how many small chocolate pieces there were in the 4 bars. Figure 7–1 is a copy of
Michele’s work. She sat down at her desk and independently worked through it.
The context was real, which helped Michele organize her thinking clearly
step-by-step. After writing the number sentence 12 12 12 12, she decom-
posed 12 into a 10 and a 2, drawing towers of 10 and 2 loose cubes each time. She
counted by 10s first, then by 2s, and finally added the subtotals. Michele had be-
gun to make connections between different mathematical experiences: counting
a collection of objects by 10s and using towers of 10 to decompose numbers into
10s and 1s to solve story problems. Facilitating these connections was one of my
goals during these sessions. What helped this to happen? It was not one particu-
lar activity or question. The class had already been working on counting by 10s,
and decomposing and recomposing numbers to add and subtract. They played
games, counted collections, shared solutions, and reflected on their counting mis-
takes. They also had conversations about why the total amount was always the
same regardless of whether they counted by 1s, 10s, or 5s. On the one hand, lis-
tening to other students share their thinking probably broadened Michele’s ex-
periences with place value. On the other hand, she also needed time to work
these ideas out by herself in order to follow and incorporate her classmates’ ex-
planations. In my planning, I had to balance opportunities for students to share
and to work independently.
Combinations of 10 Through Games
One of the district’s benchmarks for second graders is to use combinations of 10
and knowledge of doubles and place value to solve addition and subtraction
problems efficiently. My students had difficulty remembering combinations of
Assessing and Supporting Students to Make ConnectionsFigure 7–1.