Graphic Organizers

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 you gain a clearer understanding of the material • GOs help maintain the information over time

4. Graphic Organizers: • Assist in organizing and retaining information when used consistently.

5. 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.

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

7. A Simple Hierarchical Graphic Organizer

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

9. Another Hierarchical Graphic Organizer Category Subcategory Subcategory Subcategory List examples of each type

10. Hierarchical Graphic Organizer – example Algebra Equations Inequalities 6y ≠15 14 < 3x + 7 2x > y 10y = 100 2x + 3 = 15 4x = 10x - 6

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

12. 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 0 Zero Fractions What are some examples? What is it like?

13. Venn Diagram

14. Prime Numbers 5 7 11 13 2 3 Even Numbers 4 6 8 10 Multiples of 3 9 15 21 6 Venn Diagram - example

15. Multiple Meanings

16. 3 sides 3 sides 3 angles 3 angles 3 angles = 60° 1 angle = 90° 3 sides 3 angles 3 angles < 90° Multiple Meanings – example Right Equiangular TRI- ANGLES Acute Obtuse 3 sides 3 angles 1 angle > 90°

17. Series of Definitions Word = Category + Attribute = + Definitions: ______________________ ________________________________ ________________________________

18. 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

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

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

21. Matching Activity • In your Math groups, match the problem sets with the appropriate graphic organizer

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

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

24. Problem Set 2 Counting Numbers: 1, 2, 3, 4, 5, 6, . . . Whole Numbers: 0, 1, 2, 3, 4, . . . Integers: . . . -3, -2, -1, 0, 1, 2, 3, 4. . . Rationals: 0, …1/10, …1/5, …1/4, ... 33, …1/2, …1 Reals: all numbers Irrationals: π, non-repeating decimal

25. 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

26. 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.

27. 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.

28. 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 http://www.k8accescenter.org/training_resources/documents/MathGraphicOrg.pdf • Visual mapping software: Inspiration and Kidspiration (for lower grades) at http:/www.inspiration.com • Math Matrix from the Center for Implementing Technology in Education. Available at http://www.citeducation.org/mathmatrix/

29. Resources • Hall, T., & Strangman, N. (2002).Graphic organizers. Wakefield, MA: National Center on Accessing the General Curriculum. Available at http://www.cast.org/publications/ncac/ncac_go.html • 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 http://www.k8accesscenter.org/training_resources/udl/GraphicOrganizersHTML.asp

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

31. 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.

32. 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.

33. Wrap-Up • Questions

34. 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

35. 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