of 3 cubes. The two separate groups of cubes illustrated that 3 doubled is 6. Then
we wrote equations to represent the doubling: 3 3 6, 2 3 6.
I asked the students how we could use this information to help us double
numbers. The students said we could just add the number twice. One student said,
“If it is an easy number, we can multiply by 2.”
After the students had practiced with the cubes and writing equations, I re-
turned to the context of the magic pot. I asked students to take one of their stacks
of 2 cubes, and to put 1 cube in a container. I asked the group how many cubes
were not in the container. Everyone responded, “One.” I then told students to
think of their containers as magic pots and to double what was in them each time.
I gave them cubes and containers and they wrote the equations showing what was
in the container each time they doubled the number of cubes: 1 1 2, 2 2 4,
4 4 8, and so on. Students found that their containers filled up quite
quickly. They were very engaged and were fascinated to see what happened when
things kept doubling. “Wow, this is filling fast. The bigger the number, the big-
ger the double.” I felt confident that by taking the time to make this concept
more explicit, I helped my students comprehend the mathematics of the lesson.
Making Connections to a New Context
After working on the magic pot problems for a few days, I felt the students were
ready to move on to a new problem. I wanted to see if students could apply what
they had just been doing, so I made up the following problem for them to solve:
There are 22 children in a class. Each student wanted a double-scoop ice cream
cone. There were 40 scoops of ice cream. Would that be enough? We read the
problem together and discussed what was the important information, what
would we need to do to solve the problem, and what the question was asking. It
was important that these students understood what the problem was asking as
they often struggled with comprehending math story problems. We discussed
what the important information in the problem was and what it meant to have
a double scoop of ice cream. I asked questions such as: “Is the number going to
be bigger or smaller than 22?” “How do you know?” “What do you think the an-
swer will be?”
I asked students to work with a partner to figure out the answer and to use
their cubes to demonstrate how they solved the problem. The students worked
well with their partners and easily solved the problem. Some used cubes and some
used pictures. When I asked for someone to share their answer, one student said,
“The answer is 44.” We looked at the question again and he corrected himself,
saying, “The answer is no, there is not enough ice cream. We need 44 scoops and
we only have 40.”
Double or Nothing