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Welcome!
Please find your name on a table card.
Session 1
Making Meaning for Whole Number Addition and Subtraction
AGENDA
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Welcome
Sharing Student Work Samples
Case Discussions Part 1
Math Activity: Modeling Story Problems
Case Video Clips: Representing Subtraction on the
Number Line
• Case Discussions Part 2
Goals
• Exploring mathematics for ourselves
• Examining print and video cases to learn
how students develop ideas
• Investigating and sharing our own
students’ work
“Can you do addition?” the White Queen
asked.
“What’s one and one and one and one and one
and one and one and one and one?”
“I don’t know,”
said Alice.
“I lost count.”
Lewis Carroll, Through the Looking Glass
Student Work Samples
Work in pairs or triads first. Read through all
the student work and analyses first.
• What can you learn about the mathematical ideas of
these students by examining their work? What ideas
are solid and what ideas appear to be missing?
• What are some commonalities or differences that
you note across the samples?
• Share a potential next step with each child or
questions you may have about what the nest step
should be.
Case Discussion Part 1
• What are the connections do you see between
the children’s counting strategies and the
operations of addition and subtraction?
• What do you notice about the operations of
addition and subtraction?
Key Ideas
• Addition and subtraction problems can
be solved by counting strategies
• Solving a subtraction problem by
counting back requires paying attention
to what you are counting, the spaces or
the objects
Key Ideas
• The operation of addition is connected with
the action of combining, subtraction is
connected with the actions of taking away and
comparing.
• Children’s counting strategies provide a way to
get an answer to a particular problem as well
as a way to begin to make sense of the nature
of each operation; that is, the counting
strategies highlight what actions are
associated with addition and subtraction
Math Activity
Modeling Story Problems
How did you use cubes and number lines to
model the problems?
How do your number sentences match your
actions?
How were the situations different?
Math Activity
Each table
will
have five post
it notes!
• Use cubes, counters or tiles and a number line
to perform the actions indicated in each
problem.
• Use a post it note for each problem:
Record a number sentence.
Create a model that shows the action.
Show the action in your model. How does it
match your number sentence?
Later you will decide which problem type is
represented by that problem.
Math Activity Part 2
Refer to the classification chart and decide
how to classify each of your post its.
Place your post its on the chart posters.
Be sure that your table number is on each
post it.
Key Ideas
• Focusing on the actions in a story problem
highlights distinctions between problems that
are represented by the same arithmetic
expression
• Given two problems that adults would call
subtraction, children may react in different
ways, counting back to solve one problem and
adding up to solve the other
Video Clips
1. I have 375 candy bars. I sell 90 of them. How
many candy bars do I have left?
2. I am taking a trip to visit my sister in Delaware. I
drive 90 miles and then stop to rest. The total
distance to my sister’s house is 375 miles. How
much farther do I have to go?
As you watch the video, make note of the
students’ solution methods and the teacher’s
questions to set up the task
Case Discussion Part 2
• What are the connections between the action of the
story problem and the way a student represents it?
• How is it possible that the same problem can be
solved with both an addition and a subtraction
sentence?
• What do the connections among a story situation, a
number-line model, and an arithmetic expression
illustrate about the relationship between addition
and subtraction?
Key Ideas
• The same problem may be solved by some children
with addition and by others with subtraction
• The term difference is the name for the result of
subtraction, but to find two numbers with a given
difference, addition may be used
• Two subtraction situations that may seem the same
to adults can be seen as very different by children
• Examining the ways in which a student uses a
number line to model a problem can illuminate the
way the student is thinking
Exit Question
• What mathematical ideas did this session
highlight for you?
• What was the session like for you as a
learner?
Lunch Assignment
Consider the operations of multiplication
and division as you review the cases in
Chapter Two