NJCIE Summer Inclusion Conference

2014

Dynamic Differentiation: Empower your students with the results they deserve

Presented by

Brian Rawlins

brawlins@spfk12.org

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

brawlins@spfk12.org