In Dice Sums, I saw an opportunity to give Tamara access to the objective
and more experience with the 1 pattern with just a slight modification of the
activity. Working with me, she rolled two dice, found the sums, and recorded the
number models. Her dice, however, included one with written numerals 1–6 and
the other with the number 1 on every side. The probability component of the ob-
jective was eliminated. For the recording piece, I asked her to make a stick of in-
terlocking cubes for the sum she rolled on each turn, because I wanted to revisit
and build on her success with the stair step pattern and reinforce examining num-
bers as quantities. Holding the dice in her hands, she quickly noticed the die with
a 1 on every side. “Hey, what’s this?” she asked suspiciously. I asked her what she
thought and she said they were all 1.
“Hmm,” I puzzled. “So, what do you think you will get every time you roll
this die?” She responded that it would be 1, but before I could ask more about
the sum, she starting rolling. After three “rounds” of her counting all on her
fingers and then counting out all of the cubes from 1, I stopped the game. This
task was not reinforcing the 1 pattern for her, so I decided to try another
strategy.
I wrote the following on a piece of graph paper:
1 1
1 2
1 3
1 4
1 5
1 6 Upon seeing this, Tamara immediately abandoned the dice and started counting
all on her fingers. She was solving the equations and recording the sums.
TAMARA:[finishing 1 1 2 and 1 2 3 quickly] This is easy!
TEACHER: Do you notice a pattern? [Tamara keeps working without respond-
ing to my question. It is clearly satisfying work, but again it is not achieving the
objective.]
TEACHER:[covering the left side of the equations or the 1column with my hand]
What do you notice about these numbers?
TAMARA:[reads the sums she has just written] 2, 3. [Then looking down the ver-
tical column she recognizes the pattern and fills in the last four sums quickly say-
ing them aloud.] 4, 5, 6, 7.
TEACHER:[wanting her to extend the pattern further, I prompt her.] So if
1 6 7, what will 1 7 be?
TAMARA:[grabs her pencil and writes out the next equation: 1 7 8 ]LINKINGASSESSMENT ANDTEACHING