10—for example 7 3, 2 8—and each time we played a game or added a se-
ries of numbers, it was as if they were thinking about combinations of 10 for the
first time. I thought that the more children practiced through games, the more
fluent they would become with these ideas.
Sometimes I used games from first grade and games children had played ear-
lier in the year. I also included games from Constance Kamii’s book, Young
Children Reinvent Arithmetic: Implications of Piaget’s Theory, that are in the spirit
of the school’s adopted math program (Kamii 2000). I have found that for the
students to solidify their number knowledge, my sessions with them must be con-
sistent with the mathematics work they are doing in the classroom.
One of the games the math program offers for practicing the combinations of
10 is Tens Go Fish (Russell et al. 2008b). It is the same idea as the game Go Fish,
but instead of asking for the same number, students need to get 2 cards that total
- For example, if a student has a 2, he or she asks for an 8. This is a game students
had played in first grade and early in second grade, so I wasn’t sure they would be
interested in playing it again. I was very surprised to see how engaged they were. We
had been practicing combinations of 10 in many ways in and outside of the class-
room, but it was this game that provided the incentive for students to know these
combinations. Although they had played the game a few times before in first grade,
it was while working in the small group that they really enjoyed it. One reason is
that by playing the game over and over again, they began to understand it better.
Once again, the game became a meaningful context for the students: they wanted
to make as many combinations of 10 as possible, and the better they knew the com-
binations, the faster they could find the match. Because the children asked to play
the game several times, they became more familiar with combinations of 10. I
thought that as they became more fluent, they would use this knowledge to solve
number and word problems. However, as time passed, I realized that students were
not making that connection independently. I became aware that I had to ask ques-
tions that would allow students to connect these experiences.
Making Connections from Games to Problem Solving
Sylvia very easily knew 5 5 but had difficulties remembering other combina-
tions of 10. However, I noticed that as she played Tens Go Fish over and over
again, she began to remember the combinations and relied less and less on her fin-
gers to count on to 10 to figure out what card she needed. One day I was working
with Sylvia in the classroom. She had to solve the following number sentence us-
ing number combinations. The sentence was:
10 5 7 25 3 8 20 2 .LINKINGASSESSMENT ANDTEACHING