number talks. hally third grade student describe hally’s understandings and misunderstandings....
TRANSCRIPT
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NUMBER TALKS
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HallyThird Grade
Student
Describe Hally’s understandings
and misunderstandin
gs.
VIDEO
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Second Grade Student: I couldn’t take seven
from three so I borrowed ten. I made the one a
zero and the three became a thirteen, and thirteen minus seven is
six. That’s just how you do it when the bottom number is bigger than
the top.
0 13
13- 7 6
NEED FOR NUMBER TALKS
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Traditional View of Mathematics:
A discrete set of rules and procedures to be memorized and implemented with speed and accuracy……but without understanding the mathematical logic or numerical relationships that provide the foundation for these rules.
VIEW OF MATHEMATICS
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Accuracy – ability to produce an accurate answerEfficiency – ability to choose an appropriate, expedient strategy for a specific computation problemFlexibility – ability to use number
relationships with ease in computation
MATHEMATICALLY PROFICIENT STUDENTS
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Our math classrooms must provide opportunities for students:To grapple with number relationshipsApply numerical relationships to computation strategies
Discuss and analyze their reasoning
CREATING MATHEMATICALLY PROFICIENT STUDENTS
Number Talks
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DIRECTIONS
1. When the problem is put up, solve in your head.
2. When you have solved, put your thumb up in front of your chest.
3. Try to solve in a different way. For each different way you solve, put up another finger.
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HOW MANY OBJECTS DO YOU SEE?
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HOW MANY OBJECTS DO YOU SEE?
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26 + 58 = ?
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What is a number talk? What is the role of the teacher?
What is the role of the students?
Describe the classroom community and environment.
VIDEOThird Grade
38 + 37
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Number
Talks
Characteristics of Number
Talks
Classroom Community & Environment
Role of the Teacher
Role of the Students
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Classroom conversations and discussions around a few purposefully crafted computation problems
Short, ongoing daily routine (5 – 15 minutes)
Provides students with meaningful ongoing practice with computation
Intended to help students develop computational fluency
Problems are designed to elicit specific strategies that focus on number relationships
NUMBER TALKS
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Teacher presents problem
Students figure it
out
Students share their
answers
Students share their
thinking
Class agrees on
the answer
FORMAT
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1.Classroom environment & community
2.Classroom discussion3.The role of mental math4.The teacher’s role5.Purposeful computation problems
KEY COMPONENTS
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CLASSROOM ENVIRONMENT
saferisk-freecomfortableacceptingrespectfulclear
expectations
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Encourages students:To build on number relationships to solve problems instead of relying on memorized procedures
To develop efficient, flexible strategies with accuracy
To strengthen students’ understanding of place value
Ways to encourage mental math:Students solve problems without paper and pencil
Write problems in a horizontal format
MENTAL MATH
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199 + 199 11
199+199 398
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TEACHER’S ROLE
Read “What is the Teacher’s Role during Number Talks?”
What should the teacher do during Number Talks?
What should the teacher not do during Number Talks?
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Teacher
Facilitator
Listener
Questioner
Learner
TEACHER’S ROLE
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Select a designated location Give students time to think by
providing appropriate wait timeEncourage student communication
and equitable participationTurn & TalkThink/Pair/Share
Accept and record all responses without judgment
Ask students to test new strategiesCapture and record strategies so it is accessible
to others (notation should be mathematically correct)
PROCEDURES
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Provide access to tools and manipulativesNumber lines, hundred boards, cubes, counters, ten frames, place value blocks, fraction tiles, etc.
Model how to ask questions & make comments I agree with _____ because….. I do not understand ____________. Can you explain this again?
I disagree with ___ because…..How did you decide to ______?
ROLE OF THE TEACHER
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Ask students to use finger signals Number of strategies Agree/Disagree Effi cient strategy
Keep records of problems posed and the corresponding student strategies Record student’s name next to the strategy Document student participation and strategies
Smartboard fi le Notebook/Document Camera Camera
Hold small-group number talks throughout the week Pull groups based on common needs Select students who need to be challenged Work with students who are shy or reluctant to share in the
whole group
DEVELOPING ACCOUNTABILITY
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Require students to solve an exit problem using the discussed strategiesSpecific types of problems or strategies
Occasionally give a computation assessmentConsists of a few related problems Requires students to solve each problem in two ways
Create and post class strategy charts
DEVELOPING ACCOUNTABILITY
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Start with smaller problems to elicit thinking from multiple perspectives
Offer strategies from a previous student
Put a student’s strategy on the back burner
Limit number talks to 5 - 15 minutesBe patient with yourself and your students
Handout: “Tips for Implementing Number Talks”
HELPFUL TIPS & HINTS
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K-2 NUMBER TALKS
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How does the teacher build student fluency with small numbers?
What questions does the teacher pose to build understanding?
What strategies are the students using to build meaning of the numbers?
How does the teacher support student communication during the number talk?
VIDEOKindergarten
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1.Developing number sense2.Developing fluency with
small numbers3.Subitizing4.Making tens
GOALS OF K-2 NUMBER TALKS
Describe each goal. What does it mean?
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“Number sense is an awareness and understanding about what
numbers are, their relationships, their magnitude, the relative
effect of operating on numbers, including the use of mental
mathematics and estimation”
~Fennell & Landis, 1994, p. 187
NUMBER SENSE
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Conservation of numberOne-to-one correspondenceCompose and decompose numbersFact fluencySubitizingMaking tens
Place ValueTen ones is one group of 10How many more to make tenCompose and decompose 10
GOALS OF K-2 NUMBER TALKS
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Dot ImagesFive/Ten FramesNumber LinesHundred ChartStory Problems
K-2 NUMBER TALK TOOLS
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What strategies are the students using to build meaning of the numbers?
How does the teacher build student fluency with small numbers using ten-frames?
What questions does the teacher use to build understanding about decomposing and composing numbers?
VIDEOSecond Grade
8 + 6
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3-5 NUMBER TALKS
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1.Number sense2.Place value3.Fluency4.Properties5.Connecting mathematical
ideas
GOALS FOR GRADES 3-5
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How do the students’ strategies exhibit number sense?
How do the teacher and students connect math ideas throughout the number talk?
How does the progression of problems help students to apply the associative property?
VIDEOFifth Grade
12 x 15
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Carefully, purposefully select problemsBased on student needsProgression of number skills
Anticipate how students will solve the problemsSolve the problem yourself in multiple ways
Use resources to anticipate strategiesTrailblazer’s Teacher’s GuidesTeaching Student-Centered Mathematics
PLANNING
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Fluency with Dot ImagesFluency using Five- and Ten-FramesAddition:
Counting All/Counting On with Dot Images Counting All/Counting On with Double Ten-Frames Counting All/Counting On with Number Sentences 3 + 9 Doubles/Near-Doubles with Double Ten-Frames Doubles/Near-Doubles with Number Sentences 7 + 8; 16 +
15 Making Tens with Double Ten-Frames 5 + 6 Making Tens with Number Sentences 6 + 5 + 4 Making Landmark or Friendly Numbers 48 + 13 Breaking Each Number into Its Place Value 16 + 26 Compensation 19 + 26 Adding Up in Chunks 44 + 35
NUMBER & ADDITION
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Addition: Making Tens 2 + 6 + 8 + 3 + 4Making Landmark or Friendly Numbers 49 + 23Doubles/Near Doubles 24 + 26Breaking Each Number into Its Place Value 35 + 26
Adding Up in Chunks 28 + 24Subtraction:
Adding Up 60 – 49Removal/Counting Back 50 – 17Place Value and Negative Numbers 48 – 29Adjusting One Number to Create an Easier Problem 50 – 24 (49 – 24 = 25; 25 + 1 = 26)
Keeping a Constant Difference 51 – 26
ADDITION & SUBTRACTION
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Multiplication:Repeated Addition or Skip CountingMaking Landmark or Friendly Numbers 25 x 9 Partial Products 8 x 16Doubling and Halving 15 x 16 (30 x 8)Breaking Factors into Smaller Factors 4 x 9 (4 x 3 x 3)
Division:Repeated Subtraction or Sharing/Dealing OutPartial QuotientsMultiplying UpProportional Reasoning
MULTIPLICATION & DIVISION
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Number Talks: Helping Children Build Mental Math and Computation Strategies
Mental Math
Marcy Cook ResourcesNumber SENSE Books
RESOURCES
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Math Perspectives by Kathy Richardsonhttp://www.mathperspectives.com/num_talks.html
Video: 4th grade Area/Perimeter
Inside Mathematics: Number Talkshttp://www.insidemathematics.org/index.php/classroom-video-visits/number-talks
Videos: 2nd grade, 4th grade, 5th grade
get2MATH K-5: Number Talks https://sites.google.com/site/get2mathk5/home/number-talks
ONLINE RESOURCES
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Discuss with your grade level:How can we incorporate Number Talks into our daily instruction?
What practices are we currently doing well and how can we improve?
What types of number talks will we incorporate during the first quarter?
REFLECTION
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Number
Talks
Characteristics of Number
Talks
Classroom Community & Environment
Role of the Teacher
Role of the Students