N4.3
Demonstrate an understanding of multiplication of whole numbers (limited to numbers less than or
equal to 10) by:


applying mental mathematics strategies
explaining the results of multiplying by 0 and 1
Indicators
a. Explain the strategy used to determine a product.
b. Explain the strategy used in a given solution to a product. For example:
 for 4 x 3, thinking 2 x 3 = 6 and 4 x 3 = 6 + 6 or 6 + 2 = 12 (halving and doubling)
 for 3 x 7 think 2 x 7 = 14 and 14 + 7 = 21 (doubling and adding one more group)
 for 9 x 6, think 10 x 6 = 60 and 60 – 6 = 54 (multiplying by ten and subtracting one
group)
 knowing 2 x 6 = 12, then 4 x 6 = 12 x 2 = 24 (doubling)
 for 64 ÷ 8, think 8 x = 64 (relating division to multiplication)
 for 8 x 5, knowing that 5 x 5 = 25, and then skip counting by 5 three times to get 25 + 5 +
5 + 5 = 40.
c. Explain the property for determining the answer when multiplying numbers by one.
d. Explain the property for determining the answer when multiplying numbers by zero.
Developing the Goals:
 (HE + NS) Multiplication (and addition) facts are the basis of all mental math strategies, and
mental math is the most widely used form of computation in everyday life. It is empowering for
students to know their facts and this knowledge facilitates the development of other math
concepts (David McKillop).

(LT) A structured approach that involves students identifying patterns (all multiples of 5 end in
either a 5 or a 0), develop a hypothesis for their strategy, test their strategy (does it always
work), and generalize their strategy (write or explain the rule) develops logical thinking, engages
the student and helps build deep understanding.

Teaching Tip – This outcome should not be treated as a unit that stretches over a couple of
weeks. It should be done a little every day (10 – 15 minutes) over a period of months to ensure
that every student is mastering their facts along the way.
Diagnostic Pre-Assessments:
 It is important that students have developed a conceptual understanding of the meaning and
use of multiplication through problem situations (webinar – Multiplication Makes Sense)

Numeracy Nets (4)
o Checkpoint 5 - The student uses multiplication to represent the repeated addition of
equal-sized groups.

FSIM – Number Sense Course Book
o Story Problems – page 212
Learning Activities:

Caution – Be wary using computer programs or worksheets (drill sheets like Mad Minutes) designed
to practice basic facts. Drill should be done once understanding and ease of use with a single
strategy is obtained. The practice should focus on that one strategy, adding others only once they
are understood and easy to use as well. Practice of random facts will not lead students to desired
results. If computer games, flashcards or worksheets are to be used, select programs that allow the
user to choose the math fact that they are practicing.
o Flashcards – focus practice with flashcards on one strategy at a time or on a combination of
mastered strategies. Use a “don’t call it out” strategy; display a fact card, wait a predetermined amount of time (working down to a three-second or less recall), then signal
students to answer in unison. This method allows those that require the processing time to
formulate their answers before a quicker processor calls out the answer. It also discourages
children from using counting and forces reliance on understood strategies.
o Mad Minutes (or similar) – ex/ have students work through the facts to highlight all the x2
facts in blue and all the x3 facts in yellow before highlighting all the x6 facts in green.

Math Makes Sense 4
o Lesson 1 – Using Doubles to Multiply – page 82
o Lesson 2 – Multiplying by 1, by 0, and by 10 – page 86
o Lesson 3 – Using Skip Counting to Multiply – page 90
o Lesson 4 – Other Strategies for Multiplying – page 94
o Lesson 5 – Using Patterns in a Multiplication Chart – page 98
 Caution – Skip counting (Lesson 3) is an important skill that precedes the
development of multiplication and division strategies. It is important to note that
skip counting is, in essence, counting, and it needs to be replaced with a more
efficient strategy before drill is implemented.
 Caution – Following the sequence and lesson ideas presented in MMS may not be
the most effective plan for this outcome. Please consider making use of some of the
resources listed below.

FSIM – Operation Sense
o Computation Background Notes – Learning Basic Facts
 Pages 108 – 112
o
Computation (KU3) – We can think of a number as a multiplication or division in different
ways. We can rearrange the factors of a multiplication without changing the quantity.
 Learning Activities – pages 138, 139

Ontario Ministry of Education
o Approaches to Teaching Basic Facts and Multi-digit Computations
o Numeracy Modules (4 – 6) – Multiplication and Division

SECPSD Webinar – Multiplication Makes Sense

NCTM – Developing Essential Understanding of Multiplication and Division
o http://www.nctm.org/catalog/productsview.aspx?id=129

NCTM – Illuminations
o Multiplication: It’s in the Cards - In this unit, students use the properties of multiplication to
help them master the multiplication facts. The most effective and efficient way to help the
students learn the number facts is to build an understanding of the operation, then
encourage the students to use the helpful features of the number system, and finally to
provide interesting activities for retention. This unit focuses on the second and third aspects
of this learning process.
o Six and Seven as Factors - In this unit, students who have previously studied the meanings of
multiplication will use its properties to help them master the products where 6 or 7 is a
factor. Mastery will be fostered through class discussions and the playing of games. The unit
is most appropriate for students who understand the process of multiplication and have
mastered the multiplication facts where 0, 1, 2, 3, 4, and 5 are the factors.

Teaching Student-Centred Mathematics (3 – 5)
o Chapter 3 – Helping Children Master the Basic Facts (page 74)

Nova Scotia Ministry of Education
o Reinforce Doubles and Double-Double Strategy
o Assess Multiplication Facts