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!