I gave the class a sheet of story problems asking about doubling situations and
reviewed the directions with the whole group. I told the whole class they could
select partners to complete the assignment and that they could use whatever ma-
nipulatives and materials they needed. When I was sure the pairs were working
productively, I began work with the guided math group.
Working with the Guided Math Group
For the guided math group, I put out interlocking cubes, white boards with mark-
ers, containers, and scratch paper and asked the students to come to the table
with their math journals and pencils. I first asked them, “If someone told you they
were going to double your money how would you feel and why?” The students dis-
cussed their answer with a partner. (Because there were five students, one student
was my partner.) After sharing briefly as a group, I asked, “What happened to the
money?” “Who could show me with their hands?” The students showed me by
making the space between their hands grow larger and larger. We talked about
what the vocabulary word doublingmeans, and I asked the students to come up
with their own definition of the word. Their definitions included “Doubling
means that a number gets bigger. It is adding a number to itself.” We had dis-
cussed all of this as a whole class when we originally started this unit, but these
students needed a review, and I needed to make sure that they understood the
concept of doubling. I then asked the students to choose something that they
would like to have doubled. Students shared answers like video games, recess, and
money. We next talked about whether doubling everything was necessarily good
and discussed things that students would not want doubled. They came up with
examples like vegetables and homework. My goal in asking them to choose these
items was to relate the concept to their everyday lives and let them see that the
mathematics we work on is not just an abstract concept, but an everyday reality.
We then moved to manipulatives so that students would be able to physically
show doubling and see what they had done. I instructed the students to build ten
stacks of two interlocking cubes. We then reviewed how many cubes are in one
stack, two stacks, three stacks, and so on. It was extremely important for them to
see and move the cubes as they said the pattern. I then held up one stack of
2 cubes and asked the students to do the same. I asked, “What number did I dou-
ble to make this stack?” The students took a minute then said, “One.” We then
took the stack apart to show that it was two groups of 1. I then asked them to
record the addition equation that represents two groups of 1 (1 1 2). Next,
I asked them to write what the corresponding multiplication statement would
be (2 1 2). We did the same thing with more of the stacks of cubes. For
example, we took three stacks of 2 cubes and pulled them apart to make 2 groups
MAKINGMATHEMATICSEXPLICIT