My kids can : making math accessible to all learners, K–5

Her partner explicitly pointed out the relationship between 25 and 250, so that
Tasha was eventually able to use 250 in solving problems.

Checks Reasonableness of Answers

Prior to joining my class, Tasha had not had much exposure to mathematical think-
ing. She had been taught only rote procedures and didn’t view math as something
that was supposed to make sense. As a result, she had no way of judging whether
her answers were reasonable. I modeled ways to help her make sense of mathemat-
ics. In one instance, a problem asked which multiple of 100 was nearest to a series
of numbers. Tasha wrote that the multiple of 100 nearest to 130 is 200. When I
asked her why, she said because it is already over 100. I asked, “Is 130 closer to 100
or 200?” She quickly replied, “100.” I recorded the multiples of 10 between 100 and
200 and asked which are closer to 200 and which are closer to 100. She drew a line
at 150, to indicate that everything greater than 150 was closer to 200. Seeing the
multiples written out provided her with a way to structure her thinking.
Eventually, with all of the modeling I did and the strategies we shared in class,
she applied what she knew and could assess whether or not her answer was rea-
sonable. For example, this is her work for 32 9.

1

By working on ways to break up larger problems into smaller, meaningful
chunks using the multiplication facts she was fluent with, Tasha was able to recog-
nize that if 30 9 = 270, then 32 9 could not possibly equal 358 because 2  9
only equals 18. Even though Tasha made a computation error, the important point
here is that she was using mathematical reasoning to critique her own solution.

Actively Participates in Mathematical Discussions

I used a variety of specific strategies to encourage Tasha’s participation in discus-
sions and help build her confidence. I asked her questions in the large group that
I knew she could answer (e.g., what is another fraction for ?). I also did some
“preteaching”—going over directions and activities in advance so she would be

1

2

2  9  18

32  9  288

32  9  30  9  270

2  9  18

32  9  358

32  9  30  9  270

TAKINGRESPONSIBILITY FORLEARNING

But, I know that 32  10 320,

so 358 can’t be the right answer for

32  9. It’s wrong. I need to go back

and check my work. There’s a mistake.

I see what I did wrong. I added up

wrong. I did the 8 twice and it was

lined up all wrong.