Transcript Document
Standards of
Mathematical
Practice
http://thinkmath.blog.monroe.edu/
Today’s Goals
• To explore the mathematical standards for
Content and Practice
• To discuss and learn strategies for getting
students engaged in the Standards of
Mathematical Practice
• To explore how we can use existing
resources to focus on the Practices
Common Core State Standards
Mathematics
• Standards for
Content
• Standards for
Practice
Standards for Mathematical Practice
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning
of others
Model with mathematics
Use appropriate tools strategically
Attend to precision
Look for and make use of structure
Look for and express regularity in repeated reasoning
© Institute for Mathematics & Education 2011
SMP 1: Make sense of problems and persevere
in solving them.
Gather Information
Continuously
evaluate
progress
Anticipate
possible
solutions
Make a plan
Question
sense of
solutions
Check
results
© Institute for Mathematics & Education 2011
SMP 2: Reason abstractly and quantitatively
Decontextualize
Represent as symbols, abstract the situation
5
½
Mathematical
Problem
P
x x x x
Contextualize
Pause as needed to refer back to situation
© Institute for Mathematics & Education 2011
SMP 3: Construct viable arguments and
critique the reasoning of others
Make a conjecture
Build a logical progression
of statements to explore
the conjecture
Analyze situations by
breaking them into cases
Recognize and use
counter examples
© Institute for Mathematics & Education 2011
SMP 4: Model with mathematics
Problems in
everyday life…
…reasoned using
mathematical methods
Images: http://tandrageemaths.wordpress.com, asiabcs.com, ehow.com, judsonmagnet.org, life123.com, teamuptutors.com, enwikipedia.org,
© Institute for Mathematics & Education 2011
glennsasscer.com
SMP 5: Use appropriate tools strategically
© Institute for Mathematics & Education 2011
SMP 6: Attend to precision
Comic: http://forums.xkcd.com/viewtopic.php?f=7&t=66819
© Institute for Mathematics & Education 2011
SMP 7: Look for and make use of structure
© Institute for Mathematics & Education 2011
SMP 8: Look for and express regularity in
repeated reasoning
© Institute for Mathematics & Education 2011
• Over emphasis on computation obscures
understanding of the operations.
• Focus on behavior of the operations
supports computational fluency.
Deborah Schifter
Content Goals
These standards of practice will be
examined in the context of the following
content standard:
Understand properties of the operations.
Grade 1: p. 14
Grade 2: p. 18
Grade 3: p. 22
Grade 4: p. 28
Grade 5: p. 33 (paragraph #2)
What generalization is suggested by
these problems?
Video 1 – Will it always work?
Ms. Kaye’s
3rd Grade
CTB/McGraw-Hill; Mathematics Assessment Resource Services, 2003
Video 2 – Will it always work?
Video 3 – Will it always work?
What Standards for
Mathematical Practice
were focused on in this
task?
Adding 1 to a Factor
Writing prompt:
In a multiplication problem, if you add 1 to a
factor, I think this will happen to the product…
Students’ Articulation of the Claim
• “The number that is not increased is the
number that the answer goes up by.”
• “The number that is staying and not going
up, increases by however many it is.”
• “I think that the factor you increase, it goes
up by the other factor.”
Sample task
• Draw a picture for the original equation; then change it
just enough to match the new equations.
• Make an array for the original equation; then change it
just enough to match the new equations.
• Write a story for the original equation; then change it
just enough to match the new equations.
Example: Original equation 7 x 5 = 35
New equations 7 x 6 = 42
8 x 5 = 40
Frannie’s Story Context
There are 7 jewelry boxes and each box has
5 pieces of jewelry. There are 35 pieces of
jewelry altogether.
Jewelry Boxes
7x5
Seven boxes with five
pieces of jewelry in
each box
35 pieces of jewelry
Jewelry Boxes
7x5 8x5
Eight
Seven boxes with five
pieces of jewelry in each
box
35 pieces of jewelry
+ 5 pieces of jewelry
40 pieces of jewelry
Jewelry Boxes
7x5
Seven boxes with five
pieces of jewelry in
each box
35 pieces of jewelry
Jewelry Boxes
7x57x6
six
Seven boxes with five
pieces of jewelry in each
box
35 pieces of jewelry
+ 7 pieces of jewelry
42 pieces of jewelry
Other Stories
•
•
•
•
Baskets of bouncy balls
Tanks with salmon eggs
Baskets of mozzarella sticks
Rows of chairs
Making Sense of Multiplication
Explain how the array changes from 7 x 5 to 8 x 5
and from 7 x 5 to 7 x 6.
What Standards for
Mathematical Practice
were focused on in this
task?
Strategies for Implementing
the Practices
Use Rich Tasks
Where to find rich tasks.
http://www.insidemathematics.org/
http://illustrativemathematics.org/
http://www.rda.aps.edu/mathtaskbank/start.htm
http://www.galileo.org/math/MathProblems.html
http://balancedassessment.concord.org/tasksalpha.html
Rich Problems Worksheet
• Read through the tasks on the Rich Problems
worksheet
• With a partner discuss what similarities you
see in these problems
Creating Open Ended
Questions
Creating open ended questions
• With a partner choose an upcoming topic you
will be teaching.
• Create 3 open ended questions to engage your
students?
• For each questions what Math Practices would
you expect your students to be engaged in?
Additional Strategies
Where do I find these opportunities
in my resources?
With a partner, pick an upcoming lesson and
discuss how you are going to integrate the
standards of Mathematical Practice.
• Focus on 1 or 2 Practices
• What will you see the students doing if
they are engaging in the Practices?
• How will you facilitate the Practices?