TITLE: THE SQUARES OF NUMBERS IN MULTIPLICATION
AUTHOR: Glenda Lazenby; Casady School, Oklahoma City, OK
GRADE LEVEL AND SUBJECT: 2 - 3
Late second grade or early third grade mathematics
OVERVIEW: As students begin memorizing the multiplication
math facts, they need many different ways of visualizing and
practicing the multiplication concepts. They might begin
practicing with arrays, skip counting, and moving
manipulatives for the 0,1,2,3, and 4 times tables before
they begin this lesson.
PURPOSE: It is easy enough for students to memorize 3x3=9,
4x4=16, etc. but this lesson gives a visual image for these
simple patterns that will facilitate learning other
patterns for the multiplication tables and extend to later
math concepts.
OBJECTIVES: The learner will be able to: 1, memorize the
multiplication math facts for a number times itself 1-10, 2,
construct a visual image for these math facts, 3, label the
shape created and predict the shape of other numbers using
this pattern, 4, fill in a multiplication chart using the
skills and answers from this activity.
RESOURCES/MATERIALS: graph paper, colored pencils, enlarged
chart or overhead projector
ACTIVITIES AND PROCEDURES: The teacher explains that in
addition when the same number was in the problem it was
called a double, but in multiplication when a number is
times itself it has a different name. Can we find what the
label might be and why it is suitable? Pass out large block
graph paper with ten rows across and ten rows down to each
student. The teacher works on an enlarged copy at the board
or uses an overhead projector. Each student and the teacher
also need a marker shaped like a carpenter's square. Choose
a number from one to ten. Place the marker at the very top,
left-hand corner of the graph. Move down exactly that many
boxes then across the given number of boxes. The area that
appears inside the marker is the answer for how much that
number equals when it is multiplied times itself. Count to
identify. With a colored pencil, shade in this area Choose
another number one to ten and follow the same procedure
until the pattern becomes apparent. A numerical answer may
be recorded at the lower, left-hand side of each square.
Write out a list of all the math facts 1-10 times itself and
label the list MULTIPLICATION SQUARES.
TYING IT ALL TOGETHER: The student should observe that each
time a number one through ten is multiplied times itself,
the answer is a square. They can then predict that a two or
three digit number times itself will also make a square.
Later they can find square roots. Can the chart and marker
be used to find other products and will the other products
also be squares? If 5x5 is 25, what will 6x5 be? After
practicing and filling in the answers on the chart, the
student will have a complete multiplication chart to be used
meaningfully until the math facts are memorized.