These
activities reinforce students' understanding by using rhythm, physical
action, and introspection.
Learning
psychologist Howard Gardner proposed that each learner reflects
his or her unique combination of intellectual strengths and weaknesses.
Gardner's theory of seven intelligences (linguistic, mathematical,
spatial, musical, intrapersonal, interpersonal, bodilykinesthetic)
has inspired many educators to present content in a variety of ways
so individual students' learning preferences might be awakened and
connected to their intellectual strengths.
The
place value activities presented here suggest alternatives to traditional
textbook problem solving. These activities are designed to be used
during a mathematics lesson, but the concepts could be incorporated
across the curriculum: setting up a model bank in a social studies
class, reading a counting story in language arts, emphasizing the
mathematics of measurement in science. Embedding the ideas in a
variety of contexts will give different learners more opportunities
for understanding.
Physical
Action: The Place Value Board
Use a
sheet of butcher paper to create a large place value board and place
it on the floor. With a large die, roll a number and have that many
students stand in the ones column. Ask the students why they are standing
in that column. How many more students could we place in that column?
Roll
the die again and add that many more students to the ones area.
Ask: are there enough students now to make a group of ten? If yes,
have ten students link their arms and move to the tens place. Anyone
left stays in the ones area. Ask: why have we moved this group to
the ten's place? Will someone tell something about the number represented
on the place value board? Does that correspond to the number of
children standing at the place value board?
Continue
to roll the die until all the students are standing on the board,
asking for student ideas as to why groups are being moved across
the place value board.
Introspection: The Math Journal
While
mathematical conversations among students are essential for understanding,
a journal provides another avenue that may appeal to the introspective,
linguistically oriented learner. Students should write as mathematicians,
clearly communicating each idea, theory, or step to solving a problem.
They may use this writing time for exploration, reflection, or explanation.
Let the students respond to such questions as
Something
I learned today...
I found the right tool to...
I saw a pattern...
Something I didn't understand...
Something easy...
I predicted...
Math is easy when...
Something in math I'd like to learn...
My plan for tomorrow is...
Skills that I enjoyed learning...
I found...I made a connection...
I thought of a new strategy...
I estimated...
Music:
That's a Rap!
Introduce
this spoken song to the students after they have worked with the
concept of place value. If you do not feel comfortable demonstrating
your rap skills, let student volunteers assist you. (Sunglasses
and baseball caps help set the mood.)
Place
Value Rap
The number of digits
in our system is ten.
You will learn their value
if you just begin.
There's a zero,
there's a one, two, three, four,
five, six, seven, eight, nine,
no more.
Every digit has a value
on its face;
And each digit has
a value in its place.
Two can be two ones or
two can be two tens.
Either way it's two,
the value just depends
On where you put it,
On where you put it.
The value just depends on
where you put it.
Two tens are twenty and
two ones are two.
When you use
the proper place
it's easy to do.

With
this inspiration, your students may want to experiment with their
own math raps.
These
activities appear in Celebrating Multiple Intelligences: Teaching
for Success, written by the faculty at New City School in St
Louis, Missouri (1997). Available from The Bookshelf, 4301 Connecticut
Ave. N.W., Suite 432, Washington, DC 20008. 18003461834.
