GUIDED M
ATH: A
N
INSTRUCTIO
NAL
STRATE
GY YOU CAN
COUNT ON
P R E S E N T E D BY D
R . NI C
K I NE W T O N
INTRODUCTION
A. Dr. Nicki NewtonB. 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
Targeted teaching/Differentiation
On the spot error/Misconception analysis
Question Deeply
Focus on specificContent and practices
Students
Targeted Standards based instruction
Individual Attention
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.
Numeracy Rich Writing
Agreeing
Discussing
Proving
Refuting
Disagreeing
Modeling Showing
ListeningExplaining
Listening
SpeakingTalking
Connecting
Reader’s Workshop•Mini –Lesson•Word Work•Fluency Practice•Strategy Practice•Conferences•Share Time•Groups (Guided, Strategic, Discussion)
Math Workshop•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 standards-based
lesson
Work Time
30-45 Minutes
•Small guided math group
•Individual math interview or conferencing•Workstations
Share 5-10 Minutes •Discuss Major Takeaways
•Writing ResponseTotal Time 70-75
Minutes
POSTING QUESTIONS
Posting Questions Around the Room…See Shannon & PBS
60%10%
10%
10%
10%
Mini-Lesson
#Talks
Calendar
Debrief
Guided MathGroups
Centers
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+6Strategies
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 Groups2. Introducing Guided Math Groups to the Children3.Classroom Management4. 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 BOARDSCHALK BOARDSCORK BOARDS
http://www.tips-for-teachers.com/images/digital%20pics/classroom%20pics/second%20grade/Acworth/crop%20baord.jpg
ORGANIZATION
SEE EVERYBODY EVERY WEEK
http://www.tips-for-teachers.com/images/digital%20pics/classroom%20pics/second%20grade/Acworth/Guided%20Math/IMG_0465.JPG
2 OR 3 TIMES A WEEK
http://www.tips-for-teachers.com/guided_math_groups.htm - Schedule
SCHEDULE
SAMPLE SCHEDULERotation Schedule
Small Guided Math Groups
Center Work(Games and Activities)
Problem Solving Center (Models & Strategy Center)
Round 1 Tigers Bears Dolphins
Round 2 Bears Dolphins Tigers
Round 3 Dolphins Tigers Bears
Novice Apprentice Practitioner/Expert
Multiplication: Circles and StarsPartner Game
Multiplication:Arrays
Partner Game
Multiplication:Show Two Strategies
Partner Game
Problem Solving Center: Equal
Groups Problem Types: Facts 2, 4, 5
(Scaffolded with numberline)
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
Multipliation Unit: Teacher is Floating Today (Conferences and Interviews)
Tiered Writing Activity About Multiplication
EXAMPLE GUIDED MATH WEEKLY SCHEDULE
15 MINUTE SESSIONS- 2 SESSIONS A DAYMonday Tuesday Wednesda
yThursday Friday
9:30-9:45 9:30-9:45 9:30-9:45 9:30-9:45 9:30-9:45Class Math
ProjectsPodcasts/
VideoCast/Glog/Photo Essay/Class Mural/Class Book
9:45-10:00 9:45-10:00 9:45-10:00 9:45-10:00 9:45-10:00Class Math
ProjectsPodcasts/Photo
Essay/Class Mural/Class Book
Green Group Green Group-
Blue Group-y
Yellow GroupYellow Group
Blue Group
Orange GroupOrange Group
PLANNING SHEETS
DIFFERENT WAYS TO PLAN FOR INSTRUCTION.
KEY COMPONENTS: -WHO & WHAT
http://mountainview.typepad.com/guided_math/what-is-guided-math.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 Responsibilities2. Framework for a Lesson
THE TEACHER ISTeaching a small guided math groupDirect modelingWatching students do mathQuestioningScaffolding LearningGiving ExamplesTaking Notes
THE TEACHER IS ALSO
o Facilitating center worko Questioning Studentso Conferencingo Interviewing
THE STUDENT IS
ListeningParticipatingDiscussingThinkingDoing math
FRAMING GUIDED MATH LESSONS AROUND THE BIG
IDEAS Randall Charles has written about 21
Big Ideas in Math…
GUIDED MATHINFRASTRUCTURE
• Concrete (base-ten blocks, cubes, counters, etc.),
• Pictorial (model of thinking – pictures, drawing, diagrams, tables)
• Abstract (number sentences, equations, expressions)
STRUCTURE OF THE LESSON
IntroGuided PracticeSummarizing what you did that day.
ONGOING ASSESSMENT THROUGHOUT THE LESSON
• Questioning• Individual Pupil Responses
•Thumbs up•Stoplight•Entrance/Exit Slip
OBSERVATION SHEETNOTESNAME 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 Arguments- Writing 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 base-ten numerals, number names, and expanded form.
NUMBER WRITING
PoemsRace Car NumbersRainbow Numbers Jmeacham:
www.jmeacham.comSparklebox: 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 BookAct Out: People
Concrete: Dino counters Pictorial: Draw it Abstract: Number Lines &
Ladders
COUNT HOW MANYK.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 NUMBERSK.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 NUMBERSK.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 two-digit numbers based on meanings of the tens and ones digits, recording the results of comparisons with the symbols >, =, and <.
COMPARING NUMBERS2.NBT.4. Compare two three-digit 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 FACTSPlus 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-
and-guided-math-groups/
http://guidedmath.wordpress.com/2010/12/10/five-frames-and-guided-math-groups/
OPERATIONS AND ALGEBRAIC THINKINGK.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 THINKINGK.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 THINKINGK.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 THINKINGK.OA.5. Fluently add and subtract within 5.
OPERATIONS AND ALGEBRAIC THINKING1.OA.6. Add and subtract within 20, demonstrating fluency for addition and subtraction within 10.
*See posters on blog
OPERATIONS AND ALGEBRAIC THINKING1. Use strategies such as counting on; making ten (e.g., 8 + 6 = 8 + 2 + 4 = 10 + 4 = 14);
OPERATIONS AND ALGEBRAIC THINKING1. Decomposing a number leading to a ten (e.g., 13 – 4 = 13 – 3 – 1 = 10 – 1 = 9);
OPERATIONS AND ALGEBRAIC THINKING1. 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 THINKING2.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 THINKING1.OA.7. Understand the meaning of the equal sign, and determine if equations involving addition and subtraction are true or false.
OPERATIONS AND ALGEBRAIC THINKING1. 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 THINKING1.OA.8. Determine the unknown whole number in an addition or subtraction equation relating three whole numbers.
OPERATIONS AND ALGEBRAIC THINKING1.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-of-numbers-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/jennyfixmanedutunes/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-9-teaching-compensation-for-addition-problems-in-small-guided-math-groups/
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 THINKINGK.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 PROBLEMS2.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 FramesSlider StoriesRekenrekNumberlineOpen NumberlineMath MatBar 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 two-digit number represent amounts of tens and ones. Understand the following as special cases:
PLACE VALUE1.NBT.4. Add within 100, including adding a two-
digit 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 VALUE2.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 VALUE2.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 VALUE2.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/2011/08/23/an-addition-algorithm/
ADDITION STRATEGIESSchultz Math VideosCounting Up by OnesCounting Up by Tens & OnesUsing a 100's ChartExpanding Notation: Decomposing into Groups of Tens and
Ones
ADDITION STRATEGIESSchultz Math VideosLeft to Right AdditionCompensationRegroupinghttp://www.schultzcenter.org/
mathvideos.shtml
SUBTRACTION STRATEGIES
What is 67-9? How many ways can you solve this?
SUBTRACTION STRATEGIES
Number SplittingOpen NumberlineCounting UpCompensationTraditional Strategy
http://guidedmath.wordpress.com/2011/08/31/5-subtraction-algorithms-great-to-do-in-guided-math-groups/
SUBTRACTION STRATEGIES
Schultz Math VideosCounting Down by OnesCounting Down by Tens and Ones
SUBTRACTION STRATEGIES
Distance Between Two NumbersLandmark NumbersDecomposing into Groups of Tens and Ones
SUBTRACTION STRATEGIESCompensationExpanding Notation with Negative NumbersRegroupinghttp://www.schultzcenter.org/mathvideos.shtml
RTI AND GUIDED MATH GROUPSREMEMBER 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?
DefinitionComponents
Examples Non-Examples
Frayer Concept Organizer
GuidedMath
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
REFERENCESBush, K. Holland Elementary [email protected]
Deborah KrambPitner Elementary School
Norman, J –Cowden Elementary [email protected]://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
RESOURCESLaura Candler MathWireGeorgia Standards.org:
Math FrameworksPublic Schools of NC:
Problem-Solving DecksNCTM IlluminationsCobb Math BlogCobb Math Links ListPlug Into MathematicsWESTEST Prep PageTeams Educational Resources
Grades 3-5/Function MachineAgebra, Geometry and Numbers
•Mrs. Powell’s Math Tubs Explanation•Marcia’s Math Tub Fun•Mrs. Meacham’s Math Tubs
www.guidedmath.wordpress.com
YOU CAN CONTACT ME AT
drnickimath (follow me on twitter)
Thank You For Coming!