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Graphic Organizers

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**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.

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**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).

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

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**Graphic Organizers: Heighten student interest**

Should be coherent and consistently used Can be used with teacher- and student- directed approaches

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**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.

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**How to Use Graphic Organizers in the Classroom**

Teacher-Directed Approach Student-Directed Approach

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**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

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**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

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**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

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**Types of Graphic Organizers**

Hierarchical diagramming Sequence charts Compare and contrast charts

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**A Simple Hierarchical Graphic Organizer**

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**A Simple Hierarchical Graphic Organizer - example**

Geometry Algebra MATH Trigonometry Calculus

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**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

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**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

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**Compare and Contrast Category What is it? Illustration/Example**

Properties/Attributes Subcategory Irregular set What are some examples? What is it like?

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**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?

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Venn Diagram

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**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

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Multiple Meanings

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**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°

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**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.

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**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.

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**Four-Square Graphic Organizer**

1. Word: 2. Example: 4. Definition 3. Non-example:

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**Four-Square Graphic Organizer – example**

1. Word: semicircle 2. Example: 4. Definition 3. Non-example: A semicircle is half of a circle.

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**Matching Activity Divide into groups**

Match the problem sets with the appropriate graphic organizer

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

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**Problem Set 1 Parallelogram Rhombus Square Quadrilateral Polygon Kite**

Irregular polygon Trapezoid Isosceles Trapezoid Rectangle

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**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

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**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

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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.

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**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

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**Possible Solution to PS #2**

REAL NUMBERS Irrational Numbers Rational Numbers Integers Counting Numbers Whole Numbers

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**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_____

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**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…}

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**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.

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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

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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

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**How These Strategies Help Students Access Algebra**

Problem Representation Problem Solving (Reason) Self Monitoring Self Confidence

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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.

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**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.

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Wrap-Up Questions

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**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

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**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

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