Integrating the
Mathematical Practices in
Problem Solving
Grades 1 - 4
Monica Hartman
August 28 and 29, 2012
Port Huron Back to School Professional Development
Write Your Own Story
Problem
1. Think of a story problem you
would use with your students.
2. Write it down on a 3x5 card.
3. Place the card under your name
tag.
Pre & Post Teacher Survey
Complete the left side
“Before Attending
Mathematical Practices
Workshop”
Learning Target
I can integrate the Mathematical
Practices in my teaching to develop
deeper mathematical knowledge
within my students.
8 Mathematical Practices
From: Teaching Children Mathematics, March 2012, Getting Started in K – Grade 2, pg. 440-445.
Solve and Discuss Structure
• Some children go to board and solve
a problem
• Other children solve the problem at
their desk.
• Teacher asks two children at the
board to explain their method.
Solve and Discuss Structure
The explaining student:
• Relates solution to a math drawing
• Asks if there are any questions
• Responds to the questions
The listening student:
• Asks questions
• Suggests edits to the explanation or
solution
Solve and Discuss Structure
• The Solve and Discuss Structure is
actually a Solve, Explain, Question,
and Justify structure
• Aspire to make your classroom a
place where all children listen to
understand each other, not just being
quiet while someone else is talking.
Mathematical Practice
Rubric
3 min. Review Rubric
(from: Institute for Advanced Study)
http://www.ocf.berkeley.edu/~mimiyang/misc/rubric.pdf
Pair Share
1. Look at Math Practice #3 and #6
2. Discuss what a classroom might look
like where the teacher is using these
practices during instruction.
Implementing the Standards
of Mathematical Practice
In the Gum and Pretzel problem, we will
focus of Mathematical Practices 3 and 6.
 MP3 – Construct viable arguments and
critique the reasoning of others.
 MP6 – Attend to precision
Review the Mathematics Classroom
Visitation Recording Form
Content Focus
1.OA and 2.OA Cluster Statements:
Represent and solve problems
involving addition and subtraction
2.OA.3 Standard:
Determine whether a group of objects
has an odd or even number of
members; write an equation to
express an even number as a sum of
equal addends.
Content Focus
3.OA Cluster Statement:
Solve problems involving the four
operations, and identify and explain
patterns in arithmetic.
4.OA Cluster Statement:
Use the four operations with whole
numbers to solve problems.
The Gum and Pretzel Problem
gum 2¢
big pretzel 7¢
Mark has 30 cents in his pocket and he
wants to spend it all and not have any
change left in his pocket.
What can he buy for 30 cents?
What different choices does he have? Why?
The Gum and Pretzel Problem
gum 2¢
big pretzel 7¢
What can he buy for 30 cents?
What different choices does he have? Why?
 Work independently (2-3 minutes)
 Share your strategies with your partner
and with your group
 Each group should be ready to explain
their method for solving this problem.
Sharing Strategies
Remember, the explaining student:
• Relates solution to a math drawing
• Asks if there are any questions
• Responds to the questions
The listening student:
• Asks questions
• Suggests edits to the explanation or
solution
Sean’s Numbers
What mathematical practices do you
observe in this video of a third grade class
discussing odd and even numbers after
doing the Gum and Pretzel problem?
Video and Supporting Documents found at
http://deepblue.lib.umich.edu/handle/2027.42/65013
Remodeling Tasks
• Tasks can be remodeled to make them
more intellectually challenging.
• Look at the problem you wrote at the
beginning of the session
• Does it fit into one of the categories from
Table 1, Common addition and subtraction
situations?
• Look at Remodeling Tasks in Mathematics
Classroom Handout.
• Use one of the suggestions listed, or
another one, to remodel your task.
Remodeling Tasks
• Get into groups of 4.
• Rewrite your original problem to
make it more challenging, if needed
• Share your original problem and
revision with your group.
• The group chooses one to remodel
using the two page, Remodeling a
Mathematical Task handout.
• Groups will give a 2 minute report to
class.
2 Minute Report
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Requirements
Original Problem
Remodeled Problem
Mathematical Practice- refer to rubric
Part 1: Setting up the mathematical
task
Part 2: Questions to supporting
students’ during task
Part 3: Questions to use during class
discussion
Bar Diagrams
Watch Introduction Video
http://www.mhschool.com/math/com
mon/pd_video/mathconnects_bardi
agram_p1/index.html
http://www.mhschool.com/math/com
mon/pd_video/mathconnects_bardi
agram_p2/index.html
Thinking Blocks
http://www.mathplayground.com/think
ingblocks.html
Explore the site 
Learning Target
I can integrate the Mathematical
Practices in my teaching to develop
deeper mathematical knowledge
within my students.
Exit Ticket
On the back of your name tent write:
What is your take-away
from today’s session?
Pre & Post Teacher Survey
Complete the right side
“After Attending Mathematical
Practices Workshop”
&
Post Event Questions
Thanks for another great session
Monica