makes sense. He also asks Michael to help Amanda figure out where she would
land, which might help both of them think about jumps of 5.
Throughout his interactions with both students, the teacher asks them ques-
tions such as, “Why that number?” and “How do you know?” These questions al-
low Michael to hear his students’ thinking and also force the students to justify
their moves. He also asks them to name the amounts they are jumping so they are
not just jumping but also thinking about the amount they are jumping and where
that brings them on the 100 chart.
The questions the teacher asks are designed to elicit specific information
about both Michael and Amanda’s understanding. Because he spends the most
time working with Michael, there is more information about what Michael un-
derstands and doesn’t understand. Michael seems to understand that grouping a
count by 5 can be useful. He knows how many groups of 5 there are in 20, and he
knows that when he has counted 4 groups of 5, he has counted 20. He recognizes
patterns of counting by 10 and saw the pattern of 5s going down the 100 chart.
Michael still seems to be working on counting by 5s on the 100 chart and navi-
gating around the 100 chart. It seems unclear why Michael knows the number of
5s in 20 but doesn’t count by 5s and why exactly Michael is having difficulty with
directionality on the 100 chart.
In an essay he wrote about this interaction with Amanda and Michael,
Michael Flynn describes what he decided to do when these two students next
played Get to 100.
I decided to have them play Get to 100 with the numbers cubes that didn’t have 15.
That was just one more thing to worry about. I also had them begin the game by
counting off by fives and marking those numbers on their 100 charts. This would
serve as a visual reminder. I also had them play with other partners during the next
few choice times so they could see different strategies. They both had the hardest
time with the game compared to the rest of the class, but with repeated practice on
the 100 chart, they both began moving efficiently and accurately on the board.By eliminating the number 15 on the die for these two students, Michael al-
lowed them to focus on adding on 5, 10, and 20 and not be distracted by trying
to add on 15, which can be more challenging. Asking them to mark off multiples
of 5 on the 100s chart highlighted the multiples of 5, helped them to count by 5s,
and perhaps made it more likely for them to count by 5s. His decision to have
them play with other partners was designed to expose them to some other strate-
gies for adding on multiples of 5.
The work Michael did with these two students was both an assessment and a
teaching opportunity. He was able to learn about the students’ understanding of
counting, adding, and the number system, and also help them move forward in
LINKINGASSESSMENT ANDTEACHING