ACOS 2010 Standards of Mathematical Practice 1. Outcomes: Participants will review the Standards of Mathematical Practice Participants will analyze.

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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.

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

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?

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

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

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

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?”

Attend to precision

I 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

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

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 Grade

16 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?

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 Walk

1. 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 Look

1. 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.