After finishing her stick of 8, she laid it down next to the stick of 7 and in-
dependently made an observation.
TAMARA: Almost the same size.
TEACHER: Yes, they are almost the same size, but how much bigger is 8?
TAMARA:8.
TEACHER:[reminded of the interview, I try to rephrase] How many more cubes
are in 8 than in 7?
TAMARA:[slowly touching the top cube on the stick of 8] Just 1! [finishes the 10
stick and lays it in place.]
TEACHER: What about the 9 and 10? How many more is 10 than 9?
TAMARA:[running her finger horizontally from the top of the 9 to the 10 stick and
then up one to the top of the 10] 1. [moves all the sticks together on the paper
forming a stair] Look! A stair, Ms. McCarty! Everybody get up out of bed!
[lifts each stick up vertically from 1 to 10] I’m walking the stairs. [Using two fin-
gers like legs, she “walks” up the stairs.]
TEACHER: How many more cubes are there at each stair step?
TAMARA: 1. [points to each step] 1, 1, 1, 1...
TEACHER: Why?
TAMARA: Because. [She pulls out the consecutive pairs of number sticks 6 and- Then she twists of the top cube off the 7 stick and gestures to show that they are
now the same height.] You can take 1 away and you can put 1 on. [She reaf-
fixes the cube to the 7 stick].
This felt like such a success! She discovered the stair step pattern on her own,
and, through my questioning, she was able to explain that each stair step was
just 1 more than the next. Obviously, she needed more practice, but the task
was well suited to developing this understanding. My next goal was to provide
accommodations for upcoming lessons in the curriculum that would both meet
her need to explore the 1 pattern in counting and also meet the lesson’s
objective.
Learning the 1 Pattern
One lesson for which I provided accommodations was called Dice Sums from
Everyday Mathematics(Bell et al. 2007). The objective was to provide experience
with sums generated by rolling a pair of dice. First, I introduced the game to the
whole class. Then for independent practice, the children worked in pairs rolling
two dice and recording the equations. Additionally, they observed which sums
occurred most often. Last, we gathered back together and discussed strategies and
findings.
After One Number Is the Next!