Each day we talked about the next number in the series. Most children began
to come up with more complex ways to express the numbers. For example, with
5, I wrote the equations in sequential order, leaving a space between 1 4 5
and 3 2 5. I was hoping the children would notice the pattern. Lukas noticed
it first and said, “2 plus 3 equals 5 goes in that empty place.” When I asked him
how he knew, he replied, “The first numbers count up and the second numbers
count back,” referring to the addends. As we got to greater numbers, some chil-
dren began to use the number line to come up with subtraction equations. They
began seeing patterns and making generalizations about the operations of addi-
tion and subtraction.
Although I was pleased that some of the children in the class were build-
ing from each other’s ideas and were challenged to think about the numbers in
a more abstract way, I noticed that others were struggling. For example, when
we worked on the number 6, Kelvin volunteered, “6 and 0 makes 6.” Kelvin
had already become quite predictable. He knew that any number plus zero
equaled that number, so he had shared it with all the numbers so far. He also
showed some confusion when he shared other combinations and often includ-
ed the number as part of a different equation. For 6, he had volunteered, “6
plus 2.” When Owen said, “That makes 8 and we’re doing 6,” Kelvin looked
puzzled. Even after I asked Kelvin and Owen to use the linking cubes to find
combinations for 6, Kelvin seemed confused. When writing in his number
book, he most often chose to illustrate sets of quantities rather than write
equations.
Mia also struggled. She often chose to draw pictures, and when she wrote a
number sentence, it was not always accurate, even if the correct numbers were on
the board. Fernando preferred to draw rather than write numbers, and often used
1 1 ...1 as his equation for the number of the day. Stacy confused addi-
tion and subtraction and frequently gave incorrect answers.
Given their struggles, I wondered what these particular children were learn-
ing from the whole-group discussion. I decided that they could benefit from addi-
tional opportunities to practice counting and recording combinations in a small
group prior to their work with the whole class.
Sarah and I met to identify children who needed more support. We decided
that Nicole, Stacy, Fernando, Keith Allen, Connor, Mia, and Kelvin would form
the intervention group. After working with the numbers 1 through 12, my plan
was to work with the intervention group for ten to fifteen minutes two or three
times a week reviewing one of the numbers. Next I would revisit the same num-
ber as a review for the entire class. I wanted to see if the extra practice and review
in the intervention group would help those children participate more successfully
with the entire class.
What’s Another Way to Make 9?