1. Graphic Organizers

2. Graphic Organizers (GOs)
A graphic organizer is a tool or process to build word knowledge by relating similarities of meaning to the definition of a word. This can relate to any subject—math, history, literature, etc.

3. Why are Graphic Organizers Important?
GOs connect content in a meaningful way to help students gain a clearer understanding of the material (Fountas & Pinnell, 2001, as cited in Baxendrall, 2003).
GOs help students maintain the information over time (Fountas & Pinnell, 2001, as cited in Baxendrall, 2003).

4. Graphic Organizers:
Assist students in organizing and retaining information when used consistently.
Assist teachers by integrating into instruction through creative
approaches.

5. Graphic Organizers: Heighten student interest
Should be coherent and consistently used
Can be used with teacher- and student- directed approaches

6. Coherent Graphic Organizers
Provide clearly labeled branch and sub branches.
Have numbers, arrows, or lines to show the connections or sequence of events.
Relate similarities.
Define accurately.

7. How to Use Graphic Organizers in the Classroom
Teacher-Directed Approach
Student-Directed Approach

8. Teacher-Directed Approach
Provide a partially complete GO for students
Have students read instructions or information
Fill out the GO with students
Review the completed GO
Assess students using an incomplete copy of the GO

9. Student-Directed Approach
Teacher uses a GO cover sheet with prompts
Example: Teacher provides a cover sheet that includes page numbers and paragraph numbers to locate information needed to fill out GO
Teacher acts as a facilitator
Students check their answers with a teacher copy supplied on the overhead

10. Strategies to Teach Graphic Organizers
Framing the lesson
Previewing
Modeling with a think aloud
Guided practice
Independent practice
Check for understanding
Peer mediated instruction
Simplifying the content or structure of the GO

11. Types of Graphic Organizers
Hierarchical diagramming
Sequence charts
Compare and contrast charts

12. A Simple Hierarchical Graphic Organizer

13. A Simple Hierarchical Graphic Organizer - example
Geometry
Algebra
MATH
Trigonometry
Calculus

14. Another Hierarchical Graphic Organizer
Category
Subcategory
Subcategory
Subcategory
This example relates a category, subdivided into subcategories then lists or shows examples of each type.
List examples of each type

15. Hierarchical Graphic Organizer – example
Algebra
Equations
Inequalities
This example relates a category, subdivided into subcategories then lists or shows examples of each type.
6y ≠ 15
2x + 3 = 15
10y = 100
14 < 3x + 7
2x > y
4x = 10x - 6

16. Compare and Contrast Category What is it? Illustration/Example
Properties/Attributes
Subcategory
Irregular set
What are some examples?
What is it like?

17. Compare and Contrast - example
Numbers
What is it?
Illustration/Example
Properties/Attributes
6, 17, 25, 100
Positive Integers
Whole Numbers
-3, -8, -4000
Negative Integers
Zero
Fractions
What are some examples?
What is it like?

18. Venn Diagram

19. Venn Diagram - example Prime Numbers 5 7 11 13 2 3 Even Numbers 4 6
5 7
Even Numbers
8 10
Multiples of 3 3 2 6

20. Multiple Meanings

21. Multiple Meanings – example
Right
Equiangular
3 sides
3 angles
1 angle = 90°
3 sides
3 angles
3 angles = 60°
TRI-
ANGLES
Acute
Obtuse
3 sides
3 angles
3 angles < 90°
3 sides
3 angles
1 angle > 90°

22. Series of Definitions Word = Category + Attribute = +=
Definitions: ______________________
________________________________
Example 4 can be considered a sequential organizer showing the process of defining a word by combining the category and attribute.

23. Series of Definitions – example
Word = Category + Attribute
= +
Definition: A four-sided figure with four equal sides and four right angles.
4 equal sides &
4 equal angles (90°)
Square
Quadrilateral
Example 4 can be considered a sequential organizer showing the process of defining a word by combining the category and attribute.

24. Four-Square Graphic Organizer
1. Word:
2. Example:
4. Definition
3. Non-example:

25. Four-Square Graphic Organizer – example
1. Word: semicircle
2. Example:
4. Definition
3. Non-example:
A semicircle is half of a circle.

26. Matching Activity Divide into groups
Match the problem sets with the appropriate graphic organizer

27. Matching Activity
Which graphic organizer would be most suitable for showing these relationships?
Why did you choose this type?
Are there alternative choices?

28. Problem Set 1 Parallelogram Rhombus Square Quadrilateral Polygon Kite
Irregular polygon Trapezoid
Isosceles Trapezoid Rectangle

29. Problem Set 2 Counting Numbers: 1, 2, 3, 4, 5, 6, . . .
Whole Numbers: 0, 1, 2, 3, 4, . . .
Integers: , -2, -1, 0, 1, 2, 3,
Rationals: 0, …1/10, …1/5, …1/4, , …1/2, …1
Reals: all numbers
Irrationals: π, non-repeating decimal

30. Problem Set 3 Addition Multiplication a + b a times b a plus b a x b
sum of a and b a(b) ab
Subtraction Division
a – b a/b
a minus b a divided by b
a less b b) a

31. Problem Set 4
Use the following words to organize into categories and subcategories of
Mathematics:
NUMBERS, OPERATIONS, Postulates, RULE, Triangles, GEOMETRIC FIGURES, SYMBOLS, corollaries, squares, rational, prime, Integers, addition, hexagon, irrational, {1, 2, 3…}, multiplication, composite, m || n, whole, quadrilateral, subtraction, division.

32. Possible Solution to PS #1
POLYGON
Square, rectangle,
rhombus
Parallelogram:
has 2 pairs of
parallel sides
Quadrilateral
Trapezoid,
isosceles trapezoid
Trapezoid: has 1
set of parallel
sides
Kite
Kite: has 0 sets of
parallel sides
Irregular: 4 sides
w/irregular shape

33. Possible Solution to PS #2
REAL NUMBERS
Irrational
Numbers
Rational Numbers
Integers
Counting
Numbers
Whole Numbers

34. Possible Solution PS #3 Addition Subtraction Operations Multiplication
____a + b____
___a plus b___
Sum of a and b
____a - b_____
__a minus b___
___a less b____
Operations
Multiplication
Division
___a times b___
____a x b_____
_____a(b)_____
_____ab______
____a / b_____
_a divided by b_
_____a  b_____

35. Possible Solution to PS #4
Mathematics
Geometric
Figures
Numbers
Operations
Rules
Symbols
Rational
Addition
Postulate
m║n
Triangle
Prime
Subtraction √4
Corollary
Hexagon
Integer
Multiplication
Irrational
Division
Quadrilateral
Whole
Composite
{1,2,3…}

36. Graphic Organizer Summary
GOs are a valuable tool for assisting students with LD in basic mathematical procedures and problem solving.
Teachers should:
Consistently, coherently, and creatively use GOs.
Employ teacher-directed and student-directed approaches.
Address individual needs via curricular adaptations.

37. Resources
Maccini, P., & Gagnon, J. C. (2005). Math graphic organizers for students with disabilities. Washington, DC: The Access Center: Improving Outcomes for all Students K-8. Available at
Visual mapping software: Inspiration and Kidspiration (for lower grades) at
Math Matrix from the Center for Implementing Technology in Education. Available at

38. Resources
Hall, T., & Strangman, N. (2002).Graphic organizers. Wakefield, MA: National Center on Accessing the General Curriculum. Available at
Strangman, N., Hall, T., Meyer, A. (2003) Graphic Organizers and Implications for Universal Design for Learning: Curriculum Enhancement Report. Wakefield, MA: National Center on Accessing the General Curriculum. Available at

39. How These Strategies Help Students Access Algebra
Problem Representation
Problem Solving (Reason)
Self Monitoring
Self Confidence

40. Recommendations:
Provide a physical and pictorial model, such as diagrams or hands-on materials, to aid the process for solving equations/problems.
Use think-aloud techniques when modeling steps to solve equations/problems. Demonstrate the steps to the strategy while verbalizing the related thinking.
Provide guided practice before independent practice so that students can first understand what to do for each step and then understand why.

41. Additional Recommendations:
Continue to instruct secondary math students with mild disabilities in basic arithmetic. Poor arithmetic background will make some algebraic questions cumbersome and difficult.
Allot time to teach specific strategies. Students will need time to learn and practice the strategy on a regular basis.

42. Wrap-Up
Questions

43. Closing Activity Principles of an effective lesson: Before the Lesson:
Review
Explain objectives, purpose, rationale for learning the strategy, and implementation of strategy
During the Lesson:
Model the task
Prompt students in dialogue to promote the development of problem-solving strategies and reflective thinking
Provide guided and independent practice
Use corrective and positive feedback

44. Concepts for Developing a Lesson
Grades K-2
Use concrete materials to build an understanding of equality (same as) and inequality (more than and less than)
Skip counting
Grades 3- 5
Explore properties of equality in number sentences (e.g., when equals are added to equals the sums are equal)
Use physical models to investigate and describe how a change in one variable affects a second variable
Grades 6-8
Positive and negative numbers (e.g., general concept, addition, subtraction, multiplication, division)
Investigate the use of systems of equations, tables, and graphs to represent mathematical relationships