1. No category

*
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.
*
Fixed Mind-Set
STUDENT
Growth Mind-Set
*Mindset – Carol Dweck
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.
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.
Fixed Mind-Set
Growth Mind-Set
TEACHER
Differentiation
C. Tomlinson
Is a teacher’s response to learner’s needs
Guided by general principles of differentiation
Meaningful tasks
Quality Curriculum
Content
Flexible grouping
Continual assessment
Teachers can differentiate through
Process
Product
Building Community
Affect/Environment
According to students’
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.
*
*
*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.
*
How to Differentiate
Name:
Date:
Change the Content
Change the Content
 Complexity
 Resources
 Environment
Change the Content
 Complexity
Concrete to Abstract
 Resources
 Environment
Do/View/Construe
DO – Manipulatives: Concrete
• 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/
VIEW – Graphic
Organizers Representational
www.graphicorganizers.com
http://challengebychoice.wordpress.com/examples-of-tiered-math-assessments/
*3 Levels of Challenge - CbC
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
 Resources
Text/Media
 Environment
Do/View/Construe
*
*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
Compiled by Kim
Kenward and GVSU
Math Dept.
http://www.3dvinci.net/ccp0-display/splash.html
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)
* 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/
* Teaching Tables
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.
* Web2.0 for Math Educators - a Wiki
http://mathfest.wikispaces.com/Web2.0+For+Math+Educators
Change the Content
 Complexity
Concrete to Abstract
 Resources
Text/Media
 Environment
TAPS
Do/View/Construe
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
*
*
1.
2.
3.
4.
5.
6.
Awareness
Comprehension
Application
Analysis
Synthesis
Evaluation
S. Gendron, Kentwood presentation, March 2011
*
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
Levels
Bloom’s
6
5
4
3
2
1
C
D
A
B
1
2 3 4 5
Application
S. Gendron, Kentwood presentation, March 2011
Rigor/Relevance Framework
6
•
•
5
4
•
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.
C
1
•
•
•
3
2
•
• 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.
A
1
2
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.
D
• 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.
B
3
4
5
S. Gendron, Kentwood presentation, March 2011
*
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
*
*Open Questions
*Parallel Tasks
* Question 1:
Write the quadratic y = 3x2 – 12x + 17 in vertex form.
* Question 2:
Draw a graph of y = 3x2 – 12x + 17. Tell what you notice.
*
*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.
*
*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.
could the other side lengths be?
*
What
*
*
*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.
*
* 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?
*
What is your T.E.M.P.O. or Style?
Thinking Goal:
Environment:
Motivation:
Process:
Outcome:
Thoughtful Education Press/Silver, Strong
and Associates
Mastery
T.
E.
M.
P.
O.
T.
E.
M.
P.
O.
Understanding
T.
E.
M.
P.
O.
Interpersonal
Self-Expressive
T.
E.
M.
P. Thoughtful Education Press/Silver,
Strong and Associates
O.
ST Mastery Learner:
T: Remembering
E: Clarity/Consistency
M: Success
P: Step-by-Step; Exercise and Practice
O: WHAT? Correct Answers
Thoughtful Education Press/Silver, Strong
and Associates
NT Understanding Learner:
T: Reasoning
E: Critical Thinking
M: Curiosity
P: Doubt-by-Doubt; Proof/Explain
O: WHY? Argue
Thoughtful Education Press/Silver, Strong
and Associates
NF Self-Expressive Learner:
T: Reorganize
E: Choice
M: Originality
P: Dream-by-Dream; Possibilities
O: WHAT IF? Creative Products
Thoughtful Education Press/Silver, Strong
and Associates
SF Interpersonal Learner:
T: Relate
E: Cooperative/Conversation
M: Relationships
P: Friend-by-Friend; Personal Experiences
O: IF WHAT, SO WHAT? Current and Connected
Thoughtful Education Press/Silver, Strong
and Associates
35%
35%
S+T
Mastery
S+F
Interpersonal
N+T
Understanding
N+F
Self-Expressive
10%
20%
35%
35%
S+T
Mastery
S+F
Interpersonal
12%
65%
1%
22%
N+T
Understanding
10%
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
Counting Principles & Probability: Tic-Tac-Toe
Board
(Auditory, Visual, Kinesthetic)
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.
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.
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.
(Interpersonal/Linguistic)
(Bodily/Kinesthetic)
(Mathematical/Logical)
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.
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.
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!
(Musical/Rhythmic)
(Linguistic/Intrapersonal)
(Visual/Spatial)
7. Internet Research
Search the Internet to find 5 games
that use Combinatorics
(permutations or combinations).
Begin at Mrs. Thomasma’s Math 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)
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.
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.
(Visual/Spatial)
(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
Hook
Input
Interaction
Product
Assessment
Reflection
Hook – Role Play
Input –
(content)
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
As a team of educators:
Discuss with your peers the
differentiated instructional
ideas and strategies that
you recommend for
implementation in your class.
*An Old African Proverb Asks
How do you eat
an elephant?????