Introducing Multiplication

Strand: Number
Outcome: 11

Step 1: Identify Outcomes to Address

What do I want my students to learn?
What can my students currently understand and do?
What do I want my students to understand and be able to do, based on the Big Ideas and specific outcomes in the program of studies?

Strand: Number

Grade 2

Grade 3

Grade 4

Specific Outcomes

Demonstrate an understanding of addition (limited to 1- and 2-digit numerals) with answers to 100 and the corresponding subtraction by:

using personal strategies for adding and subtracting with and without the support of manipulatives
creating and solving problems that involve addition and subtraction
using the commutative property of addition (the order in which numbers are added does not affect the sum)
using the associative property of addition (grouping a set of numbers in different ways does not affect the sum)
explaining that the order in which numbers are subtracted may affect the difference.

Specific Outcomes

11.

Demonstrate an understanding of multiplication to 5 x 5 by:

representing and explaining multiplication using equal grouping and arrays
creating and solving problems in context that involve multiplication
modelling multiplication using concrete and visual representations, and recording the process symbolically
relating multiplication to repeated addition
relating multiplication to division.

Specific Outcomes

Demonstrate an understanding of multiplication (2- or 3-digit by 1-digit) to solve problems by:

using personal strategies for multiplication with and without concrete materials
using arrays to represent multiplication
connecting concrete representations to symbolic representations
estimating products
applying the distributive property.

In order to multiply numbers effectively, students need to understand multiplication in terms of concrete examples and mathematical models.
Students need to construct their own understanding of multiplication by using personally meaningful strategies in a problem-solving context.
Multiplication can be thought of in different ways; for example, as repeated addition, as numbers of equal groups, as arrays and as proportional relationships.
Students develop a robust understanding of multiplication over a number of years.
Although multiplication can be understood as repeated addition, a complete understanding of multiplication is more complex, and involves the ability to think of numbers as ways to represent relationships as well as concrete quantities, the ability to think in terms of
many-to-one relationships and the ability to reason proportionally.
Being able to relate the idea of arriving at a whole by repeating equal groups to the idea of partitioning a whole into equal groups is the foundation for relating multiplication to division.