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Learner Profile Card Gender Stripe Auditory, Visual, Kinesthetic Analytical, Creative, Practical Modality Sternberg Student’s Interests Multiple Intelligence Preference Array Gardner Inventory Array Interaction Inventory Directions: • Rank order the responses in rows below on a scale from 1 to 4 with 1 being “least like me” to 4 being “most like me”. • After you have ranked each row, add down each column. • The column(s) with the highest score(s) shows your primary Personal Objective(s) in your personality. In your normal day-to-day life, you tend to be: Nurturing Logical Spontaneous Quiet Sensitive Systematic creative Insightful Caring Organized Playful reflective In your normal day-to-day life, you tend to value: Harmony Work Stimulation Reflection Relationships are Time schedules are Having fun is Having some time important important important alone is important In most settings, you are usually: Authentic Traditional Active Inventive Compassionate Responsible Opportunistic Competent Harmonious Parental Spontaneous Seeking In most situations, you could be described as: Empathetic Practical Impetuous Conceptual Communicative Competitive Impactful Knowledgeable Devoted Loyal Daring Composed Array Interaction Inventory, cont’d You approach most tasks in a(n) _________ manner: Affectionate Conventional Courageous Rational Inspirational Orderly Adventurous Philosophical Vivacious Concerned Impulsive Complex When things start to “not go your way” and you are tired and worn down, what might your responses be? Say “I’m sorry” Over-control “It’s not my fault” Withdraw Make mistakes Become critical Manipulate Don’t talk Feel badly Take charge Act out Become indecisive When you’ve “had a bad day” and you become frustrated, how might you respond? Over-please Be perfectionistic Become physical Disengage Cry Verbally attack Be irresponsible Delay Feel depressed Overwork Demand attention Daydream Add score: Harmony Production Connection Status Quo Personal Objectives/Personality Components Teacher and student personalities are a critical element in the classroom dynamic. The Array Model (Knaupp, 1995) identifies four personality components; however, one or two components(s) tend to greatly influence the way a person sees the world and responds to it. A person whose primary Personal Objective of Production is organized, logical and thinking-oriented. A person whose primary Personal Objective is Connection is enthusiastic, spontaneous and action-oriented. A person whose primary Personal Objective is Status Quo is insightful, reflective and observant. Figure 3.1 presents the Array model descriptors and offers specific Cooperative and Reluctant behaviors from each personal objective. Personal Objectives/Personality Component HARMONY PRODUCTION CONNECTION STATUS QUO COOPERATIVE Caring Logical Spontaneous Quiet Sensitive Structured Creative Imaginative (Positive Behavior) Nurturing Organized Playful Insightful Harmonizing Systematic Enthusiastic Reflective Feeling-oriented Thinking-oriented Action-oriented Inaction-oriented RELUCTANT Overadaptive Overcritical Disruptive Disengaging Overpleasing Overworks Blames Withdrawn (Negative Behavior) Makes mistakes Perfectionist Irresponsible Delays Cries or giggles Verbally attacks Demands attention Despondent Self-defeating Demanding Defiant Daydreams PSYCHOLOGICAL Friendships Task completion Contact with people Alone time NEEDS Sensory experience Time schedule Fun activities Stability WAYS TO MEET Value their feelings Value their ideas Value their activity Value their privacy NEEDS Comfortable work place Incentives Hands-on activities Alone time Pleasing learning Rewards Group interaction Independent activities environment Leadership positions Games Specific directions Work with a friend Schedules Change in routine Computer activities sharing times To-do lists Routine tasks There are two keys to differentiation: 1. Know your kids 2.Know your content “In times of change, the learners inherit the earth while the learned find themselves beautifully equipped to deal with a world that no longer exists.” Eric Hoffer It Begins with Good Instruction The greatest enemy to understanding is coverage. Howard Gardner facts, vocabulary, dates, These are the places, names, and examples you want students to give you. Facts 2X3=6, b b 4ac The know is massively 2 2a forgettable. Vocabulary numerator, slope “Teaching facts in isolation is like trying to pump water uphill.” -Carol Tomlinson KNOW (Facts, Vocabulary, Definitions) • Definition of numerator and denominator • The quadratic formula • The Cartesian coordinate plane • The multiplication tables Skills • Basic skills of any discipline • Thinking skills • Skills of planning, independent learning, etc. The skill portion encourages the students to “think” like the professionals who use the knowledge and skill daily as a matter of how they do business. This is what it means to “be like” a mathematician, an analyst, or an economist. Research about teaching suggests that learning by struggling at first with a concept enables students to benefit from an explanation that brings the ideas together (Schwartz & Bransford, 2000). BE ABLE TO DO (Skills: Basic Skills, Skills of the Discipline, Skills of Independence, Social Skills, Skills of Production) • Describe these using verbs or phrases: • Analyze, test for meaning • Solve a problem to find perimeter • Generalize your procedure for any situation • Evaluate work according to specific criteria • Contribute to the success of a group or team • Use graphics to represent data appropriately Juicy Verbs compose influence adopt unify devise promote elaborate designate detail substitute merchandize limit deconstruct prove formulate structure predict simulate shadow illustrate propose tailor inscribe refresh eliminate transform wonder transfer improve advise visualize reflect expand emphasize access concentrate minimize convert immerse approximate connect ponder justify regroup portray design compete simulate incorporate concentrate disguise modify produce compartmentalize personify anchor energize integrate uncover deviate Certain methods of teaching, particularly those that emphasize memorization as an end in itself tend to produce knowledge that is seldom, if ever, used. Students who learn to solve problems by following formulas, for example, often are unable to use their skills in new situations. (Redish, 1996) It Begins with Good Instruction Adding It Up (National Research Council) – Rule-based instructional approaches that do not give students opportunities to create meaning for the rule, or to learn when to use them, can lead to forgetting, unsystematic errors, reliance on visual clues, and poor strategic decisions. Research about teaching suggests learning may be hindered by • isolated sets of facts that are not organized and connected or organizing principles without sufficient knowledge to make them meaningful (NRC, 1999) • Students have become accustomed to receiving an arbitrary sequence of exercises with no overarching rationale.” (Black and Wiliam, 1998)) Major Concepts and Subconcepts These are the written statements of truth, the core to the meaning(s) of the lesson(s) or unit. These are what connect the parts of a subject to the student’s life and to other subjects. It is through the understanding component of instruction that we teach our students to truly grasp the “point” of the lesson or the experience. Understandings are purposeful. They focus on the key ideas that require students to understand information and make connections while evaluating the relationships that exist within the understandings. UNDERSTAND (Essential Truths That Give Meaning to the Topic) Begin with I want students to understand THAT… – Multiplication can have different meanings in different contexts, including repeated addition, groups and creation of area. – Fractions always represent a relationship of parts and wholes. – Addition and subtraction show a final count of the same thing. – Functions can be represented in many ways (graphs, words, tables, equations) but all representations are of the same function. Some questions for identifying truly “big ideas” – Does it have many layers and nuances, not obvious to the naïve or inexperienced person? – Do you have to dig deep to really understand its meanings and implications even if you have a surface grasp of it? – Is it (therefore) prone to misunderstanding as well as disagreement? – Does it yield optimal depth and breadth of insight into the subject? – Does it reflect the core ideas as judged by experts? Hints for Writing Essential Understandings Essential understandings synthesize ideas to show an important relationship, usually by combining two or more concepts. For example: People’s perspectives influence their behavior. Time, location, and events shape cultural beliefs and practices. Tips: • When writing essential understandings, verbs should be active and in the present tense to ensure that the statement is timeless. • Don’t use personal nouns- they cause essential understanding to become too specific, and it may become a fact. • Make certain that an essential understanding reflects a relationship of two or more concepts. • Write essential understandings a complete sentences. • Ask the question: What are the bigger ideas that transfer to other situations. Concepts Some concepts • span across several subject areas • represent significant ideas, phenomena,intellectual process, or persistent problems • Are timeless • Can be represented though different examples, with all examples having the same attributes • And universal For example, the concepts of patterns, interdependence, symmetry, system and power can be examined in a variety of subjects or even serve as concepts for a unit that integrates several subjects. Discipline-based Concepts • Art-color, shape, line, form, texture, negative space Literature-perception, heroes and antiheroes, motivation, interactions, voice Mathematics-number, ratio, proportion, probability, quantification Music-pitch, melody, tempo, harmony, timbre • Physical Education-movement, rules, play, effort, quality, space, strategy Science-classification, evolution, cycle, matter, order Social Science- governance, culture, revolution, conflict, and cooperation Mortimer Adler’s List of the Most Important Concepts in Western Civilization 1. Angel 37. Idea 73. Punishment 2. Animal 38. Immortality 74. Quality 3. Aristocracy 39. Induction 75. Quantity 4. Art 40. Infinity 76. Reasoning 5. Astronomy 41. Judgment 77. Relation 6. Beauty 42. Justice 78. Religion 7. Being 43. Labor 79. Revolution 8. Cause 44. Language 80. Rhetoric 9. Chance 45. Law 81. Same/Other 10. Change 46. Liberty 82. Science 11. Citizen 47. Life and death 83. Sense 12. Constitution 48. Logic 84. Sign/Symbol 13. Courage 49. Love 85. Sin 14. Custom and convention 50. Man 86. Slavery 15. Definition 51. Mathematics 87. Soul 16. Democracy 52. Matter 88. Space 17. Desire 53. Mechanics 89. State 18. Dialectic 54. Medicine 90. Temperance 19. Duty 55. Memory/Imagination 91. Theology 20. Education 56. Metaphysics 92. Time 21. Element 57. Mind 93. Truth 22. Emotion 58. Monarchy 94. Tyranny 23. Eternity 59. Nature 95. Universe 24. Evolution 60. Necessity 96. Virtue/Vice 25. Experience 61. Oligarchy 97. War & Peace 26. Family 62. One and Many 98. Wealth 27. Fate 63. Opinion 99. Will 28. Form 64. Opposition 100. Wisdom 29. God 65. Philosophy 101. World 30. Good and Evil 66. Physics 31. Government 67. Pleasure and Pain 32. Habit 68. Poetry 33. Happiness 69. Principle 34. History 70. Progress 35. Honor 71. Prophecy 36. hypothesis 72. Prudence • Mathematical Concepts Number Error / Uncertainty Ratio Measurement Proportion Behavior Symmetry Relationships Pattern ProbabilityFunction Truth Order Problem solving Change System Quantification Prediction Representation • Mathematical Understandings Our number system maintains order and is rich with patterns. Mathematicians quantify data in order to establish real-world probabilities. All measurement involves error and uncertainty. Strands of Mathematical Proficiency Adding It Up, 2001 • Conceptual Understanding • Procedural Fluency • Strategic Competence • Adaptive Reasoning • Productive Disposition Adding It Up: Helping Children Learn Mathematics, NRC, 2001 Strands of Mathematical Proficiency: Adding It Up, 2001 • Conceptual Understanding - Comprehension of mathematical concepts, operations and relations Strands of Mathematical Proficiency: Adding It Up, 2001 • Conceptual Understanding - “Refers to an integrated and functional grasp of mathematical ideas. Students with conceptual understanding know more than isolated facts and methods. They understand why a mathematical idea is important and the kinds of contexts in which it is useful. They have organized their knowledge into a coherent whole, which enables them to learn new ideas by connecting those ideas to what they already know. Conceptual understanding also supports retention.” P. 118 Strands of Mathematical Proficiency: Adding It Up, 2001 • Procedural Fluency - Skill in carrying out procedures flexibly, accurately, efficiently, and appropriately Strands of Mathematical Proficiency: Adding It Up, 2001 • “Understanding makes learning skills easier, less susceptible to common errors, and less prone to forgetting. By the same token, a certain level of skill is required to learn many mathematical concepts with understanding.” Page 122 Strands of Mathematical Proficiency: Adding It Up, 2001 • Strategic Competence - Ability to formulate, represent, and solve mathematical problems, especially with multiple approaches. Strands of Mathematical Proficiency: Adding It Up, 2001 • Adaptive Reasoning - Capacity for logical thought, reflection, explanation, and justification Strands of Mathematical Proficiency: Adding It Up, 2001 • Productive Disposition - Habitual inclination to see mathematics as sensible, useful, and worthwhile, coupled with a belief in diligence and one’s own efficacy Research suggests that learning is enhanced by providing opportunities for • Struggling • Choosing and evaluating strategies • Contrasting cases • Organizing information • Making connections (NRC, 1999) Dividing Fractions Demonstrating the 5 Strands • What does it mean to divide? What meanings does division have? – Repeated subtraction – Partitioning or dividing up into groups – Measurement (fits into) • Of these meanings, which one works with dividing fractions? Dividing Fractions Demonstrating the 5 Strands • Measurement Model 6 Divided by 2 Can you think of examples where you would need to divide fractions? Dividing Fractions Demonstrating the 5 Strands • Dividing fractions with fraction strips 4 1 5 5 4 1 4 5 5 Dividing Fractions Demonstrating the 5 Strands • Try dividing some fractions with like denominators on your own using the fraction strip model • Share your findings. • Do you see a pattern in dividing fractions with like denominators? Dividing Fractions Demonstrating the 5 Strands • Do you know a rule that can help speed up the process for dividing fractions without strips? • Can you think of a way to use the pattern discovered with dividing common denominators to make sense of this rule? Dividing Fractions Demonstrating the 5 Strands 2 1 3 2 Write problem with common denominators 4 3 Divide the numerators 6 6 4 43 3 2 1 4 3 2 3 Dividing Fractions Demonstrating the 5 Strands • Now relate the pattern to the algorithm of invert and multiply… • Where does the common denominator come from? 2 1 2 2 1 3 4 3 4 3 2 3 2 2 3 6 6 3 2 1 22 4 Invert and multiply! 3 2 3 1 3 Dividing Fractions Demonstrating the 5 Strands • How can knowing how to divide fractions help you in your life? • Think of as many ideas as you can for the benefits of knowing how to divide fractions! Fraction Activity • What went well for you? • What was a challenge for you? • What did you learn from this activity? USE OF INSTRUCTIONAL STRATEGIES. The following findings related to instructional strategies are supported by the existing research: • Techniques and instructional strategies have nearly as much influence on student learning as student aptitude. • Lecturing, a common teaching strategy, is an effort to quickly cover the material: however, it often overloads and over-whelms students with data, making it likely that they will confuse the facts presented • Hands-on learning, especially in science, has a positive effect on student achievement. • Teachers who use hands-on learning strategies have students who out-perform their peers on the National Assessment of Educational progress (NAEP) in the areas of science and mathematics. • Despite the research supporting hands-on activity, it is a fairly uncommon instructional approach. • Students have higher achievement rates when the focus of instruction is on meaningful conceptualization, especially when it emphasizes their own knowledge of the world. Make Card Games! Make Card Games! Build – A – Square • Build-a-square is based on the “Crazy” puzzles where 9 tiles are placed in a 3X3 square arrangement with all edges matching. • Create 9 tiles with math problems and answers along the edges. • The puzzle is designed so that the correct formation has all questions and answers matched on the edges. • Tips: Design the answers for the edges first, then write the specific problems. • Use more or less squares to tier. m=3 • Add distractors to outside edges and b=6 -2/3 “letter” pieces at the end. Nanci Smith Flippers! • You will need 2 sheets of construction paper, of different colors. (You’ll only use ½ a sheet of the second color though.) • Fold the frame color into fourths horizontally (hamburger folds). • Back-fold the same piece in the opposite directions so that it is well creased and flexible. • Fold the frame at the center only, and make cuts from the fold up to the next fold line. 7 cuts for 8 sections is easy to do, but cut as many as you like. • Fold the second color of paper into fourths as well. Cut these apart. You will only use 2 of the strips. • Basket-weave the two strips into the cut strips of the frame. The two sides need to be woven in opposite directions. • To use the flipper, write questions on the woven colors. To find the answers, fold the flipper so that the center is pointed at you, then pull the center apart to reveal answer spaces. • Flipper works in this way on both sides! Nanci Smith, 2004 RAFT ACTIVITY ON FRACTIONS Role Audience Format Topic Fraction Whole Number Petitions To be considered Part of the Family Improper Fraction Mixed Numbers Reconciliation Letter Were More Alike than Different A Simplified Fraction A Non-Simplified Fraction Public Service A Case for Simplicity Announcement Greatest Common Factor Common Factor Nursery Rhyme I’m the Greatest! Equivalent Fractions Non Equivalent Personal Ad How to Find Your Soul Mate Least Common Factor Multiple Sets of Numbers Recipe The Smaller the Better Like Denominators in an Unlike Denominators in an Application form To Become A Like Additional Problem Addition Problem Denominator A Mixed Number that 5th Grade Math Students Riddle What’s My New Name Needs to be Renamed to Subtract Like Denominators in a Unlike Denominators in a Story Board How to Become a Like Subtraction Problem Subtraction Problem Denominator Fraction Baker Directions To Double the Recipe Estimated Sum Fractions/Mixed Numbers Advice Column To Become Well Rounded Angles Relationship RAFT Role Audience Format Topic One vertical angle Opposite vertical angle Poem It’s like looking in a mirror Interior (exterior) angle Alternate interior (exterior) Invitation to a family My separated twin angle reunion Acute angle Missing angle Wanted poster Wanted: My complement An angle less than 180 Supplementary Persuasive speech Together, we’re a straight angle angle **Angles Humans Video See, we’re everywhere! ** This last entry would take more time than the previous 4 lines, and assesses a little differently. You could offer it as an option with a later due date, but you would need to specify that they need to explain what the angles are, and anything specific that you want to know such as what is the angle’s complement or is there a vertical angle that corresponds, etc. Algebra RAFT Role Audience Format Topic Coefficient Variable Email We belong together Scale / Balance Students Advice column Keep me in mind when solving an equation Variable Humans Monologue All that I can be Variable Algebra students Instruction manual How and why to isolate me Algebra Public Passionate plea Why you really do need me! ROLE AUDIENCE FORMAT TOPIC Equivalent Fractions Farmers Poster Ad for Fertilizer How do I get bigger Event Mutually exclusive Love letter We’ll never be event together… sob, sob, sob 3 line segments Polygons Application Do we belong? Pythagoras Home Buyers Floor plan It’s hip to be Square! Basic Facts Students working on a Persuasive Speech You need me! multi-step problem Denominator Numerator Song You’re a part of me Equivalent Fractions TV viewers Reality TV Show Biggest Reducer Divisor Dividend Rap Song Let me Count the ways 3-D shapes Humans Photo Journal Where do you find me? Area of Circle Humans Sales Ad Get the most pi for your dollar Scientific Notation Large numbers Health Ad The benefits of being small Radius Diameter Letter How do I fit into your life? Scale Map Poem Why do we need to be together 2 line segments All segments Wanted Poster for a Are you our missing complete triangle link? Multiples Factors Storyboard To Infinity and RAFT Planning Sheet Know Understand Do How to Differentiate: • Tiered? (See Equalizer) • Profile? (Differentiate Format) • Interest? (Keep options equivalent in learning) • Other? Role Audience Format Topic CUBING 1. Describe it: Look at the subject closely (perhaps with your senses as well as Or you can . . . . your mind) • Rearrange it 2. Compare it: What is it similar to? • Illustrate it What is it different from? • Question it 3. Associate it: What does it make you think of? What comes to your mind • Satirize it when you think of it? Perhaps people? • Evaluate it Places? Things? Feelings? Let your mind go and see what feelings you have • Connect it for the subject. • Cartoon it 4. Analyze it: Tell how it is made? What are it’s traits and attributes? • Change it • Solve it 5. Apply it: Tell what you can do with it. How can it be used? 6. Argue for it or against it: Take a stand. Use any kind of reasoning you want – logical, silly, anywhere in between. Cubing Cubing Ideas for Cubing Cubing • Arrange ________ into a 3-D collage to show ________ Ideas for Cubing in Math • Make a body sculpture to show • Describe how you would solve ______ ________ • Analyze how this problem helps us use mathematical thinking and problem solving • Create a dance to show • Compare and contrast this problem to one • Do a mime to help us understand on page _____. • Present an interior monologue with • Demonstrate how a professional (or just a dramatic movement that ________ regular person) could apply this kink or problem to their work or life. • Build/construct a representation of • Change one or more numbers, elements, or ________ signs in the problem. Give a rule for what that • Make a living mobile that shows and change does. balances the elements of ________ • Create an interesting and challenging word problem from the number problem. (Show us • Create authentic sound effects to how to solve it too.) accompany a reading of _______ • Diagram or illustrate the solutionj to the • Show the principle of ________ with a problem. Interpret the visual so we understand it. rhythm pattern you create. Explain to us how that works. Multiplication Think Dots • Struggling to Basic Level It’s easy to remember how to multiply by 0 or 1! Tell how to remember. Jamie says that multiplying by 10 just adds a 0 to the number. Bryan doesn’t understand this, because any number plus 0 is the same number. Explain what Jamie means, and why her trick can work. Explain how multiplying by 2 can help with multiplying by 4 and 8. Give at least 3 examples. We never studied the 7 multiplication facts. Explain why we didn’t need to. Jorge and his ____ friends each have _____ trading cards. How many trading cards do they have all together? Show the answer to your problem by drawing an array or another picture. Roll a number cube to determine the numbers for each blank. What is _____ X _____? Find as many ways to show your answer as possible. Multiplication Think Dots • Middle to High Level There are many ways to remember multiplication facts. Start with 0 and go through 10 and tell how to remember how to multiply by each number. For example, how do you remember how to multiply by 0? By 1? By 2? Etc. There are many patterns in the multiplication chart. One of the patterns deals with pairs of numbers, for example, multiplying by 3 and multiplying by 6 or multiplying by 5 and multiplying by 10. What other pairs of numbers have this same pattern? What is the pattern? Russell says that 7 X 6 is 42. Kadi says that he can’t know that because we didn’t study the 7 multiplication facts. Russell says he didn’t need to, and he is right. How might Russell know his answer is correct? Max says that he can find the answer to a number times 16 simply by knowing the answer to the same number times 2. Explain how Max can figure it out, and give at least two examples. Alicia and her ____ friends each have _____ necklaces. How many necklaces do they have all together? Show the answer to your problem by drawing an array or another picture. Roll a number cube to determine the numbers for each blank. What is _____ X _____? Find as many ways to show your answer as possible. Describe how you would Explain the difference 1 3 solve or roll between adding and 5 5 the die to determine your multiplying fractions, own fractions. Compare and contrast Create a word problem these two problems: that can be solved by 1 2 11 + 3 5 15 and (Or roll the fraction die to 1 1 determine your fractions.) 3 2 Describe how people use Model the problem fractions every day. ___ + ___ . Nanci Smith Roll the fraction die to determine which fractions to add. Nanci Smith Describe how you would Explain why you need 2 3 1 solve or roll a common denominator 13 7 91 the die to determine your when adding fractions, own fractions. But not when multiplying. Can common denominators Compare and contrast ever be used when dividing these two problems: fractions? 1 1 3 1 and 3 2 7 7 Create an interesting and challenging word problem A carpet-layer has 2 yards that can be solved by of carpet. He needs 4 feet ___ + ____ - ____. of carpet. What fraction of Roll the fraction die to his carpet will he use? How determine your fractions. Nanci Smith do you know you are correct? Diagram and explain the solution to ___ + ___ + ___. Roll the fraction die to determine your fractions. Designing a Differentiated Learning Contracthas the following components A Learning Contract 1. A Skills Component Focus is on skills-based tasks Assignments are based on pre-assessment of students’ readiness Students work at their own level and pace 2. A content component Focus is on applying, extending, or enriching key content (ideas, understandings) Requires sense making and production Assignment is based on readiness or interest 3. A Time Line Teacher sets completion date and check-in requirements Students select order of work (except for required meetings and homework) 4. The Agreement The teacher agrees to let students have freedom to plan their time Students agree to use the time responsibly Guidelines for working are spelled out Consequences for ineffective use of freedom are delineated Signatures of the teacher, student and parent (if appropriate) are placed on the agreement Differentiating Instruction: Facilitator’s Guide, ASCD, 1997 MY CONTRACT Student Name Date What I will do What I will use When I will finish How I feel about my project How my teacher feels about my project because because Student signature Teacher’s Signature Learning Contract Chapter: _______ Name:______________________ Ck Page/Concept Ck Page/Concept Ck Page/Concept ___ ___________ ___ ___________ ___ ___________ ___ ___________ ___ ___________ ___ ___________ ___ ___________ ___ ___________ ___ ___________ ___ ___________ ___ ___________ ___ ___________ Enrichment Options: ______________________________________________ Special Instructor ______________________________ _____ _____ _____ _____ _____ _____ _____ ______________________________ _____ _____ _____ _____ _____ _____ _____ ______________________________ _____ _____ _____ _____ _____ _____ _____ Your Idea: ______________________________ _____ _____ _____ _____ _____ _____ _____ Working Conditions ________________________________________________________________________ ________________________________________________________________________ _________________________________ ___________________________________ Teacher’s signature Student’s signature Work Log Date Goal Actual The Red Contract Key Skills: Graphing and Measuring Key Concepts: Relative Sizes Note to User: This is a Grade 3 math contract for students below grade level in these skills Read Apply Extend How big Work with a Make a is a foot? friend to graph group story the size of at or one of least 6 things your own – on the list of that uses “10 terrific measuremen things.” Label t and at least each thing with one graph. how you know Turn it into a the size book at the author center The Green Contract Key Skills: Graphing and Measuring Key Concepts: Relative Sizes Note to User: This is a Grade 3 math contract for students at or near grade level in these skills Read Apply Extend Alexande Complete the Now, make a r Who math madness math Used to book that goes madness be Rich with the story book based Last you read. on your Sunday or story about Ten Kids, kids and pets No Pets or money that comes and goes. Directions are at the author center The Blue Contract Key Skills: Graphing and Measuring Key Concepts: Relative Sizes Note to User: This is a Grade 3 math contract for students advanced in these skills Read Apply Extend Dinosaur Research a kind of Make a book Before dinosaur or in which you Dark or airplane. Figure combine math Airport out how big it is. and dinosaurs Control Graph its size on or airplanes, graph paper or on or something the blacktop else big. It outside our room. can be a Label it by name number fact and size book, a counting book, or a problem book. Instructions are at the author center Proportional Reasoning Think-Tac-Toe □ Create a word problem that □ Find a word problem from □ Think of a way that you use requires proportional the text that requires proportional reasoning in your reasoning. Solve the proportional reasoning. life. Describe the situation, problem and explain why it Solve the problem and explain why it is proportional requires proportional explain why it was and how you use it. reasoning. proportional. □ Create a story about a □ How do you recognize a □ Make a list of all the proportion in the world. proportional situation? proportional situations in the You can write it, act it, Find a way to think about world today. video tape it, or another and explain proportionality. story form. □ Create a pict-o-gram, poem □ Write a list of steps for □ Write a list of questions to ask or anagram of how to solve solving any proportional yourself, from encountering a proportional problems problem. problem that may be proportional through solving it. Directions: Choose one option in each row to complete. Check the box of the choice you make, and turn this page in with your finished selections. Nanci Smith, 2004 Menu Planner Use this template to help you plan a menu for your classroom Menu: ____________________ Due: All items in the main dish and the specified number of side dishes must be completed by the due date. You may select among the side dishes and you may decide to do some of the dessert items as well. ......................................................... Main Dish (complete all) ........................................................... Side Dish (select ____) .......................................................... Dessert Winning Strategies for Classroom Management Similar Figures Menu Imperatives (Do all 3): 1. Write a mathematical definition of “Similar Figures.” It must include all pertinent vocabulary, address all concepts and be written so that a fifth grade student would be able to understand it. Diagrams can be used to illustrate your definition. 2. Generate a list of applications for similar figures, and similarity in general. Be sure to think beyond “find a missing side…” 3. Develop a lesson to teach third grade students who are just beginning to think about similarity. Similar Figures Menu Negotiables (Choose 1): 1. Create a book of similar figure applications and problems. This must include at least 10 problems. They can be problems you have made up or found in books, but at least 3 must be application problems. Solver each of the problems and include an explanation as to why your solution is correct. 2. Show at least 5 different application of similar figures in the real world, and make them into math problems. Solve each of the problems and explain the role of similarity. Justify why the solutions are correct. Similar Figures Menu Optionals: 1. Create an art project based on similarity. Write a cover sheet describing the use of similarity and how it affects the quality of the art. 2. Make a photo album showing the use of similar figures in the world around us. Use captions to explain the similarity in each picture. 3. Write a story about similar figures in a world without similarity. 4. Write a song about the beauty and mathematics of similar figures. 5. Create a “how-to” or book about finding and creating similar figures. Begin Slowly – Just Begin! Low-Prep Differentiation High-Prep Differentiation Choices of books Tiered activities and labs Homework options Tiered products Use of reading buddies Independent studies Varied journal Prompts Multiple texts Alternative assessments Orbitals Learning contracts Varied pacing with anchor options 4-MAT Student-teaching goal setting Multiple-intelligence options Work alone / together Compacting Whole-to-part and part-to-whole explorations Spelling by readiness Flexible seating Entry Points Varied computer programs Varying organizers Design-A-Day Lectures coupled with graphic organizers Varied Supplementary materials Community mentorships Options for varied modes of expression Interest groups Tiered centers Varying scaffolding on same organizer Interest centers Let’s Make a Deal projects Personal agendas Computer mentors Literature Circles Think-Pair-Share by readiness, interest, learning profile Stations Use of collaboration, independence, and cooperation Complex Instruction Open-ended activities Group Investigation Mini-workshops to reteach or extend skills Tape-recorded materials Jigsaw Teams, Games, and Tournaments Negotiated Criteria Choice Boards Explorations by interests Think-Tac-Toe Simulations Games to practice mastery of information Problem-Based Learning Multiple levels of questions Graduated Rubrics Flexible reading formats Student-centered writing formats OPTIONS FOR DIFFERENTIATION OF INSTRUCTION To Differentiate To Differentiate To Differentiate Instruction By Instruction By Instruction by Readiness Interest Learning Profile ٭equalizer adjustments (complexity, ٭encourage application of broad ٭create an environment with flexible open-endedness, etc. concepts & principles to student interest learning spaces and options ٭add or remove scaffolding areas ٭allow working alone or working with ٭vary difficulty level of text & ٭give choice of mode of expressing peers supplementary materials learning ٭use part-to-whole and whole-to-part ٭adjust task familiarity ٭use interest-based mentoring of adults approaches ٭vary direct instruction by small group or more expert-like peers ٭Vary teacher mode of presentation ٭adjust proximity of ideas to student ٭give choice of tasks and products (visual, auditory, kinesthetic, concrete, experience (including student designed options) abstract) ٭give broad access to varied materials & ٭adjust for gender, culture, language technologies differences. useful instructional strategies: useful instructional strategies: useful instructional strategies: - tiered activities - interest centers - multi-ability cooperative tasks - Tiered products - interest groups - MI options - compacting - enrichment clusters - Triarchic options - learning contracts - group investigation - 4-MAT - tiered tasks/alternative forms of - choice boards assessment - MI options - internet mentors CA Tomlinson, UVa „97 Whatever it Takes!

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