*
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
• Versa Tiles
• Didax Geofix (nets)
• Models of shapes (surface area and volume)
• Virtual Manipulatives
http://www.neirtec.org/activities/math_portal.htm
VIEW – Graphic
Organizers Representational
www.graphicorganizers.com
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:
* Question 2:
To which fact family does the fact 3 x 4 = 12 belong?
Describe the picture below by using a mathematical
equation.
x
x
x
x
x
x
x
x
x
x
x
x
*
*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 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.
could the other side lengths be?
*
What
How is the number 85 like the number
100 and how is it different?
*
*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.
*
*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.
*
*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.
*
Change the Product
 Entry Points
How they learn
 Expressive Modes
How they express it
 Accountability
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.
Rhyme Time Choices
1. Feel a Rhyme
.
2. Act out a Nursery Rhyme.
4. Mother Goose
Listening Center
5. Retell a Nursery Rhyme
with the Flannel Board.
7. Rhyming Puzzles
.
8. Writing Rhyming
Word Families
3. Write your own
Nursery Rhyme.
6. Rhyming Buckets
9. Computer:
Starfall or Gamequarium
Goal – 7 Points
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?
Angela had 8
computer games.
She got 3 more for
her birthday.
How many computer
games did Angela
have then?
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?
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
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?
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?
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?
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
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?
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?
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?
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
Goal – 4 Points
Goal – 40 Points
Goal – 4 Points
Goal – 60 Points
Goal – 8 Points
Goal – 40 Points
Goal – 20 Points
Goal – 250 Points
Goal – 30 Points
Change the Product
 Entry Points
How they learn
 Expressive Modes
How they express it
 Accountability
How we grade/score it
Formative/Portfolios/Performance Based
Name ______________________________
STUDENT ANALYSIS PAPER
Question
Learning
Target
1
I can name each coin.
2
I can name each coin.
3
I can name each coin.
4
I can name each coin.
5
I can tell the value of
each coin.
I can tell the value of
each coin.
I can tell which group
of same coins has
more value.
I can tell the value of
a group of same
coins.
I can tell the value of
a group of same
coins.
I can write the value
of a group of coins
using the cent symbol.
6
7
8
9
10
I CAN
do this!
I am still
learning
about this!
Station for
Practice
Pot of Gold!
Money game
Pot of Gold!
Money game
Pot of Gold!
Money game
Pot of Gold!
Money game
Smart Board
Money Match
Smart Board
Money Match
Who Has
More?
Mystery Money
Mystery Money
Mystery Money
Pot of Gold!
This is a board game with pictures of different coins arranged in a game board
format. A student rolls a die and moves the game piece that number of spaces.
Before the next player rolls, the student has to say the name of the coin. The Math
Helper has to give a thumbs up if it is right, or a thumbs sideways if they should try
again. Then, it is the next player’s turn.
Smart Board Money Match
This is an interactive game created using the Notebook Software for the Smart
Board. A student selects two cards to touch and flip. If the cards match a picture of
a coin to the correct coin value, the student has to show the Math Helper a thumbs
up. If the Math Helper agrees the cards are a match, he/she will return the thumbs
up or put a thumb sideways to try again. If the cards do indeed match, the cards
remain flipped over as a match. If the cards do not match a picture with a coin
value, the cards are flipped back over.
Who Has More?
Students will work in groups of two or three. The Math Helper will monitor the
groups assisting where needed. One student in a group will roll a number die and a
money die. The number die will show how many coins to grab from the money
bank and the money die will show the type of coin to select. The student will grab
the money, count the money and say, “I have ____.” The partner student will repeat
directions. The partner with the most money will say, “_____(amount of money) is
more than _____ (partner amount of money).” Students will put the coins back and
repeat.
Mystery Money
The Math Helper will select a number of same coins from the money bank and lay
in the center of the group. Each student in the group will count the money and
write the amount using a cent symbol on a small white board and dry erase marker.
Students will show the Math Helper the amount and the Math Helper will show
each student a thumbs up for the correct answer or a thumb sideways to try again.
The Math Helper will finish by teaching/showing how to count the money. The
Math Helper will put the coins back and repeat activity.
Race to $1.00
One partner rolls a die. He/she will take the same number of pennies as the die
shows. If the partner can do any trades, he/she should do so before the next partner
rolls. Once a partner has five pennies, he/she may trade for a nickel. After they
have two nickels, they may trade for a dime. Partners may continue trading as their
money banks increase. Partners continue to roll, get money, and make trades up to
one dollar. After someone reaches one dollar, partners can start over.
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?????