totals.
Group structure still needs to be modeled e.g. Cuisenaire rods.

• ### Purpose

Understanding multiplication requires that a student understands the principles of unitising (the making and counting of composite units of equal size). These activities help build an understanding of multiplication based on the process of unitising. From here, students can begin to meaningfully make representations of multiplication expressions and build fluency around the quantities so expressed.

‘Fluency with basic multiplication facts allows for ease of computation, especially mental computation, and therefore aids in the ability to reason numerically in every number-related area.  Although calculators and tedious counting are available for students who do not have command of the facts, reliance on these methods for simple number combinations is a serious handicap to mathematical growth’ (p 167, Elementary and Middle School Mathematics)

• ### Building Multiplication and Division skills:

The skill of multiplying and dividing draws on all of the skills studied in the whole number, addition and subtraction sections.  A failure to progress will generally indicate one or more of these skills needs to be revisited.

Student’s early multiplication and division knowledge is based fundamentally on the development of counting sequences and arithmetic strategies, along with skills of combining, partitioning and patterning (CMIT P30, LFN).  Early multiplication and division strategies focus on the structure and use of groups of things.  Rather than emphasizing individual items or number words, students develop increasingly sophisticated ideas of “composites”.  As they develop the concept of multiplication, students focus on groups of items and learn to treat the groups as countable units (CMIT, LFN, P. 6).

Important concepts in moving from step 5 to step 6:

Moving from key concept of Recognising and using the structure of equal groups to determine totals

To the key concept of  Seeing composite units as countable objects in themselves, leading to the meaningful calculation of products.

References to other resources:

Developing Efficient Numeracy Strategies Book 2 pp 92 – 107

### Activities and Assessments

Double Dice Multi (Adapted from CMIT, Developing Efficient Numeracy Strategies © (Creative Commons) 1999 NSW Department of Education and Training)

Focus: Students determine the product of two randomly generated whole numbers (within a specific range) using arrays or concrete manipulatives.

How: see Double Dice Multi (Array) instructions. The number of groups and the size of each group can also be effectively modeled using Unifix cubes.

Double Dice Multi (Arrays) instruction sheet

10 by 10 Array

Bingo Card (x1, x2 and x3)

Spinners (x1, x2 and x3)

Bingo Card (x2, x3 and x4)