Small-Group Intervention: Addition Equations
After school, Sarah and I debriefed the small-group lesson. We realized that these
children needed much work in seeing the numbers within the larger number—
subitizing. Most of the six children, with the exception of Keith Allen, had diffi-
culty even remembering the starting number. After they broke the train of 9
cubes into 2 parts, they counted the cubes in each group separately, and then
counted the total over again, not realizing or trusting that the original number
they began with was 9. Sarah was also surprised with the amount of time it took
the children to make the original train of 9 accurately. We both felt that the dis-
traction of all the colors of linking cubes led this group to think of color patterns
rather than focus on the 9 cubes. I decided that next time we worked together, I
would only give the children 2 colors of cubes.
For the next small-group lesson, the children only used white and red cubes,
which were already separated. I showed them Meredith’s page in her number
book that depicted 8 and asked them what they noticed about the addition equa-
tions. I hoped that the students would be able to model the equations with cubes
but also notice the order of the equations and maybe represent the patterns found
in Meredith’s book (see Figure 13–2).
“I see 44,” Mia offered. My response was, “Can you build 44 using the
cubes?” Connor and Nicole went right to work, while the rest of the children
watched. I asked Nicole to share about her train, and she pointed to the colors and
said, “Here’s 4 red and 4 white. That makes 8.” We then went on to build the rest of
the addition equations in Meredith’s book. As the children were building, I listened
for someone to mention something about the way Meredith arranged her equations.
Not one child mentioned the patterns. From this conversation, I could see that the
children needed more practice with building and naming each combination before
they were ready to discover the patterns. At the end of the small-group discussion, I
asked the children to place their trains on the chalk tray so that they could share some
of them during the whole-class discussion. I again wanted to have their representa-
tions available to help them recall the work they did and participate in the group talk.
Whole-Class Talk
After recess, the whole class gathered to review the number 8. Mia explained how
we used Meredith’s book to make the cube trains for 8. Then I asked the class to
look carefully at the cubes to find 4 4. Connor volunteered and chose the train
that showed 2 white and 6 red. I wanted him to be explicit about his choice and
asked, “How many cubes are white? How many are red?” He counted each time,
and Keith Allen said, “2 plus 6 makes 8.” Then I directed the class back to the
original question by asking again, “Can you find the 4 4?” Mia picked out the
BUILDINGUNDERSTANDINGTHROUGHTALK