acos 2010 standards of mathematical practice
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ACOS 2010 Standards of Mathematical Practice. 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. - PowerPoint PPT PresentationTRANSCRIPT
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ACOS 2010 Standards of Mathematical Practice
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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.
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Standards for Mathematical Practice Carry across all grade levels
Describe habits of mind of a mathematically expert student
1. Make sense of problems and persevere in solving them
2. Reason abstractly and quantitatively3. Construct viable arguments & critique the
reasoning of others4. Model with mathematics5. Use appropriate tools strategically6. Attend to precision7. Look for and make use of structure8. Look for and express regularity in repeated
reasoning3
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Make sense of problems and persevere in solving them.
When presented with a problem, I can make a plan,
carry out my plan, and evaluate its success.
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…PERSEVEREMONITOR my work.CHANGE my plan if it isn’t working out.ASK myself, “Does this make sense?”
#1AFTER…
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?
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Reason abstractly and quantitatively
I can use reasoning habits to help me contextualize
and decontextualize problems.
CONTEXTUALIZEI 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.
DECONTEXTUALIZEI can take numbers out of context and work mathematically with them.
For example, if givenI 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.
#2
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Construct viable arguments and critique the reasoning of others
I can make conjectures and critique the mathematical
thinking of others.
I can construct, justify, and communicate arguments by…• considering context.• using examples and non- examples.• using objects, drawings, diagrams and actions.
I can critique the reasoningof others by…• listening.• comparing arguments.• identifying flawed logic.• asking questions to clarify or improve arguments.
#3
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Model with mathematicsI can recognize math in everyday life and use math I know to solve everyday problems.
#4
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.
Represent
Math
real-world situations
oral languag
e
symbols
concrete
models
pictures
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Use appropriate tools strategically
I know when to use certain tools to help me explore and deepen my math understanding.
#5I have a math toolbox.I know HOW to use math tools.I know WHEN to use math tools.I can reason: “Did the tool I used give me an answer that makes sense?”
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Attend to precisionI can use precision when
solving problems and communicating my ideas.
#6
Problem SolvingI can calculate accurately.I can calculate efficiently.
My answer matches what the problem asked me to do–estimate or find an exact answer.
CommunicatingI can SPEAK, READ, WRITE, and LISTEN mathematically.
I can correctly use…• math symbols• math vocabulary• units of measure
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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
NUMBERSFor example:• Base 10 structure•Operations and properties•Terms, coefficients, exponents
SHAPESFor example:• Dimension• Location • Attributes • Transformation
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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.#8Patterns:1/9 = 0.1111….2/9 = 0.2222…3/9 = 0.3333…4/9 = 0.4444….5/9 = 0.5555….
I notice the pattern which
leads to an efficient
shortcut!!!
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Number TalksHelping Children Build Mental Math and Computation Strategies Grades K-5
By Sherry Parrish
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Number talks help students develop efficient, flexible,
and accurate computational strategies that build upon key foundational ideas of
mathematics.
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Classroom conversations and discussions centered around
purposefully crafted computation problems are the at very core of number talks.
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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.
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Video 3.5
Third Grade7 x 7
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Key Components of Number Talks
Students Teacher Environment
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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
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Sharing and Discussing Computation Strategies1. Clarify their own thinking2. Consider and test other
strategies3. Investigate and apply
mathematical relationships4. Build a repertoire of efficient
strategies5. Make decisions about choosing
effective strategies
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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.
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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.
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Teacher’s RoleMoves into the role of facilitatorKeeps 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
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Video 5.3 – Fifth Grade16 x 35Work mentally two ways
Look for Standards for Mathematical Practice
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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?
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Standards for Mathematical Practice Carry across all grade levels
Describe habits of mind of a mathematically expert student
1. Make sense of problems and persevere in solving them
2. Reason abstractly and quantitatively3. Construct viable arguments & critique the
reasoning of others4. Model with mathematics5. Use appropriate tools strategically6. Attend to precision7. Look for and make use of structure8. Look for and express regularity in repeated
reasoning25
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Standards for Mathematical PracticeSMP1: 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…
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Purposeful Computation ProblemsProblems 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.
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Grade Level Groups-ChartsWrite an addition number
talk problem. Solve each problem using
at least two strategies students might commonly use.
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Gallery Walk1. How do the strategies build from
grade level to grade level?2. What math concepts need to be
developed at each grade level to allow students to be mathematically powerful?
3. How does this affect student understanding in future grade levels?
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Your Practice: A Closer Look1. How are the student and teacher
roles in your classroom similar to or different from the classroom clips?
2. 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?
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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?
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Parrish, S. (2010). Number Talks: Helping Children Build Mental Math and Computation Strategies Grades K-5. Sausalito: Math Solutions.