Mathematics 3 – 8
Standards for Mathematical Practice
TLQP 2013-14
Tom Sweeney
The Sage Colleges
Sources
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http://www.corestandards.org/
http://www.parcconline.org/
http://engageny.org/
http://www.illustrativemathematics.org/
http://www.achievethecore.org/
http://commoncoretools.me/
http://insidemathematics.org/
https://www.teachingchannel.org/videos/
Common Core State Standards for
Mathematics (CCSSM)
• Standards for Mathematical Practice &
(recurring throughout the grades)
(our focus today)
• Standards for Mathematical Content
(different at each grade level)
Objectives
Gain a deeper understanding of the eight
Standards for Mathematical Practice (SMP)
Identify evidence of teachers using SMP in
their classrooms
Identify evidence of students using SMP in
their work.
Video
• The Importance of Mathematical Practices
(4:02)
• Mathematical Practices, Focus and
Coherence in the Classroom
(1:14)
Standards for Mathematical Practice
Initial Activity
Newspaper problem
Compliments of Brenda Lidistri
Standards for Mathematical Practice
1. Make sense of problems and persevere in solving them.
2. Reason abstractly and quantitatively.
3. Construct viable arguments and critique the reasoning of others.
4. Model with mathematics.
5. Use appropriate tools strategically.
6. Attend to precision.
7. Look for and make use of structure.
8. Look for and express regularity in repeated reasoning.
Pass out paragraph descriptors assign a stand to each neighboring
pair of participants
Standards for Mathematical Practice
ACTIVITY (initial)
For your assigned Standard of Mathematical Practice:
What are the verbs that illustrate the student actions
for your assigned mathematical practice?
Circle, highlight or underline them.
Discuss with a partner:
What stands out?
SMP1: Explain and make conjectures…
SMP2: Make sense of…
SMP3: Understand and use…
SMP4: Apply and interpret…
SMP5: Consider and detect…
SMP6: Communicate precisely to others…
SMP7: Discern and recognize…
SMP8: Notice and pay attention to…
Standards for Mathematical Practice
Activity B
Divide a piece of chart paper in half and on one
side label it Student Evidence and on the other
side label it Teacher Evidence. Don’t forget to
write the number of the MP you selected on
your chart paper as well.
Standards for Mathematical Practice
ACTIVITY B (cont’d)
Brainstorm with members at your table what students
would be doing in the classroom if this MP was being
implemented effectively and list evidence on your chart
paper.
Next, brainstorm with members at your table what
teachers would be doing in the classroom if this MP
was being implemented effectively and list evidence on
your chart paper.
Standards for Mathematical Practice
ACTIVITY B (cont’d)
Locate all those tables that worked on the same MP as
you and come together as one group and share your
work.
Review the evidence and determine if it should stay on
the chart or be deleted. Be prepared to report out.
Standards for Mathematical Practice
MP 1:
Make sense of problems and
persevere in solving them.
Standards for Mathematical Practice
MP 2:
Reason abstractly and
quantitatively.
Standards for Mathematical Practice
MP 3:
Construct viable arguments and
critique the reasoning of others.
Standards for Mathematical Practice
MP 4:
Model with mathematics.
Standards for Mathematical Practice
MP 5:
Use appropriate tools
strategically.
Standards for Mathematical Practice
MP 6:
Attend to precision.
Standards for Mathematical Practice
MP 7:
Look for and make use of
structure.
Standards for Mathematical Practice
MP 8:
Look for and express regularity
in repeated reasoning.
Standards for Mathematical Practice
PROBLEM
A rectangle has sides of length 6 in.
and 2 in. What is its area ?
Standards for Mathematical Practice
Identify the MPs that align with this
problem. Discuss at your tables.
Standards for Mathematical Practice
Pose a different problem that could go
deeper but require the same mathematical
content knowledge?
Standards for Mathematical Practice
Explain what students might learn from the
second question compared to the first
question?
Standards for Mathematical Practice
Explain what a teacher might learn from
how students answer the first question
compared to how students answer the
second question?
McDonald’s Claim
Wikipedia reports that 8% of all Americans eat at
McDonalds every day.
310 million Americans and 12,800 McDonalds…
Do you believe the Wikipedia report to be true?
Create a mathematical argument to
justify your position.
MCDONALD’S CLAIM
PROBLEM
Which mathematical practices are
needed to complete the task?
Integrating the Standards for Mathematical
Practice
Inside +=x
Mathematics
Fran Dickenson
http://www.insidemathematics.org/index.php/
math-standards-together
(3:53)
Watch the video using the Inside Mathematics
link above and collect evidence from the lesson
that exemplifies the Standards for Mathematical
Practice. Focus on both the students and the
teacher.
Guess My Rule from the Video
X 0
X
10
6
8
? 5
Y
27
15
21
12
0
Integrating the Standards for Mathematical
Practice
(Continued)
Inside +=x
Mathematics Fran Dickenson
Compare your evidence with an elbow partner
and then engage in a conversation with
members at your table to come to consensus as
to which MPs you observed.
Integrating the Standards for Mathematical
Practice
(continued)
Inside +=x
Mathematics
(video)
For a more in-depth study of the Standards for
Mathematical Practice, please visit
http://www.insidemathematics.org/index.php/c
ommmon-core-math-intro.
Standards for Mathematical Practice
MP PLACEMAT ACTIVITY
Everyone will need the MP Placemat and the MP
Activity Cards. Read through the MP Activity Cards on
your own. Once you have read the activity cards, you
need to decide where you would put them on your
placemat. You have 16 activity cards and 16 boxes on
your placemat.
Standards for Mathematical Practice
MP PLACEMAT ACTIVITY (cont’d)
First you will have time to work independently
and then in small groups at your table. In the
end, your table must come to consensus and a
representative needs to come up and post their
results on the master placemat.
Instructional Self-assessment
• Examine tasks in your instructional
materials:
– Higher cognitive demand?
– Lower cognitive demand?
• Where are the challenging tasks?
• Do all students have the opportunity to
grapple with challenging tasks?
• Examine the tasks in your assessments:
– Higher cognitive demand?
– Lower cognitive demand?
SMP 3. Construct viable arguments and critique
the reasoning of others
• Students make conjectures
• Students justify their conclusions and communicate
them to others
• Students compare the effectiveness of two plausible
arguments
• Students listen and respond to the arguments of others
for sense making and clarity
Thank you!
sweent@sage.edu