Getting to Know You... Math Style Grab a bingo card from the
middle of your table Circulate the room searching for teachers who
can "sign" a box on your bingo card (one signature per box
please)
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Readers and Math Writers = Workshop Workshop Framework
Framework Math Workshop
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Math Review is............. Time to reinforce a previously
taught concept Formative and based on daily student understanding
Work that is de-briefed and discussed Used to guide instruction 3
to 6 review problems (based on grade level) An opportunity to
circulate and observe common misconceptions or understandings
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Math Review is............... Not time to teach a new concept
or trick the students Not pre-printed or planned by yearlong or
unit objectives Not work completed without discussion Not used as a
grade or graded by others Not more than six problems Not busy
work
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Math Review and Mental Math
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Problem Solving - happens daily in the classroom.
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Conceptual Understanding This is where you teach your
curriculum. You will use Math Expressions, Glencoe and DMI
experiences as a resource.
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Standards for Mathematical Practice Mathematically Proficient
Students... 1. Make sense of problems and persevere in solving
them. 2. Reason abstractly and quantitatively. 3. Construct viable
arguments and critique the reasoning of others. 4. Model with
mathematics. 5. Use appropriate tools strategically. 6. Attend to
precision. 7. Look for and make use of structure. 8. Look for and
express regularity in repeating reasoning.
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The Standards for Mathematical Practice Take a moment to
examine the first three words of each of the 8 mathematical
practices... what do you notice? Mathematically Proficient
Students...
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The Standards for [Student] Mathematical Practice What are the
verbs that illustrate the student actions of each mathematical
practice?
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Mathematical Practice #3: Construct viable arguments and
critique the reasoning of others Mathematically proficient
students: understand and use stated assumptions, definitions, and
previously established results in constructing arguments. make
conjectures and build a logical progression of statements to
explore the truth of their conjectures. analyze situations by
breaking them into cases, and can recognize and use
counterexamples. justify their conclusions, communicate them to
others, and respond to the arguments of others. reason inductively
about data, making plausible arguments that take into account the
context from which the data arose. compare the effectiveness of two
plausible arguments, distinguish correct logic or reasoning from
that which is flawed, and-if there is a flaw in an argument-explain
what it is. construct arguments using concrete referents such as
objects, drawings, diagrams, and actions. Such arguments can make
sense and be correct, even though they are not generalized or made
formal until later grades. determine domains to which an argument
applies. listen or read the arguments of others, decide whether
they make sense, and ask useful questions to clarify or improve the
arguments.
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In the SJSD curriculum...
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Standards for Mathematical Practice Buttons Task
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Standards for [Student] Mathematical Practices "Not all tasks
are created equal, and different tasks will provoke different
levels and kinds of student thinking." ~ Stein, Smith, Henningsen,
& Silver, 2000 "The level and kind of thinking in which
students engage determines what they will learn." ~ Hiebert,
Carpenter, Fennema, Fuson, Wearne, Murray, Oliver, & Human
1997
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Comparing Two Mathematical Tasks Martha was re-carpeting her
bedroom which was 15 feet long and 10 feet wide. How many square
feet of carpeting will she need to purchase? ~ Stein, Smith,
Henningsen, & Silver, 2000, p. 1
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Comparing Two Mathematical Tasks Ms. Brown's class will raise
rabbits for their spring science fair. They have 24 feet of fencing
with which to build a rectangular rabbit pen in which to keep the
rabbits. 1. If Ms. Brown's students want their rabbits to have as
much room as possible, how long would each of the sides of the pen
be? 2. How long would each of the sides of the pen be if they had
only 16 feet of fencing? 3. How would you go about determining the
pen with the most room for any amount of fencing? Organize your
work so that someone else who read it will understand it. ~ Stein,
Smith, Henningsen, & Silver, 2000, p.2
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Comparing Two Mathematical Tasks Discuss: How are Martha's
Carpeting Task and the Fencing Task the same and how are they
different?
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Comparing Two Mathematical Tasks Lower-Level Tasks Higher-Level
Tasks
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Reflection My definition of a good teacher has changed from
"one who explains things so well that students understand" to "one
who gets students to explain things so well that they can be
understood." (Steven C. Reinhart, "Never say anything a kid can
say!" Mathematics Teaching in the Middle School 5, 8 [2000]:
478)
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Richard Schaar What I learned in school may be growing
increasingly obsolete today, but how I learned to learn is what
helps me keep up with the world around me. I have the study of
mathematics to thank for that.
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Rigor and Relevance
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Rigor & Relevance Framework Relevance makes RIGOR possible,
but only when trusting and respectful relationships among students,
teachers, and staff are embedded in instruction. Relationships
nurture both rigor and relevance.
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Rigor is...
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Article: Tips for Using Rigor, Relevance and
Relationships.
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Rigor is... Work that requires students to work at high levels
of Bloom's Taxonomy combined with application to the real
world.
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3 Misconceptions of Rigor MORE does not mean more rigorous.
DIFFICULT increased difficulty does not mean increased rigor. RIGID
all assignments are due by no exception.
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RIGOR
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Relevance Why do I need to know this?
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Misconceptions of Relevance COOL relevance doesnt exclusively
mean what the students do for fun EXCLUSIVE relevance without rigor
does not ensure success.
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Relevance
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Application Model 1. Knowledge in one discipline 2. Application
within discipline 3. Application across disciplines 4. Application
to real-world predictable situations 5. Application to real-world
unpredictable situations
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Putting it all together
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Activity Rigor and Relevance Card Sort
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Six Questions All Students Must Be Able to Answer When seeking
rigor, relevance, and relationships, all students should be able to
answer the following questions: 1. What is the purpose of this
lesson? 2. Why is this important to learn? 3. In what ways are you
challenged to think in this lesson? 4. How will you apply, assess,
or communicate what you've learned? 5. Do you know how good your
work is and how you can improve it? 6. Do you feel respected by
other students in this class?
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Mastery of Math Facts After students have reached conceptual
understanding, the following fluencies are required by the CAS: K
K.OA.5 Add/subtract within 5 1 1.OA.6 Add/subtract within 10 2
2.OA.2 Add/subtract within 20 (know single digit products from
memory) 2.NBT.5 Add/subtract within 100 3 3.0A.7 Multiply/divide
within 100 (know single-digit products from memory). 3.NBT.2
Add/subtract within 1000 4 4.NBT.4 Add/subtract within 1,000,000 5
5.NBT-5 Multi-digit multiplication 6 6.NS.2,3 Multi-digit division
Multi-digit decimal operations
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Common Formative Assessment Kindergarten and First Grade
Mathematics Interviews Math Fact Fluency - Reflex Conference Notes
- anecdotal records and Math Reasoning Inventory Performance Tasks
Mathematics Predictive Exams Math Review and Mental Math
Developing Mathematical Ideas August 15 & 16, 2013
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DMI is about developing YOUR mathematical understanding If our
goal is to create mathematically powerful children then we must
also create mathematically powerful teachers. --Lance Menster
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What is DMI? Developing Mathematical Ideas (DMI) is a
professional development curriculum presented through a series of
seminars. The premise of the DMI materials is that the art of
teaching involves helping students move from where they are into
the content to be learned.
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DMI Premises DMI seminars bring together teachers from
kindergarten through middle grades to: learn mathematics content
learn to recognize key mathematical ideas with which their students
are grappling learn how core mathematical ideas develop across the
grades learn how to continue learning about children and
mathematics
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DMI is a Process This year we are working through the first
module: Building a System of Tens Today and tomorrow we are working
in the first 3 sessions Session 1: Analyzing Addition Strategies
Session 2: Place Value and Multiplication Session 3: The
Mathematics of Algorithms
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Session One: Building a System of Tens Student's Addition and
Subtraction Strategies
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Mathematical Goals for Session One I can use multiple
strategies relying on the base ten structure and properties of
operation to add and subtract multi-digit computations. I can use a
logical visual or physical representation, such as a number line,
base ten blocks, arrays, etc. to explain why my strategy works. I
can express the same amount in different ways using powers of 10.
For example, I can decompose numbers using the powers of 10 (100 is
100 ones, or ten tens, or one ten and 90 ones, etc.).
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Mental Math 57 + 24
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Mental Math 83-56
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Mathematical Goals for Session One I can use multiple
strategies relying on the base ten structure and properties of
operation to add and subtract multi-digit computations. I can use a
logical visual or physical representation, such as a number line,
base ten blocks, arrays, etc. to explain why my strategy works. I
can express the same amount in different ways using powers of 10.
For example, I can decompose numbers using the powers of 10 (100 is
100 ones, or ten tens, or one ten and 90 ones, etc.).
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Second Grade Strategies 40 - 26
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Seventh Grade Strategies 123 - 76
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Mathematical Goals for Session One I can use multiple
strategies relying on the base ten structure and properties of
operation to add and subtract multi-digit computations. I can use a
logical visual or physical representation, such as a number line,
base ten blocks, arrays, etc. to explain why my strategy works. I
can express the same amount in different ways using powers of 10.
For example, I can decompose numbers using the powers of 10 (100 is
100 ones, or ten tens, or one ten and 90 ones, etc.).
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Break
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Chapter 1 Case Discussion In your group, examine Focus
Questions 3, 4, and 5. Use any manipulatives or chart paper you
need to work through these questions.
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Small Group Discussion
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Whole Group Discussion
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Mathematical Goals for Session One I can use multiple
strategies relying on the base ten structure and properties of
operation to add and subtract multi-digit computations. I can use a
logical visual or physical representation, such as a number line,
base ten blocks, arrays, etc. to explain why my strategy works. I
can express the same amount in different ways using powers of 10.
For example, I can decompose numbers using the powers of 10 (100 is
100 ones, or ten tens, or one ten and 90 ones, etc.).
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Math Activity: Close to 100 Game The object of the game is to
create two 2-digit numbers whose sum is as close to 100 as
possible. Each game has five rounds. At the end of five rounds the
player with the lowest total score wins.
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Mathematical Goals for Session One I can use multiple
strategies relying on the base ten structure and properties of
operation to add and subtract multi-digit computations. I can use a
logical visual or physical representation, such as a number line,
base ten blocks, arrays, etc. to explain why my strategy works. I
can express the same amount in different ways using powers of 10.
For example, I can decompose numbers using the powers of 10 (100 is
100 ones, or ten tens, or one ten and 90 ones, etc.).
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For Session 2, please be sure to read: Case studies 6, 7, &
10
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1. What mathematical ideas did this session highlight for you?
2. What was this session like for you as a learner? 3. What burning
questions do you have about this session? Exit cards
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Session Two: Building a System of Tens The Base Ten Structure
of Numbers August 16, 2013
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Mathematical Goal for Session Two The value of a number is
determined by multiplying the value of each digit by the value of
the place that it occupies and then summing. For whole numbers, the
value of the place farthest to the right is 1; the value of every
other place is 10 times the value of the place to its right.
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Math Activity
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Small Group: Representing Multiplication
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Whole-group Discussion: Sharing Representations
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Mathematical Goal for Session Two The value of a number is
determined by multiplying the value of each digit by the value of
the place that it occupies and then summing. For whole numbers, the
value of the place farthest to the right is 1; the value of every
other place is 10 times the value of the place to its right.
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DVD: Interview with Three Students
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Mathematical Goal for Session Two The value of a number is
determined by multiplying the value of each digit by the value of
the place that it occupies and then summing. For whole numbers, the
value of the place farthest to the right is 1; the value of every
other place is 10 times the value of the place to its right.
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Break
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Case Discussion Think about: 1. What is right about the
student's thinking? 2. Where has the student's thinking gone
awry?
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Small-Group: Ideas about the Number System
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Whole-Group: Number Lines
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Mathematical Goal for Session Two The value of a number is
determined by multiplying the value of each digit by the value of
the place that it occupies and then summing. For whole numbers, the
value of the place farthest to the right is 1; the value of every
other place is 10 times the value of the place to its right.
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During your working lunch please be sure to read Case 14 (pages
65 - 70 Casebook).
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Lunch
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Session Three: Building a System of Tens Making Sense of
Addition and Subtraction Algorithms
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Mathematical Goals for Sessions Three Extend students knowledge
of place value (ones, tens, hundreds) to solving addition and
subtraction problems efficiently. Understand how place value
underlies the traditional algorithms for addition and
subtraction.
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Whole Group: Addition and Subtraction Strategies Investigating
addition strategies: Creating Verbal Descriptions Visual
Representations Story Context
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Small-Group: Addition and Subtraction Strategies Creating
Subtraction Posters
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Gallery Walk: addition and subtraction strategies
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Mathematical Goals for Sessions Three Extend students knowledge
of place value (ones, tens, hundreds) to solving addition and
subtraction problems efficiently. Understand how place value
underlies the traditional algorithms for addition and
subtraction.
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Break!
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DVD: Addition and Subtraction
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Mathematical Goals for Sessions Three Extend students knowledge
of place value (ones, tens, hundreds) to solving addition and
subtraction problems efficiently. Understand how place value
underlies the traditional algorithms for addition and
subtraction.
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Small Group Discussion: Addition and Subtraction Algorithms
Case 14 Focus Questions 3 and 4
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Whole Group Discussion: Addition and Subtraction Algorithms
What is the same about the two strategies in case 14? What is
different about the two strategies? What are the mathematical
principles underlying each of the strategies the students use?
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Mathematical Goals for Sessions Three Extend students knowledge
of place value (ones, tens, hundreds) to solving addition and
subtraction problems efficiently. Understand how place value
underlies the traditional algorithms for addition and
subtraction.
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Task #1 - Read and discuss the article "Orchestrating
Discussions" Task #2 - Do the Writing Assignment: A math
interview
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Exit Cards.............. What was important or significant to
you in the mathematics discussed at this session? What mathematics
are you still wondering about from this session? What do you want
to tell us about how the seminar is working for you?