Marvelous multiplication
Wonder why children should learn multiplication facts? Without a sound conceptual knowledge of
multiplication and fluency in recalling and applying their multiplication facts, students are at a profound
disadvantage. Instead of spending time on more meaningful applications, students without
multiplication fact fluency end up spending more time determining routine answers. Thus, helping
students develop fluency with their multiplication facts is perhaps one of the most important goals of
teachers of grades 3–5.
Wonder how we should teach multiplication? Multiplication can be modeled and described as repeated
addition of equal-sized groups, and it can be further visualized and articulated by purposefully
arranging objects into an array. An array is a group of objects arranged in rows of equal length and
columns of equal height. These rows and columns show the number of equal groups and the number in
each group (the factors). The product is the total number of objects in the array. Arrays can help
students understand the commutative property of multiplication. For example, a 3 X 4 array consists of
3 rows of 4 objects, whereas a 4 X 3 array consists of 4 rows and 3 columns. Although both arrays are
visually and physically different, arrays shows that mathematically, in multiplication, it does not matter
which factor represents the groups and which factor represents the quantity in each group.
Figure 3
Figure 4
As early as second grade, students should begin exploring the conceptual underpinnings of
multiplication using concrete manipulatives. For example, the Common Core recommends that
students in second grade work with equal groups of objects to gain foundations for multiplication, and
to use addition to find the total number of objects arranged in rectangular arrays. Purposefully
arranging objects into rows and columns can help students more accurately count a quantity of
objects. Creating and viewing arrays to determine the total number of objects in a group also provides
a smooth transition when students begin to explore the formula for the area of a rectangle, which
requires students to perform multiplication. Thus, providing younger students with opportunities to
create arrays using manipulatives and pictures to aid in counting will assist students in later connecting
and justifying why we use multiplication as the operation when determining the area of a rectangle,
which the Common Core advocates for students in third grade.
Wonder what Pop art is?
Gathered on the classroom carpet, second graders
watched a short BrainPOP® video
(www.brainpop.com/artsandmusic/artconcepts/
popart/), wondering what this thing called “Pop art”
was all about. Pop art was an art movement that
flourished in the 1960s in America and abroad, and
which drew its inspiration from sources in the
popular culture, such as advertising, Hollywood
movies, and pop music. As the BrainPOP® video
described, Pop art was a “reaction against
STEAMed Magazine
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Figure 4
April 2016 Edition