1. Did you know
robots have
24 fingers?
A 3rd Grade
Learning Story
Counting
Rachel Pelletier
February 2016

2. What Happened?
Two weeks ago the 3rd grade class was introduced to story problems. Previously, they worked
on multiplication, and then division. On this particular day they were given a worksheet with both
types of story problems where they had to distinguish which was which and complete the 6
problems. The teacher began on the carpet, walking through the worksheet as a whole class but
varying each problem. Then they were released to their desks where they could choose to work
alone or with their study buddy.
I came over to observe and support “Linda” while she worked her way through the first problem.
She is looking at her 100 chart that has been highlighted for the multiples of six.
Linda writes “6 x 4 =“ on her paper
Rachel: “How did you know how to write that equation?”
Linda: “First we put the bigger number and the lower number has to be last”
Rachel: “Oh I see. Let’s reread the problem so we can show our work”
Linda: “A robot has 4 hands. On each hand he has 6 fingers. How many fingers does the robot
have all together?”
Rachel: “So what could you draw”
Linda draws six tallies in one group, then four tallies in another group
Rachel: “Why did you choose to draw that?”
Linda: “Because there are six so you have to put six fingers”
Rachel: “Okay, what could you draw for the 4 hands?”
Linda draws four circles
Rachel: “Great! Now lets see, how many fingers does each hand have?”
Linda puts two dots in each circle until she gets to the 3rd hand and she stopped
Rachel: “Lets read this sentence again”
Linda: “Each hand has 6 fingers”
Rachel: “So how many dots should be in each circle?”
Linda: “Six” She works off her previous dots drawn and counts six dots in each circle
Rachel: “So how many fingers does the robot have all together?”
Linda: Linda counts quietly to herself pointing to the dots as she counts “25”
Rachel: “Lets count again”
Linda: “24”
Rachel: “Does that answer your equation ‘6 x 4’?”
Linda: “Yes”
Rachel: “Great job!”

3. What does this story
demonstrate?
Linda has been working on her multiplication and division facts. According to the Common
Core State Standards, she is expected to be able to solve all multiplication and division
problems within 100 and apply them to word problems. Linda is still working on knowing her
multiplication problems, and often struggles deconstructing word problems into pictures
unless she is working with a classmate or teacher. However once she goes through a
problem she does demonstrate growth by being able to explain what she just did and why.
In this learning story, we see Linda mixing up some of the rules she learned in class. She
states “First we put the bigger number and the lower number has to be last”. This is a
strategy for division. In fact, the problem presented should have been written “4 x 6”
because each one of the 4 hands had 6 fingers.
She also thought that between the four hands, their were only six fingers. After rereading
the problem she was able to complete the picture hearing that each hand had six fingers.
Then she knew to count the number of dots she drew to represent thing fingers to find her
answer. However she either miscounted or counted one dot twice the first time, prompting
me to ask her to count again. The second time she got the correct answer. Because she
was able to get 24 the second time, I assume she knows how to count to 24, but simply
counted one dot twice.
She is still working towards knowing her multiplication problems, and resorts to pictures to
find her answer. She may not have made the connection that should could count each
hand by sixes, or she may not be comfortable counting by sixes.
Common Core State Standards
CCSS.MATH.CONTENT.3.OA.A.1
Interpret products of whole numbers, e.g.,
interpret 5 × 7 as the total number of objects
in 5 groups of 7 objects each.
CCSS.MATH.CONTENT.3.OA.A.3
Use multiplication and division within 100 to
solve word problems in situations involving
equal groups, arrays, and measurement
quantities, e.g., by using drawings and
equations with a symbol for the unknown
number to represent the problem

4. Where do we go from
here?
Linda has made large strides in
her mathematical abilities.
Often after I work with her I see
her applying concepts we had
just discussed in her next
problem. This tells me she can
comprehend the idea of what
to do, but may not always know
why she is doing it.
I believe that working through
more word problems is crucial
so she can understand why
we are doing multiplication or
division. I think she would
benefit from creating the
problems from manipulatives or
creating our own realistic
problem to solve. This way she
understands what we are
looking for, and how we get
there. It also would be easier to
understand the concept of
“each” and “equally” that she
seems to get confused with.
In addition it is important to
continue working on math facts
so she can know them off the
top of her head and apply them
to these word problems, or
check her work.
Linda seems to be at a similar
level in her mathematical
abilities as her classmates.
Everyone is still learning
multiplication and division
currently. Will more practice
and repetition she will be get
the correct answer with ease in
the near future!