Transcript newtonberguidedmathspringtourz1

INTRODUCTION
A. Dr. Nicki Newton
B. Guests
GOALS OF THIS WORKSHOP
1.Learn to Implement Guided Math
Groups
2.Learn to Engage Students in
Purposeful Practice through Math
Workstations
ESSENTIAL QUESTIONS FOR
THIS WORKSHOP
• How do guided math groups help us to
differentiate instruction in meaningful
ways so that we can reach all
learners?
• How do math workstations help
reinforce skills in meaningful ways?
WHAT IS GUIDED MATH?
• One component of a math workshop
• Students learn in small flexible groups
based on their readiness level
• Students practice with the teacher,
with each other and then by
themselves during the guided math
lesson
WHY DO GUIDED MATH
GROUPS?
“When a teacher tries to teach something to the
entire class at the same time, chances are, one
third of the kids already know it, one third will get
it, and the remaining third won’t get it. So two
thirds of the children are wasting their time.”
~Lillian Katz
BENEFITS OF A GUIDED MATH
GROUPS
Teachers
Students
Targeted teaching/
Differentiation
Targeted Standards based
instruction
On the spot error/
Misconception analysis
Individual Attention
Question Deeply
Focus on specific
Content and practices
Opportunity to Speak
& Listen about Mathematical
Thinking
Mathematical Disposition
Levels Increase
MATHEMATICAL POWER
Comes from the belief that
“I can do this…with practice I can do this”
“If I just keep trying I can do this”
“If I persevere, I can do this”
Mathematical Power comes from the belief
that math fluency is possible with
practice.
GUIDED MATH VERSUS WHOLE
GROUP MATH
Whole Class
• Mini Lesson
• Non-targeted
• Large Group
Guided Math
• Mini Lesson
• Differentiated
• Small group
BALANCED MATHEMATICS
• GUIDED MATH IS PART OF A GUIDED
MATH PROGRAM. IT TAKES PLACE IN A
NUMERACY-RICH ENVIRONMENT.
Proving
Explaining
Listening
Showing
Modeling
Numeracy Rich
Discussing
Connecting
Disagreeing
Listening
Talking
Refuting
Writing
Speaking
Agreeing
Reader’s Workshop Math Workshop
•Mini –Lesson
•Word Work
•Fluency Practice
•Strategy Practice
•Conferences
•Share Time
•Groups
(Guided, Strategic, Discussion)
•Lessons
•Vocabulary Practice
•Fact Fluency Practice
(Automaticity)
•Strategy Practice
•Conferences
•Share Time
•Small Guided Math
Groups
Math Energizers
5-7
Minutes
Review and Practice
Whole Group Mini
Lesson
7-10 Minutes
Whole group standardsbased lesson
Work
Time
30-45
Minutes
Share
5-10 Minutes
Total Time
70-75 Minutes
•Small guided math
group
•Individual math interview
or conferencing
•Workstations
•Discuss Major
Takeaways
•Writing Response
POSTING QUESTIONS
Posting Questions Around the
Room…See Shannon & PBS
Debrief
Calendar
10%
10%
10%
#Talks
10%
Mini-Lesson
60%
Guided Math Centers
Groups
MATH ENERGIZERS
Bingo, Disappearing Dan &
Dana; 24; Tell Me All You
Can Number of the Day;
Silent Math; What’s the
Question?; Rock, Paper,
Scissors Numbers
CALENDAR TALK
Individual Calendars can give
distributed practice over
time.
NUMBER TALKS
What is 8+6
Strategies
Models
LEARNING ENVIRONMENT
KEY TO THE WHOLE OPERATION!
CLASSROOM “SET UP”
Understanding the Schedule-What are we doing today? When?
Movement – Leaders are Key? Who’s on first?
Cooperative Learning Components – Check Ins (How’s your group
doing?)
“The ultimate goal of mathematics
instruction is to teach students to
solve problems independently. The
flexible nature of these
components encourages the
gradual release of responsibility.”
Laney Sammons
TURN AND TALK
Talk to your shoulder buddy about how math is taught in
your building (think about the differences in classrooms
& grade levels). Are these components are part of the
math instruction?
____ whole group instruction
____ mini-lesson
____ debrief
____ small guided math group
____ workstations
ORGANIZATION
Classroom Management:
• Rules, Rewards and Consequences
• Cooperative Learning
GETTING STARTED
1. Forming Groups
2. Introducing Guided Math Groups to
the Children
3.Classroom Management
4. Scheduling Students
DATA-DRIVEN INSTRUCTION
•Small group instruction is always based on
data (Unit Assessments, student interviews
or conferences, anecdotal notes, teacher
observations, etc.)
•Data will point to student misconceptions,
error patterns, and levels of understanding
(see Depth of Knowledge)
HOW DO I SET UP THE
GROUPS?
BEN
•
•
•
•
BENCHMARK TEST
QUIZZES
INTERVIEWS
CHAPTER TESTS
SMALL GUIDED MATH GROUPS
ARE FOR ALL STUDENTS
•
•
•
•
Novice
Apprentice
Practitioner
Expert
FLEXIBLE GROUPING
• Students move in and out of groups based
on need. In geometry John could be in
group A and in measurement he could be in
group b.
ORGANIZATION
WHITE BOARDS
CHALK BOARDS
CORK BOARDS
http://www.tips-forteachers.com/images/digital%20pics/clas
sroom%20pics/second%20grade/Acwort
h/crop%20baord.jpg
ORGANIZATION
SEE EVERYBODY EVERY WEEK
http://www.tips-forteachers.com/images/digital%20pics/clas
sroom%20pics/second%20grade/Acwort
h/Guided%20Math/IMG_0465.JPG
SCHEDULE
2 OR 3 TIMES A WEEK
http://www.tips-forteachers.com/guided_math_groups.htm Schedule
SAMPLE SCHEDULE
Rotation Schedule
Small Guided Math Center Work
Groups
(Games and
Activities)
Problem Solving
Center (Models &
Strategy Center)
Round 1
Tigers
Bears
Dolphins
Round 2
Bears
Dolphins
Tigers
Round 3
Dolphins
Tigers
Bears
Multipliation Unit: Teacher is Floating Today (Conferences and
Interviews)
Novice
Multiplication:
Circles and Stars
Partner Game
Problem Solving
Center: Equal
Groups Problem
Types: Facts 2, 4, 5
(Scaffolded with
numberline)
Tiered Writing
Activity About
Multiplication
Apprentice
Multiplication:
Arrays
Partner Game
Practitioner/Expert
Multiplication:
Show Two Strategies
Partner Game
Problem Solving
Center: Arrays: Facts
through 6
(Scaffolded with
arrays)
Problem Solving
Center: Variety of
Strategies
Tiered Writing
Activity About
Multiplication
Tiered Writing
Activity About
Multiplication
EXAMPLE GUIDED MATH WEEKLY
SCHEDULE
Monday
15 MINUTE SESSIONS- 2 SESSIONS A DAY
9:30-9:45
Green Group
9:45-10:00
Orange Group
Tuesday
9:30-9:45
Blue Group
9:45-10:00
Yellow Group
Wednesday
9:30-9:45
Green Group
-
Thursday
Friday
9:30-9:45
9:30-9:45
Blue Group
Class Math
Projects
Podcasts/VideoCas
t/Glog/Photo
Essay/Class
Mural/Class Book
-y
9:45-10:00 9:45-10:00
9:45-10:00
Yellow Group
Class Math
Projects
Podcasts/Photo
Essay/Class
Mural/Class Book
Orange Group
PLANNING SHEETS
DIFFERENT WAYS TO PLAN FOR
INSTRUCTION.
KEY COMPONENTS:
-WHO & WHAT
http://mountainview.typepad.com/guided_math/what-is-guidedmath.html
ORGANIZATION
• Introduce the math workshop to the
students during the first 2 weeks. Practice
games together and practice the guided
math groups.
GETTING STARTED
1. Roles and Responsibilities
2. Framework for a Lesson
THE TEACHER IS
Teaching a small guided math group
 Direct modeling
 Watching students do math
 Questioning
 Scaffolding Learning
 Giving Examples
 Taking Notes
THE TEACHER IS ALSO
o
o
o
o
Facilitating center work
Questioning Students
Conferencing
Interviewing
THE STUDENT IS
Listening
Participating
Discussing
Thinking
Doing math
FRAMING GUIDED MATH LESSONS
AROUND THE BIG IDEAS
 Randall Charles has written about 21 Big
Ideas in Math…
GUIDED MATH
INFRASTRUCTURE
• Concrete (base-ten blocks, cubes, counters,
etc.),
• Pictorial (model of thinking – pictures, drawing,
diagrams, tables)
• Abstract (number sentences, equations,
expressions)
STRUCTURE OF THE LESSON
Intro
Guided Practice
Summarizing what you did that day.
ONGOING ASSESSMENT
THROUGHOUT THE LESSON
• Questioning
• Individual Pupil Responses
• Thumbs up
• Stoplight
• Entrance/Exit Slip
OBSERVATION SHEET
NAME
NOTES
NOTES
John
Using level 1 strategies
Maria
Used some level 3 strategies
today…said 5+7 was a
doubles +2 fact so it was 12
FRAMING GUIDED MATH
LESSONS
• Mathematical Proficiency
• Mathematical Practices
• Content Domains
CONCEPTUAL UNDERSTANDING
• Kyle had 6 marbles. John
had 2 more than Kyle. How
many did John have?
*Number Bond Practice:
Where is the unknown?
*NLVM Computers
PROCEDURAL FLUENCY
o What is 245 + 37?
o 300 – 299 =
*Skip Counting *Double Digit Subtraction with dice
STRATEGIC COMPETENCE
8+7 =
29+ 35 =
12 x 4 =
*Roll and Compose/Decompose
*Composing/Decomposing Club
*Show 2 different ways to subtract 300-299.
Talk about which was faster and why.
ADAPTIVE REASONING
 Accountable Math Talk
 Thinking Posters
 Thinking Notebooks
 Can you prove that?
 How do you know?
 *Convince Me Paper *Challenge It Paper
MATHEMATICAL PROFICIENCY
o ADAPTIVE REASONING: IN ORDER TO
TALK YOU NEED MATH VOCABULARY:
 POWERPOINT
 GRAPHIC ORGANIZERS
 MATH SPELLING CITY
MATHEMATICAL PROFICIENCY
MATHEMATICAL DISPOSITION…
WHAT’S YOURS?
LEVELS 1-5
MATHEMATICAL PRACTICES
• Problem Solving - Word
Problems
• Reasoning - Riddles
• Construct Viable Arguments
and Critique ArgumentsWriting in math
• Modeling –Open Numberline;
Bar Modeling
MATHEMATICAL PRACTICES
•
•
•
•
Use appropriate tools- Calculators
Attend to precision- Vocabulary
Look for and make use of structure
Look for and express regularity in
repeated reasoning
NUMBER WRITING
K.CC.3. Write numbers from 0
to 20. Represent a number of
objects with a written numeral
0-20 (with 0 representing a
count of no objects).
NUMBER WRITING
1.NBT.1. Count to 120,
starting at any number less
than 120. In this range, read
and write numerals and
represent a number of objects
with a written numeral.
NUMBER WRITING
2.NBT.3. Read and write
numbers to 1000 using baseten numerals, number names,
and expanded form.
NUMBER WRITING
Poems
Race Car Numbers
Rainbow Numbers
Jmeacham: www.jmeacham.com
Sparklebox:
http://www.sparklebox.co.uk/md/index.html#.Tot7jnN-sVA
COUNT TO TELL THE NUMBER
OF OBJECTS.
Understand that each successive
number name refers to a quantity
that is one larger.
COUNT TO TELL THE NUMBER
OF OBJECTS.
Dinosaur Book
Act Out: People
Concrete: Dino counters
Pictorial: Draw it
Abstract: Number Lines &
Ladders
COUNT HOW MANY
K.CC.5. Count to answer “how many?”
questions about as many as 20 things
arranged in a line, a rectangular array, or
a circle, or as many as 10 things in a
scattered configuration; given a number
from 1–20, count out that many objects.
Mosaic Activity
COMPARE NUMBERS
K.CC.6. Identify whether the
number of objects in one group
is greater than, less than, or
equal to the number of objects
in another group, e.g., by
using matching and counting
strategies.1
COMPARE NUMBERS
Alligator Poem
Alligator Puppets
Matching: Roll and compare
Counting: Number Lines,
Ladders, Grids
Superteacher Activities
*http://guidedmath.wordpress.com/2011/06/
COMPARE NUMBERS
K.CC.7. Compare two numbers
between 1 and 10 presented as
written numerals.
Cards, Dice and Dominos: Highest
Number/Lowest Number
*http://guidedmath.wordpress.com/2011/06/
COMPARING NUMBERS
1.NBT.3. Compare two twodigit numbers based on
meanings of the tens and
ones digits, recording the
results of comparisons with
the symbols >, =, and <.
COMPARING NUMBERS
2.NBT.4. Compare two threedigit numbers based on meanings
of the hundreds, tens, and ones
digits, using >, =, and <
symbols to record the results of
comparisons.
FACT FLUENCY
100 Basic Facts –
The Dolch Words
of Math
A 3-STEP APPROACH TO
LEARNING THE BASIC MATH
FACTS
•A. Conceptual Understanding
(Concrete/ Pictorial)
•B. Development of Efficient
Strategies (Abstract)
•C. Practice that Works (Naming
Strategies)
ADDITION FACTS
Plus Zero - Poem
Plus 1 – One Red Dot; Numberlines;
Numberladders; NumberGrids; One
more and one less game
Plus 2
FIVE FRAME
1. http://guidedmath.wordpress.com/2010/12/10/five-frames-andguided-math-groups/
OPERATIONS AND ALGEBRAIC
THINKING
K.OA.1. Represent addition and
subtraction with objects,
fingers, mental images,
drawings1, sounds (e.g., claps),
acting out situations, verbal
explanations, expressions, or
equations.
OPERATIONS AND ALGEBRAIC
THINKING
K.OA.3. Decompose numbers less
than or equal to 10 into pairs in
more than one way, e.g., by using
objects or drawings, and record
each decomposition by a drawing
or equation (e.g., 5 = 2 + 3 and 5
= 4 + 1).
OPERATIONS AND ALGEBRAIC
THINKING
K.OA.4. For any number from 1 to
9, find the number that makes 10
when added to the given number,
e.g., by using objects or drawings,
and record the answer with a
drawing or equation.
OPERATIONS AND ALGEBRAIC
THINKING
K.OA.5. Fluently add and
subtract within 5.
OPERATIONS AND ALGEBRAIC
THINKING
1.OA.6. Add and subtract
within 20, demonstrating
fluency for addition and
subtraction within 10.
*See posters on blog
OPERATIONS AND ALGEBRAIC
THINKING
1. Use strategies such as
counting on; making ten
(e.g., 8 + 6 = 8 + 2 + 4 =
10 + 4 = 14);
OPERATIONS AND ALGEBRAIC
THINKING
1. Decomposing a number
leading to a ten (e.g., 13 –
4 = 13 – 3 – 1 = 10 – 1 =
9);
OPERATIONS AND ALGEBRAIC
THINKING
1. And creating equivalent
but easier or known sums
(e.g., adding 6 + 7 by
creating the known
equivalent 6 + 6 + 1 = 12
+ 1 = 13).
OPERATIONS AND ALGEBRAIC
THINKING
2.OA.2. Fluently add and
subtract within 20 using
mental strategies.2 By end
of Grade 2, know from
memory all sums of two
one-digit numbers.
OPERATIONS AND ALGEBRAIC
THINKING
1.OA.7. Understand the
meaning of the equal sign,
and determine if equations
involving addition and
subtraction are true or
false.
OPERATIONS AND ALGEBRAIC
THINKING
1. For example, which of the
following equations are
true and which are false?
6 = 6, 7 = 8 – 1, 5 + 2 =
2 + 5, 4 + 1 = 5 + 2.
2. Prove It Papers!
OPERATIONS AND ALGEBRAIC
THINKING
1.OA.8. Determine the
unknown whole number in an
addition or subtraction
equation relating three
whole numbers.
OPERATIONS AND ALGEBRAIC
THINKING
1.OA.8. For example,
determine the unknown
number that makes the
equation true in each of
the equations 8 + ? = 11, 5
= _ – 3, 6 + 6 = _.
EQUIVALENT NAMES
• Focus Question: Can different number
combinations of quantities result in the
same sum?
• Literature Connections (12 Ways to Get
to 11)-Quack and Count; Math Fables;
Mathter pieces; Two Ways to Count to
Ten; A Quarter from the Tooth Fairy;
Grapes of Math; One is a Snail Ten is a
Crab; A Dozen Ducklings; Ten Puppies)
FACT FAMILIES
Teach from concrete, pictorial,
abstract.
http://guidedmath.wordpress.com/2010/04/01/teaching-fact-families-in-guided-math-groups/
http://guidedmath.wordpress.com/2010/08/30/number-bonds-fact-families-complements-ofnumbers-and-guided-math/
DOUBLES AND NEAR DOUBLES
• A. Focus Question: What are doubles?
How do they help us to add fast?
• B. Literature Connections: (Dice Game,
Double the Ducks; Minnie’s Diner; Double
those Wheels; Two of Everything)
http://www.songsforteaching.com/jennyfix
manedutunes/doubleitup.htm
FACT SORT
• Name That Fact (Domino Fact Sort, Domino
Book, Card Fact Sort, Card Book) http://guidedmath.wordpress.com/2010/01/23
/
LUCKY 8 & LUCKY 9
Concrete (double ten frames)
Pictorial (illuminations)
Abstract (Poems)
http://guidedmath.wordpress.com/2010/12/17/lucky-8-and-lucky-9teaching-compensation-for-addition-problems-in-small-guided-mathgroups/
PROBLEM SOLVING
• A. Focus Question: What are word problems?
What are some ways to think about them?
What are some ways to practice solving them?
• B. Literature Connections: Ten Little Fish,
How Many Blue Birds Flew Away?; How Many
Snails?; Number One Number Fun; Follow the
Line; Each Orange had 8 Slices
WORD PROBLEMS
Understand addition as
putting together and adding
to, and understand
subtraction as taking apart
and taking from.
WORD PROBLEMS
Know the Types
4 Types for Kindergarten
8 Types for 1st Grade
12 Types for 2nd grade
*See progressions/ See NYC Exemplars/ See Exemplars/
See Balanced Assessments
OPERATIONS AND ALGEBRAIC
THINKING
K.OA.2. Solve addition and
subtraction word problems,
and add and subtract within
10, e.g., by using objects
or drawings to represent
the problem.
WORD PROBLEMS
Represent and solve problems
involving addition and
subtraction.
WORD PROBLEMS
1.OA.1. Use addition and subtraction
within 20 to solve word problems
involving situations of adding to,
taking from, putting together, taking
apart, and comparing, with unknowns
in all positions,
WORD PROBLEMS
e.g., by using objects,
drawings, and equations with
a symbol for the unknown
number to represent the
problem.1
WORD PROBLEMS
1.OA.2. Solve word problems
that call for addition of
three whole numbers whose
sum is less than or equal to
20.
WORD PROBLEMS
2.OA.1. Use addition and
subtraction within 100 to solve
one- and two-step word problems
involving situations of adding to,
taking from, putting together,
taking apart, and comparing, with
unknowns in all positions,
WORD PROBLEM
e.g., by using drawings and
equations with a symbol for
the unknown number to
represent the problem.1
PROBLEM SOLVING POWER
TOOLS
Number Frames
Slider Stories
Rekenrek
Numberline
Open Numberline
Math Mat
Bar Diagram
PROBLEM SOLVING
Multiple Intelligence Centers
•1. Visual/Spatial- Sticker/Stamp Stories
•2. Intrapersonal- Individual Story Book
•3. Interpersonal- Group Story Book
PLACE VALUE
Concrete (bundles, base ten
blocks)
Pictorial (nlvm)
Abstract (roll and show)
PLACE VALUE
1.NBT.2. Understand that
the two digits of a twodigit number represent
amounts of tens and ones.
Understand the following as
special cases:
PLACE VALUE
1.NBT.4. Add within 100, including adding a twodigit number and a one-digit number, and adding a
two-digit number and a multiple of 10, using
concrete models or drawings and strategies based
on place value, properties of operations, and/or
the relationship between addition and subtraction;
relate the strategy to a written method and
explain the reasoning used. Understand that in
adding two-digit numbers, one adds tens and tens,
ones and ones; and sometimes it is necessary to
compose a ten.
PLACE VALUE
2.NBT.5. Fluently add and
subtract within 100 using
strategies based on place
value, properties of
operations, and/or the
relationship between addition
and subtraction.
PLACE VALUE
2.NBT.7. Add and subtract within
1000, using concrete models or
drawings and strategies based on
place value, properties of
operations, and/or the relationship
between addition and subtraction;
PLACE VALUE
2.NBT.7. relate the strategy to
a written method. Understand
that in adding or subtracting
three-digit numbers, one adds
or subtracts hundreds and
hundreds, tens and tens, ones
and ones;
PLACE VALUE
and sometimes it is
necessary to compose or
decompose tens or
hundreds. (see NLVM)
ADDITION STRATEGIES
What is 29+34?
How many strategies and
algorithms do you have in
your pocket?
http://guidedmath.wordpress.com/2011/0
8/23/an-addition-algorithm/
ADDITION STRATEGIES
Schultz Math Videos
Counting Up by Ones
Counting Up by Tens & Ones
Using a 100's Chart
Expanding Notation: Decomposing into
Groups of Tens and Ones
ADDITION STRATEGIES
Schultz Math Videos
Left to Right Addition
Compensation
Regrouping
http://www.schultzcenter.org/mathvideos
.shtml
SUBTRACTION STRATEGIES
What is 67-9? How many
ways can you solve this?
SUBTRACTION STRATEGIES
Number Splitting
Open Numberline
Counting Up
Compensation
Traditional Strategy
http://guidedmath.wordpress.com/2011/08/31/5-subtraction-algorithms-great-to-do-inguided-math-groups/
SUBTRACTION STRATEGIES
Schultz Math Videos
Counting Down by Ones
Counting Down by Tens and
Ones
SUBTRACTION STRATEGIES
Distance Between Two
Numbers
Landmark Numbers
Decomposing into Groups of
Tens and Ones
SUBTRACTION STRATEGIES
Compensation
Expanding Notation with
Negative Numbers
Regrouping
http://www.schultzcenter.org/mathvideos.shtml
RTI AND GUIDED MATH GROUPS
REMEMBER THAT RTI TECHNICALLY IS IN
ADDITION TO THE REGULAR MATH
PERIOD!
A BIT OF REVIEW
FILL IN YOUR FRAYER MODEL WITH
YOUR TABLEMATES. WHAT HAVE YOU
LEARNED?
Frayer Concept Organizer
Components
Guided
Math
Examples
Non-Examples
117
ACTION PLAN
• Decide on rules and
routines
• Set up groups
• Create a schedule
• Decide on the focus content strand
• Decide on the mathematical practices that
you will highlight
ACTION PLAN
• Plan group and mini-lessons
• Design workstations
• Put an accountability system in place
ACTION PLAN: STARTING
• START SMALL.
• START WHERE YOU ARE COMFORTABLE.
• JUST START
REFERENCES
Bush, K.
Holland Elementary [email protected]
Deborah Kramb
Pitner Elementary School
Norman, J –Cowden Elementary [email protected]
http://sps.k12.mo.us/cowden/jaustin/
November 2009
Spruiell, K. (2010). The Road to Guided Math-How to Get Your
Engine Started and Take Off Down the Road. GCTM
RESOURCES
Laura Candler
MathWire
Georgia Standards.org:
•Mrs. Powell’s Math Tubs Explanation
Math Frameworks
Public Schools of NC:
•Marcia’s Math Tub Fun
Problem-Solving Decks
•Mrs. Meacham’s Math Tubs
NCTM Illuminations
Cobb Math Blog
Cobb Math Links List
www.guidedmath.wordpress.com
Plug Into Mathematics
WESTEST Prep Page
Teams Educational Resources
Grades 3-5/Function Machine
Agebra, Geometry and Numbers
YOU CAN CONTACT ME AT
[email protected]
www.guidedmath.wordpress.com
drnickimath (follow me on twitter)
Thank You For Coming!