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NJCIE Summer Inclusion Conference
2014
Dynamic Differentiation: Empower your students with the results they deserve
Presented by
Brian Rawlins
Scotch Plains-Fanwood School District
Montclair State University
Wednesday, June 25, 2014
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What are your concerns or barriers to implementing
differentiation in the classroom?
What would you like to learn more about?
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Tangram Challenge—Homework
Choose a figure and write specific directions for your classmate to create that figure out of the tangrams.
To help your classmate, be certain to use the following terminology:
Midpoint
Hypotenuse
Vertex
Rotate
Bisect
Right Angle
Acute Angle
Square
Isosceles Right Triangle
Parallelogram
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Name: _________________________________ Date: _________________ Period: _______ #: ______
FIDO & SPOT
The Jones place their dog FIDO outside on a 7 ft leash
anchored in the ground by a stake. The Smith family want
to treat their dog to a more open experience and place Spot
into a pen that measures 7’ x 7’.
Which dog has more room to play?
Investigating Circles Pre-Assessment
1. What is the diameter of this circle? __________
2. What is the radius of the circle? __________
3. What is the circumference of the circle? __________
4. What is the perimeter of the circle? __________
5. What is the area of the circle? ___________
7 ft
Helpful Formulas:
Area of Circle = r2
Circumference of Circle = 2r
= d
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Name: __________________________________ Date: ___________________ Period: ______ #: ____
Investigation of Circles
Vocabulary:
Radius: any line segment that connects the center of the circle with any point on
the circle. The length of a radius segment is also called the radius.
Diameter: any segment that passes through the center of the circle and has
both endpoints on the circle. The length of a diameter segment is also called the
diameter.
On the circles above, find the radius and diameter in centimeters. Record your answers in the chart below.
Circle Radius in cm(s) Diameter in cm(s)
A
B
C
D
Examine the data in the table. What is the relationship between the radius and diameter of a circle?
A
B
C
D
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1. Match each circle with its circumference.
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2. Find the circumference for each circle. Important: Circumference = 2πr or π * d.
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Write the answers in the boxes.
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3. The figure is made up of a triangle and a semicircle. (Take π = 3.14)
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DIFFERENTIATED MATERIALS APPENDIX (Developed by Adam Hoppe of Curry School of Education, University of Virginia, Charlottesville, VA)
DIFFERENTIATED MATERIALS – LESSON 1: Tiered Questioning Script
This script is for a point in the book where 12 guests are trying to seat themselves together at the same table.
Before this point, six guests were seated around two tables (as in Figure 1). The guests add two more tables,
thinking that this will allow six more people to sit (see Figure 2). The next step in the book is Figure 3 – the
guests add an additional 2 tables, still trying to seat 12. These questions examine the change from figure one to
figure two, and anticipate the change to figure 3.
Low-readiness:
How many tables are together now? How many tables were added?
How many chairs were there before? How many chairs fit around the table now?
How many seats did they gain? Do they have enough seats? How many more seats do they still need?
Middle-readiness:
What is the perimeter of this table?
How does the perimeter of this table compare to the perimeter of the previous table?
What is the area of this table?
How does the area of this table compare to the area of the previous table?
How many people can sit at each table now? How does this compare with the previous table?
Higher-readiness:
Why didn’t adding two more tables make it so six more people could sit at the table?
Would it help if they had added the tables to the ends, making a long line instead of a square? Why or why not?
Will adding two more tables (for a total of six tables) solve their problem? Why (or why not)?
Is there any way to add tables and gain more than two seats (while still keeping the shape a rectangle)? Explain.
Fig. 3
Fig. 2
Fig. 1
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DIFFERENTIATED MATERIALS – LESSON 2: Tiered Party Planning Math Journal Task
These materials are tiered for readiness. The more difficult task provides much less support for students as they
must find optimal solutions to the problem. The task designed for middle-readiness students reduces the
demand by not requiring optimal solutions, but still requires students to think of multiple routes to the same
goal of 24 chairs around the table. The task designed for the least-ready students provides additional supports
by directing students towards two possible solutions. The students are still responsible for creating the
solutions themselves. All students do similar actions – measuring area and perimeter - and they all ultimately
work with the same understanding – the relationship between area and perimeter.
Task for Highest-Readiness Group:
You are hosting a picnic at Washington Park. Unlike Mrs. Comfort (from Spaghetti and Meatballs for All!), you
know that all your guests want to sit at the same table. Like Mrs. Comfort, you have to rent small square tables
to use. Each table costs $10 to rent (the chairs are free). You have three tasks.
1. Find the least expensive way to seat all 24 guests. Use pictures, numbers and words to prove you’re
right. Make sure you draw a picture of your table and label the sides, perimeter and area.
2. Next, find the most expensive way to seat all 24 guests without having any extra chairs. Use pictures,
numbers and words to prove you’re right. Make sure you draw a picture of your table and label the
sides, perimeter and area.
3. Once you find both, answer these questions on this paper:
a. How do the perimeters of each table compare?
b. How do the areas of each table compare?
c. How does the shape of the table affect the price?
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Task for Middle-Readiness Group:
You are hosting a picnic at Washington Park. Unlike Mrs. Comfort (from Spaghetti and Meatballs for All!), you
know that all your guests want to sit at the same table. Like Mrs. Comfort, you have to rent small square tables
to use. Each table costs $10 to rent (the chairs are free). You have three tasks.
1. Draw at least three different ways to seat all 24 guests at the same table with no extra chairs. Use
pictures, numbers and words to prove your tables will seat 24 people (no less, no more). Make sure you
draw a picture of your table and label the sides, perimeter and area.
2. For each table, calculate how much you will have to pay to rent the tables you will need:
Table 1: Table 2: Table 3:
3. Answer these questions:
a. Compare the perimeter of your most expensive table and your least expensive table
b. Compare the area of your most expensive table and your least expensive table
c. Compare the shapes of your most expensive table and your least expensive table
Task for Lower-Readiness Group:
You are hosting a picnic at Washington Park. Unlike Mrs. Comfort (from Spaghetti and Meatballs for All!), you know
that all your friends want to sit at the same table. Like Mrs. Comfort, you have to rent small square tables to use.
1. Use 20 square tiles to make a table that will seat your 24 friends (with no extra seats). Use all of the tiles.
Draw your table here:
The perimeter of this table is:
The area of this table is:
2. Use 32 tiles to make another table that will seat your 24 friends (with no extra seats). Use all of the tiles. Draw
your table here:
The perimeter of this table is:
The area of this table is:
3. Answer these questions:
a. Each table costs $10 to rent. Which table will cost more to rent? How do you know?
b. Describe the shape of the more expensive table.
c. Describe the shape of the less expensive table.
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The Cube Challenge
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CHOICE BOARD ACTIVITY
Unit/Theme: Fractions, Decimals and Percents (Objective: Determine equivalent forms of Fractions, Decimals and Percents)
MAKE A QUILT
Use the cm graph paper (provided) to design a quilt. Use 4 colors. When your quilt is complete and every square is shaded determine the fraction, decimal and percent for each color. See sample.
COLOR CODING Review the numbers on the color-coding work sheet. Color equivalent fractions, decimals and percents all in one color. Once a matching set of 3 is found pick a new color and search for another matching set. Continue until all numbers are shaded.
RUMMY CARD GAME Use the deck of number cards provided to play rummy with a classmate. Your objective is to find 2 sets of equivalent fractions, decimals, and percents. See the rummy instruction page for further directions.
I HAVE, WHO HAS Create an I have, Who has activity for a class of 24 students. Include equivalent fractions,
decimals and percents. See the template sheets with more
directions. (May change this to play I have, who has
with 3 friends)
COMPUTER Go to the website
given below to play The Ameba
(Equivalent Fraction Game)
http://mathforum.org/te/ exchange/hosted/ameba/
POSTER Design a poster that illustrates how to convert decimals to fractions and fractions to decimals.
SURVEY Design a survey and then poll at least 20 friends. Display your data as fractions, decimals and percents.
MUSIC On your own or with a partner create a song that teaches the steps for converting a fraction to a decimal and a decimal to a fraction.
YOU ARE THE TEACHER
Design a study guide that reviews what a student needs to know about determining equivalent forms of fractions, decimals and percents. Include
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some practice problems and answer guide.
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Additional Questions that MUST be asked within the pre-assessment.
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“When teachers differentiate instruction,
they move away from seeing themselves
as keepers and dispensers of knowledge
and move toward seeing themselves as
organizers of learning opportunities.”
—Carol Ann Tomlinson
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Other Resources
“Differentiating Instruction in Inclusive Classrooms,” Diane Haager, Janette
Klingner
“How to Differentiate Instruction in Mixed-Ability Classrooms,” Carol Ann
Tomlinson
“The Differentiated Classroom: Responding to the Needs of All Learners,”
Carol Ann Tomlinson
“Integrating Differentiated Instruction: Understanding by Design,” Carol Ann
Tomlinson and Jay McTighe
“The Differentiated Math Classroom: A guide for Teachers, K-8,” Miki
Murray
“Differentiating Instruction for Students with Learning Disabilities,” William
Bender
Differentiationcentral.com
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Thank You for Your Participation!
Any Questions?
Brian Rawlins