1. ACOS 2010 Standards of Mathematical Practice

2. Outcomes:
Participants will review the Standards of Mathematical Practice
Participants will analyze K-5 number talks.
Participants will form a global perspective for the school community.
Participants will identify one change they plan to make in their classroom practice related to number talks.

3. Standards for Mathematical Practice
Carry across all grade levels
Describe habits of mind of a mathematically expert student
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments & 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 3 3

4. Make sense of problems and persevere in solving them.#1
When presented with a problem, I can make a plan, carry out my plan, and evaluate its success.
AFTER…
CHECK
Is my answer correct?
How do my representations connect to my algorithms?
EVALUATE
What worked?
What didn’t work?
What other strategies were used?
How was my solution similar to or different from my classmates?
BEFORE…
EXPLAIN the problem to myself.
Have I solved a problem like this before?
ORGANIZE information.
What is the question I need
to answer?
What is given?
What is not given?
What tools will I use?
What prior knowledge do I
have to help me?
DURING…
PERSEVERE
MONITOR my work.
CHANGE my plan if
it isn’t working out.
ASK myself, “Does this
make sense?”

5. Reason abstractly and quantitatively
I can use reasoning habits to help me contextualize and decontextualize problems. #2
CONTEXTUALIZE
I can take numbers and put them in a real-world context.
For example, if given
3 x 2.5 = 7.5,
I can create a context:
I walked 2.5 miles per day for 3 days. I walked a total of 7.5 miles.
DECONTEXTUALIZE
I can take numbers out of context and work mathematically with them.
For example, if given
I walked 2.5 miles per day for 3 days, How far did I walk?
I can write and solve
3 x 2.5 = 7.5.

6. Construct viable arguments and critique the reasoning of others#3
I can make conjectures and
critique the mathematical
thinking of others.
I can critique the reasoning
of others by…
listening.
comparing arguments.
identifying flawed logic.
asking questions to
clarify or improve
arguments.
I can construct, justify, and
communicate arguments by…
considering context.
using examples and non-
examples.
using objects, drawings,
diagrams and actions.

7. Model with mathematics#4
I can recognize math in everyday life and use math I know to solve everyday problems.
concrete
models
I can…
make assumptions and
estimate to make
complex problems
easier.
identify important
quantities and use tools
to show their relation-
ships.
evaluate my answer and
make changes if needed.
pictures
symbols
Represent
Math
oral
language
real-world situations

8. Use appropriate tools strategically#5
I know when to use certain tools to help me explore and deepen my math understanding.
I have a math toolbox.
I know HOW to use math
tools.
I know WHEN to use math
I can reason: “Did the tool I
used give me an answer
that makes sense?”

9. I can use precision when solving problems and communicating my ideas.#6
Attend to precision
I can use precision when solving problems and communicating my ideas.
Problem Solving
I can calculate accurately.
I can calculate efficiently.
My answer matches what the problem asked me to do–estimate or find an exact answer.
Communicating
I can SPEAK, READ, WRITE, and LISTEN mathematically.
I can correctly use…
math symbols
math vocabulary
units of measure

10. Look for and make use of structure
I can see and understand how numbers and spaces are organized and put together as parts and wholes. #7
SHAPES
For example:
Dimension
Location
Attributes
Transformation
NUMBERS
For example:
Base 10 structure
Operations and properties
Terms, coefficients, exponents

11. Look for and express regularity in repeated reasoning
I can notice when calculations are repeated. Then, I can find more efficient methods and short cuts. #8
Patterns:
1/9 = ….
2/9 = …
3/9 = …
4/9 = ….
5/9 = ….
I notice the pattern which leads to an efficient shortcut!!!

12. Number Talks Helping Children Build Mental Math and Computation Strategies Grades K-5
By Sherry Parrish

13. Number talks help students develop efficient, flexible, and accurate computational strategies that build upon key foundational ideas of mathematics.

14. Classroom conversations and discussions centered around purposefully crafted computation problems are the at very core of number talks.

15. By sharing and defending their solutions and strategies, students are provided with the opportunity to collectively reason about numbers while building connections to key conceptual ideas in mathematics.

16. Video 3.5
Third Grade
7 x 7

17. Key Components of Number Talks
Students Teacher Environment

18. Classroom Environment and Community
Safe and risk free
Students are comfortable offering responses for discussion, questioning themselves and others, and investigating new strategies
Culture of acceptance is based on a common quest for learning and understanding

19. Sharing and Discussing Computation Strategies
Clarify their own thinking
Consider and test other strategies
Investigate and apply mathematical relationships
Build a repertoire of efficient strategies
Make decisions about choosing effective strategies

20. Mental computation is a key component of number talks because it encourages students to build on number relationships to solve problems instead of relying on memorized procedures.

21. When students approach problems without paper and pencils, they are encouraged to rely on what they know and understand about the numbers and how they are interrelated. Mental computation causes them to be efficient with the numbers and avoid holding numerous quantities in their heads.

22. Teacher’s Role Moves into the role of facilitator
Keeps discussion focused on the important mathematics
Helps students learn to structure their comments and wonderings
Guides students to ponder and discuss examples that build upon their purposes

23. 16 x 35 Work mentally two ways
Video 5.3 – Fifth Grade
16 x 35
Work mentally two ways
Look for Standards for Mathematical Practice

24. Questions to be thinking about:
What are the similarities and differences between the grades?
Classroom community?
Teacher’s role?
Student’s role?
Communication?
How do the content skills build from grade to grade?

25. Standards for Mathematical Practice
Carry across all grade levels
Describe habits of mind of a mathematically expert student
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments & 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 25 25

26. Standards for Mathematical Practice
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: Note and pay attention to…

27. Purposeful Computation Problems
Problems are crafted to guide students to focus on mathematical understanding and knowledge. The goals and purposes for the number talk should determine the numbers and operations chosen.

28. Grade Level Groups-Charts
Write an addition number talk problem.
Solve each problem using at least two strategies students might commonly use.

29. Gallery Walk
How do the strategies build from grade level to grade level?
What math concepts need to be developed at each grade level to allow students to be mathematically powerful?
How does this affect student understanding in future grade levels?

30. Your Practice: A Closer Look
How are the student and teacher roles in your classroom similar to or different from the classroom clips?
Think about a recent math lesson you have taught. What role does a learning community play in your lesson? What opportunities exist for students to learn through inquiry-based tasks? How does your lesson build number sense?

31. What is one change you plan to make?
What instructional strategies can you incorporate into future math lessons to help support student thinking and mathematical understanding?
Remember to start small in making shifts in your classroom practice related to number talks.
What is one change you plan to make?

32. Parrish, S. (2010). Number Talks: Helping Children Build Mental Math and Computation Strategies Grades K-5. Sausalito: Math Solutions.