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Jacque Melin - GVSU

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Differentiation is a set of instructional strategies. Reality: Differentiation is a philosophy—a way of thinking (MINDSET) about teaching and learning. It is, in fact, a set of principles.

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STUDENT TEACHER Fixed Mind-Set Growth Mind-Set Both teacher and student accept the student’s difficulties as given, and neither exerts the effort needed for high levels of student achievement. Both also accept high grades on grade-level work as adequate for advanced learners. Teacher may underestimate student capacity and willingness to work hard and “teach down” because of the student’s language, culture, economic status, race, label, etc. Teacher encourages and insists on student effort and growth. Over time, the student’s mind- set can change to a growth orientation with evidence that effort leads to success. Students at all readiness levels have maximum opportunity for challenge, growth, and success. Both teacher and student study student growth, set goals for progress, and look for ways to continue development. Students at all readiness levels have maximum opportunity for challenge, growth, and success.

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Differentiation Is a teacher’s response to learner’s needs Guided by general principles of differentiation Meaningful tasksFlexible groupingContinual assessment Teachers can differentiate through Content Process ProductAffect/Environment According to students’ ReadinessInterestLearning Profile Through a variety of instructional strategies such as: RAFTS…Graphic Organizers…Scaffolding …Cubing…Tic-Tac-Toe…Learning Contracts….Tiering… Learning/Interest Centers… Independent Studies…Intelligence Preferences….Orbitals…..Complex Instruction…ETC. Quality Curriculum Building Community C. Tomlinson

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* It’s adequate for a district or school leader (or professional developers) to tell, or even show, teachers how to differentiate instruction effectively. * Reality: Learning to differentiate instruction well requires rethinking one’s classroom practice and results from an ONGOING process of trial, reflection, and adjustment in the classroom itself.

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* Differentiation is something a teacher does or doesn’t do (as in, “I already do that,” or “I tell our teachers that they already differentiate instruction.”). * Reality: Most teachers who remain in a classroom for longer than a day do pay attention to student variation and respond to it in some way. * However, very few teachers proactively plan instruction to consistently address student differences in readiness, interest, and learning profile.

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How to Differentiate Name: Date:

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Change the Content

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Complexity Resources Environment

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Change the Content Complexity Concrete to Abstract Do/View/Construe Resources Environment

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DO – Manipulatives: Concrete Versa Tiles Didax Geofix (nets) Models of shapes (surface area and volume) Virtual Manipulatives http://www.neirtec.org/activities/math_portal.htm

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VIEW – Graphic Organizers - Representational www.graphicorganizers.com

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Change the Content Complexity Concrete to Abstract Do/View/Construe Resources Text/Media Environment

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* Alternative Textbooks * Transitional Mathematics Program (Woodward & Stroh, 2004) – clear direct instruction and explanations. * Internet * Hotlists and Webquests and High quality websites * http://questgarden.com/search/ http://questgarden.com/search/ * http://www.fi.edu/learn/hotlists/math.php http://www.fi.edu/learn/hotlists/math.php

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* 3Dvinci http://www.3dvinci.net/ccp0-display/splash.html 3D design is a great motivational and instructional tool. It exercises both left- brain and right-brain skills, and appeals to students of all abilities. ModelMetricks books contain easy-to-follow projects based on the free Google SketchUp application, to show how to model anything in 3D. http://www.3dvinci.net/ccp0-display/splash.html * Algebasics http://www.algebasics.com This site contains a variety of interactive Algebra help/ problems/activities http://www.algebasics.com * Archimy http://www.archimy.com This site has a service for drawing the graphs of all kinds of functions. With Archimy, you will draw the graph of any function and form, just use your imagination. The program must be downloaded and is free. http://www.archimy.com * Arcademic Skill Builder http://www.arcademicskillbuilders.com Our research-based and standards-aligned free educational math games and language arts games will engage, motivate, and help teach students. Click a button below to play our free multi-player and single-player games! http://www.arcademicskillbuilders.com Compiled by Kim Kenward and GVSU Math Dept.

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* Chart Gizmo http://chartgizmo.com This site has an incredible chart builder for any type of data that can be typed or uploaded to this tool http://chartgizmo.com * Chart Tool http://www.onlinecharttool.com This site is another great tool for creating Charts and graphs On Onlinecharttool.com you can design and share your own graphs online and for free We support a number of different chart types like: bar charts, pie charts, line charts, bubble charts and radar plots. http://www.onlinecharttool.com * Concord Consorium http://www.concord.org/work/software This site features free downloadable Math & Science software. http://www.concord.org/work/software * CrickWeb http://www.crickweb.co.uk/ks1numeracy.html Math interactive tools for white boards http://www.crickweb.co.uk/ks1numeracy.html * Flash Card Creator http://www.aplusmath.com/Flashcards/Flashcard_Creator.html This site from aplusMath allows for the easy creation of online/printable math flash cards http://www.aplusmath.com/Flashcards/Flashcard_Creator.html

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* Futures Channel http://www.thefutureschannel.com/ The Futures Channel Videos and Activities Deliver Hands-On, Real World Math and Science Lessons for the Classroom. http://www.thefutureschannel.com/ * Interactive Simulations for Math and Science http://phet.colorado.edu/simulations/index.php?cat=Featured_Sims This site is from The University of Colorado http://phet.colorado.edu/simulations/index.php?cat=Featured_Sims * Interactives http://www.learner.org/interactives Interactives" provides educators and students with strategies, content, and activities that can enhance and improve students' skills in a variety of curricular areas. http://www.learner.org/interactives * Introducing Integers (6-8) http://mathstar.lacoe.edu/newmedia/integers/intro/media/media.html This site contains hands-on approaches for teaching the sometimes challenging concept of integers. Included are video clips, concrete models and Mat Board for solving the problems. Quick-Time media player is required. http://mathstar.lacoe.edu/newmedia/integers/intro/media/media.html

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* Java Math & Science Applets http://www.falstad.com/mathphysics.html http://www.falstad.com/mathphysics.html * Johnnie's Math Page http://jmathpage.com/index.html Links to interactive math tools and activities for students and teachers. http://jmathpage.com/index.html * Lure of the Labyrinth http://labyrinth.thinkport.org/www This site contains a interesting digital game for middle-school pre-algebra students. It includes a wealth of intriguing math-based puzzles wrapped into an exciting narrative game in which students work to find their lost pet - and save the world from monsters. http://labyrinth.thinkport.org/www * Math.com http://www.math.com/students/puzzles/puzzleapps.html This site has a large number of math puzzles and games. Many can be used with an interactive white board http://www.math.com/students/puzzles/puzzleapps.html * MathsNet (K-12) www.mathsnet.net MathsNet is an independent educational website providing free mathematics resources to the education community. Its aim is to offer truly interactive resources that are both wide and deep in terms of their applicability and usefulness. MathsNet is not an online textbook. It is interactive, requiring the user to participate rather than be a passive observer. www.mathsnet.net * Math Forum http://mathforum.org/library/resource_types/simulations This site contains a listing of a number of additional sites that contain Math interactive simulations. http://mathforum.org/library/resource_types/simulations

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* MathNet Number Cruncher http://mathsnet.net/cruncher/index.html http://mathsnet.net/cruncher/index.html * Math Playground http://www.mathplayground.com/index.html Welcome to Math Playground, an action-packed site for elementary and middle school students. Practice your math skills, play a logic game and have some fun! http://www.mathplayground.com/index.html * MathTV http://www.mathtv.org This site has interactive games and simulation related to math problem solving. http://www.mathtv.org * MathVids http://www.mathvids.com MathVids.com is a website dedicated to providing high quality, instructional, free math videos to middle school, high school, and college students who need math help. http://www.mathvids.com * Mathway http://mathway.com This site is powered by Bagatrix Solved!™ technology, Mathway provides students with the tools they need to solve their math problems. With tens of millions of problems already solved, Mathway is the #1 online problem solving resource available for students, parents, and teachers. http://mathway.com * Math Wire – Elementary (especially early elementary) http://mathwire.com/ http://mathwire.com/

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* Calcoolate http://www.calcoolate.com (Also available as a download for Windows machines.) http://www.calcoolate.com * Create a Graph http://nces.ed.gov/nceskids/createagraph (creates five kinds of graphs) http://nces.ed.gov/nceskids/createagraph * Online Conversion http://www.onlineconversion.com This site can convert just about anything to anything else. http://www.onlineconversion.com * NumberNut http://www.numbernut.com/index.html This site has a variety of activities and games that can be used in conjunction with interactive white boards Random Number Generator www.random.org This site allows for the generation of true random numbers. Teachers could use this for probability and statistics activities as well as drawings, random sampling and more http://www.numbernut.com/index.html * SqoolTools MathFacts (K-6) http://sqooltools.com/freeworkshops/mathfacts.html Explore all of the best K-6 math tools the web has to offer! From basic addition to geometry and fractions, from virtual manipulates to interactive games, from online calculators and converters to graphing tools. You will discover resources for every math topic you teach. http://sqooltools.com/freeworkshops/mathfacts.html

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* Teaching Time http://www.teachingtime.co.uk/ http://www.teachingtime.co.uk/ * Teaching Tables http://www.teachingtables.co.uk/ http://www.teachingtables.co.uk/ * Visual Math Learning (4-8) www.visualmathlearning.com This site is a free interactive multimedia on-line tutorial for math students. Its first level, Numbers and Arithmetic, is a pre-Algebra level course suitable for grades 4-8. Unlike traditional textbooks, Visual Math Learning is designed to run on any personal computer with a modern browser. www.visualmathlearning.com * Web2.0 for Math Educators - a Wiki http://mathfest.wikispaces.com/Web2.0+For+Math+Educators http://mathfest.wikispaces.com/Web2.0+For+Math+Educators

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Change the Content Complexity Concrete to Abstract Do/View/Construe Resources Text/Media Environment TAPS

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Change the Process

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Direct Instruction Cooperative Learning Inquiry

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Change the Process Direct Instruction Hook them Curiosity NoveltyNovelty Cooperative Learning Each one – Teach one Inquiry PBL

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1.Awareness 2.Comprehension 3.Application 4.Analysis 5.Synthesis 6.Evaluation S. Gendron, Kentwood presentation, March 2011

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1. Knowledge in one discipline 2. Application within discipline 3. Application across disciplines 4. Application to real-world predictable situations 5. Application to real-world unpredictable situations S. Gendron, Kentwood presentation, March 2011

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Levels CDCDABABCDCDABAB 1 2 3 4 5 4 5 6 3 2 1 Bloom’s Application S. Gendron, Kentwood presentation, March 2011

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1 2 3 4 5 6 12345 A B D C Rigor/Relevance Framework Express probabilities as fractions, percents, or decimals. Classify triangles according to angle size and/or length of sides. Calculate volume of simple three- dimensional shapes. Given the coordinates of a quadrilateral, plot the quadrilateral on a grid. Analyze the graphs of the perimeters and areas of squares having different-length sides. Determine the largest rectangular area for a fixed perimeter. Determine and justify the similarity or congruence for two geometric shapes. Obtain historical data about local weather to predict the chance of snow, rain, or sun during year. Test consumer products and illustrate the data graphically. Plan a large school event and calculate resources (food, decorations, etc.) you need to organize and hold this event. Make a scale drawing of the classroom on grid paper, each group using a different scale. Calculate percentages of advertising in a newspaper. Tour the school building and identify examples of parallel and perpendicular lines, planes, and angles. Determine the median and mode of real data displayed in a histogram Organize and display collected data, using appropriate tables, charts, or graphs. S. Gendron, Kentwood presentation, March 2011

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Questgarden The Buck Institute

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Change the Product

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Entry Points Expressive Modes Accountability

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Change the Product Entry Points How they learn Expressive Modes Accountability

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* Open Questions * Parallel Tasks

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* Question 1: To which fact family does the fact 3 x 4 = 12 belong? * Question 2: Describe the picture below by using a mathematical equation. x x

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* Turning around a question. * Asking for similarities and differences. * Replacing a number, shape, measurement unit, and so forth with a blank. * Asking for a number sentence.

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* Instead of: What is half of 20? * 10 is a fraction of a number. What could the fraction and number be? * Instead of : What is the hypotenuse of a right triangle if the legs are 3 units and 4 units long? * One side of a right triangle is 5 units long. What could the other side lengths be?

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How is the number 85 like the number 100 and how is it different?

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* Instead of asking - How many students are there altogether if there are 25 students in one class and 31 in another? * ask students to choose numbers for the two classes then determine the total numbers in both classes.

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* Create a sentence that includes the words “and” and “more” as well as the numbers 3 and 4. * 3 and 4 are more than 2. * 4 is more than 3 and more than 1. * 3 and 4 together are more than 6. * 34 and 26 are more than 34 and 20.

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* Turning around a question. * Asking for similarities and differences. * Replacing a number, shape, measurement unit, and so forth with a blank. * Asking for a number sentence.

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Change the Product Entry Points How they learn Expressive Modes How they express it Accountability

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Rhyme : Tic-Tac-Toe Board (Multiple Intelligences) TARGETS: I can recognize if two words rhyme. I can supply a rhyme for a given word. I can isolate and name the ending sound of a pair of rhyming words. I can produce and verbalize a pair of rhyming words. I can identify the letters that make up the ending sound of a rhyme. I can identify word family words that rhyme.

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Goal – 7 Points

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Ned rode his bike 7 miles to the library. He took a shortcut on the way home which was only 5 miles long. How many miles did Ned ride altogether? Anne ate 6 cookies. Samantha ate 4 more cookies than Anne. How many cookies did Samantha eat? Henry gave 5 stickers to his younger brother. Now he only has 9 stickers. How many stickers did Henry have at first? Derek and Larry have 15 books together. 6 of the books belong to Derek. How many books does Larry have? Angela had 8 computer games. She got 3 more for her birthday. How many computer games did Angela have then? Lisa made 8 apple muffins for the bake sale. Trevor made 6 banana muffins. They sold 5 muffins altogether. How many muffins were left? 1 Point Questions

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Carl bought 18 stickers. He used 9 of them that afternoon. He used 3 more after dinner. How many stickers did Carl have left? Alex found 12 pennies on the playground. He spent 5 pennies. Then he found 3 more. How many pennies did Alex have then? Suzanne has 8 pairs of white socks and 6 pairs of blue socks. Her sister has 12 pairs of white socks. How many pairs of socks does Suzanne have? Scott, Frankie, and Corey played in the snow for 4 hours. Scott made 5 snowballs and 2 snowmen. Corey made 7 snowballs. Frankie made 4 snowballs and a snow fort. How many snowballs did the boys make? Chris found 14 colorful leaves at the park. He gave 4 to his sister. Later he found 6 more. How many leaves did Chris have then? Alan has 10 pennies. Bonnie has 6 fewer pennies than Alan. Jack has 5 more pennies than Alan. How many pennies does Bonnie have? 3 Point Questions

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Scott had $15 in his wallet. He spent $8 for a toy. He earned $5 for doing a chore. He spent $3 for lunch. How much money did Scott have left? A bag contains 20 marbles. 7 are red, 5 are blue, 2 are yellow, and the rest are green. How many green marbles are in the bag? Anthony has saved $8. He gets $4 more for his allowance. He spends $3 for a toy. He gets another allowance of $4. How much money does Anthony need to buy a $20 robot? Ben walks from school to Danny’s house which is 6 blocks east of the school. Ben then walks 11 blocks west to his own house. How many blocks away does Ben live from school? Angela opens a saving account with $12. She then deposits $5. She withdraws $9 and then later deposits $6. How much does Angela have in the account then? Jordan found one seashell at the beach on Monday. She found 2 seashells the next day. If Jordan finds 2 seashells every day after that, how many days until Jordan has 21 seashells altogether? 6 Point Questions

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Goal – 4 Points

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Goal – 40 Points

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Goal – 4 Points

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Goal – 60 Points

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Goal – 8 Points

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Goal – 40 Points

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Goal – 20 Points

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Goal – 250 Points

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Goal – 30 Points

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Change the Product Entry Points How they learn Expressive Modes How they express it Accountability How we grade/score it Formative/Portfolios/Performance Based

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Do we differentiate by: Whole group? Small group? Individual?

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Do we differentiate by: Whole group? Multimodal – tap into many ways of learning Small group? Instructional Interventions Individual? Tutorials

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Hook Input Interaction Product Assessment Reflection

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Hook – Role Play (content) Input – Direct Instruction (Little Book) - Novelty (content/process) Interaction – 3 Musketeers (process) Product – Little Book on DI Theory (product) Assessment – Tell and Retell Reflection – Scale of 1-10

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As a team of educators: Discuss with your peers the differentiated instructional ideas and strategies that you recommend for implementation in your class.

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How do you eat an elephant?????

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