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Jacque Melin - GVSU

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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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.
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 .
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.
Fixed Mind-Set
Teacher encourages and insists on student effort and growth.
Over time, the student’s mindset 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.
Growth Mind-Set
TEACHER

C. Tomlinson
Differentiation
Is a teacher’s response to learner’s needs
Guided by general principles of differentiation
Meaningful tasks
Quality Curriculum
Flexible grouping Continual assessment
Teachers can differentiate through
Building Community
Content
Process
Product
According to students’
Affect/Environment
Readiness Interest Learning 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.

* 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:

Change the Content

Change the Content
 Complexity
 Resources
 Environment

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

• Algebra Tiles (for linear and quadratic equation solving)
• Didax Geofix (nets)
• Models of shapes (surface area and volume)
• Soft 1 cm squares http://www.etacuisenaire.com
• Virtual Manipulatives http://www.neirtec.org/activities/math_portal.htm
• Wolfram Alpha http://www.wolframalpha.com/

www.graphicorganizers.com

http://challengebychoice.wordpress.com/examples-of-tiered-math-assessments/

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Green —Tasks are foundational and appropriate for the current grade level. Success depends on understanding and applying required knowledge and skills. Green level tasks meet a rigorous grade level proficiency standard.
Blue —Tasks are advanced and complex. Success depends on extending one’s skills in order to recognize and address the added layers of complexity.
Black—Tasks are extremely advanced and highly complex.
Success depends on creatively applying and extending one’s skills, at times in very unfamiliar territory.

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://www.fi.edu/learn/hotlists/math.php

* 3Dvinci http://www.3dvinci.net/ccp0-display/splash.html
Compiled by Kim
Kenward and GVSU
Math Dept.
3D design is a great motivational and instructional tool. It exercises both leftbrain 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.
* Algebasics http://www.algebasics.com
This site contains a variety of interactive Algebra help/ problems/activities
* 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.
* 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!

* 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
* 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.
* Concord Consorium http://www.concord.org/work/software
This site features free downloadable Math & Science software.
* CrickWeb http://www.crickweb.co.uk/ks1numeracy.html
Math interactive tools for white boards
* 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

* Futures Channel http://www.thefutureschannel.com/
The Futures Channel Videos and Activities Deliver Hands-On, Real World Math and Science Lessons for the Classroom.
* Interactive Simulations for Math and Science http://phet.colorado.edu/simulations/index.php?cat=Featured_Sims
This site is from The University of Colorado
* 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.
* 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.

* Java Math & Science Applets 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.
* 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.
* 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
* 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.
* 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.

* MathNet Number Cruncher 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!
* MathTV http://www.mathtv.org
This site has interactive games and simulation related to math problem solving.
* 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.
* 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.
* Math Wire – Elementary (especially early elementary) http://mathwire.com/

* Calcoolate http://www.calcoolate.com
(Also available as a download for Windows machines.)
* Create a Graph http://nces.ed.gov/nceskids/createagraph
(creates five kinds of graphs)
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Online Conversion http://www.onlineconversion.com
This site can convert just about anything to anything else.
* 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
* 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.

* Teaching Time http://www.teachingtime.co.uk/
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Teaching Tables http://www.teachingtables.co.uk/
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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.
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Web2.0 for Math Educators - a Wiki http://mathfest.wikispaces.com/Web2.0+For+Math+Educators

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

Change the Process

Change the Process
 Direct Instruction
 Cooperative Learning
 Inquiry

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

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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

3
2
1
6
5
4
C
D
A B
1 2 3 4 5
S. Gendron, Kentwood presentation, March 2011

6
5
4
3
2
1
• Analyze the graphs of the perimeters and areas of squares having different-length sides.
• Determine the largest rectangular area for a fixed perimeter.
C 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.
D 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
• Express probabilities as fractions, a newspaper.
percents, or decimals.
• Classify triangles according to angle size and/or length of sides.
A B
• Given the coordinates of a quadrilateral, plot the
• 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 quadrilateral on a grid. graphs.
1 2 3 5

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Questgarden
The Buck Institute

Change the Product

Change the Product
 Entry Points
 Expressive Modes
 Accountability

Change the Product
 Entry Points
How they learn
 Expressive Modes
 Accountability

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Question 1: Write the quadratic y = 3x 2 – 12x + 17 in vertex form.
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Question 2: Draw a graph of y = 3x 2 – 12x + 17. Tell what you notice.
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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 75% of 20?
* 15 is a percent of a number. What percent of what number is it?
* 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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*

* Instead of asking a the surface area of a cone with a radius 4” and a height 15”,
* ask students to choose numbers for the radius and the height and then determine the surface area.
*

* Create a sentence that includes the words
“linear” and “increasing” as well as the numbers 4 and 9.
* An increasing linear pattern could include the numbers 4 and 9.
* In a linear pattern starting at 4 and increasing by 9, the tenth number will be 85.
* A linear pattern that is increasing by 9 grows faster than one that is increasing by 4.
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* Graph and solve this linear system of equations
0.5x + 0.6y = 5.4
-x + y = 9
Solve for m:
4m – 1 = -25
5 2 2
Matthew has 20 ounces of a 40% salt solution. How much salt should he add to make it a 45% solution?
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Thoughtful Education Press/Silver, Strong and Associates

Mastery
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M.
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T.
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M.
P.
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Understanding
Interpersonal
T.
E.
M.
P.
O.
Self-Expressive
T.
E.
M.
P.
O.
Thoughtful Education Press/Silver,
Strong and Associates

T:
E:
M:
P:
Thoughtful Education Press/Silver, Strong and Associates

T:
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M:
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Thoughtful Education Press/Silver, Strong and Associates

T:
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Thoughtful Education Press/Silver, Strong and Associates

T:
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Thoughtful Education Press/Silver, Strong and Associates

35%
S + T
Mastery
S + F
Interpersonal
35%
10%
N + T
Understanding
N + F
Self-Expressive
20%

35%
S + T
Mastery
S + F
Interpersonal
35%
10%
12%
1%
N + T
Understanding
65%
22%
N + F
Self-Expressive
20%

Hook
Have you ever ridden a bike or a skateboard down a really steep hill? How steep was it? How about a roller coaster? Share your stories with the class. For those of your who have had two or more of these experiences, which hill was steepest?
Come up with a number that tells how steep it was.
What number did you choose? Why did you choose that number? Your number actually has a specific meaning as it applies to steepness. Now let’s investigate to see if your hill really is that steep.
Thoughtful Education Press/Silver, Strong and Associates

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

Targets:
• I can write the steps of a math induction proof for a given series.
• I can apply Pascal’s Triangle to find the coefficients of a binomial expansion.
• I can apply the Binomial Theorem to expand a binomial.
• I can find probabilities of mutually exclusive & independent events.
V. Thomasma, Kentwood

Counting Principles & Probability
Tic-Tac-Toe Board
Choose three activities in a row (horizontally, vertically, or diagonally) to complete. The activities are designed to help you relate to and remember probability concepts. They are due at the end of the unit, so please work on them after completing daily work in class, or at home. You may work by yourself or with one other person on any or all three activities.
1. Letter of Advice
Write a letter to a friend who is in
Algebra 2 this year, and going to take Precalculus next year. Don’t scare them! Instead, list and describe four pieces of advice that would help them succeed in
Precalculus. Stretch your brain, and make at least 2 pieces of advice relevant to this unit.
(Interpersonal/Linguistic)
4. Poem or Rap
Write a poem or rap about either permutations & combinations,
Pascal’s Triangle, or The Binomial
Theorem. Be sure to include information that will give your fellow math students a clever way of remembering how to use the mathematical skill you chose! Your work may be either read or performed for the class.
(Musical/Rhythmic)
7. Internet Research
Search the Internet to find 5 games that use Combinatorics
(permutations or combinations).
Begin at Mrs. Thomasma’s Mat h of
Games website: www.mathematicsofgames.pbwiki.co
m
For each game, write a brief description of the game, which combinatorics are used, and how knowledge of the math might help with strategy!
(Intrapersonal)
2. In The News
Pretend you are a journal reporter in the 1600s. (You’ll also need to pretend they had TV and reporters then!) Your job is to describe the controversy over Pascal’s
Triangle…did Blaise Pascal really discover it? Should it be named after him? Use the internet to conduct some research. Plan it out ahead of time, then create a short clip (less than 5 minutes) with a video camera.
(Bodily/Kinesthetic)
5. Jeopardy Review Game
Write Jeopardy questions that can be used to review our Probability Unit.
Include 10 questions with answers.
Use an index card for each question, with the answer on the back. We will use 6 categories, which are the titles of the lessons in your book.
Write at least one question for each category.
(Linguistic/Intrapersonal)
8. Comic Strip
Create a comic strip that highlights a concept about probability, counting principles, math induction, or another topic from our unit.
Include illustrations and dialogue.
(Visual/Spatial)
3. Graphing Calculator Activity
Create 5 probability problems that are solved most efficiently with a
Graphing Calculator . (Hint: using combinations, permutations and
The Binomial Theorem guarantees this). Make at least 2 of the problems real-life scenarios.
Include the answers as well.
(Mathematical/Logical)
6. Poster
It is your chance to make a cheat sheet for your classroom! Design and make a poster that includes the important concepts from this unit.
Make it colorful, and include at least
2 relevant pictures or drawings. It will be displayed in the classroom, until test day of course!
(Visual/Spatial)
9. Nature Walk
Take a walk outside to brainstorm examples of arithmetic and geometric patterns that occur in nature. You may consider architecture also. Record at least four of your observations. Draw or take pictures of them, and explain which type of sequence each exemplifies.
(Naturalist)

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

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

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

Direct Instruction (Little Book) - Novelty

Discuss with your peers the differentiated instructional ideas and strategies that you recommend for implementation in your class.

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