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 kbess@spsmail.org

Deborah KrambPitner Elementary School

Norman, J –Cowden Elementary jnorman592@spsmail.orghttp://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

drnicki7@gmail.comwww.guidedmath.wordpress.com

drnickimath (follow me on twitter)

Thank You For Coming!