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 1.Provide clearly labeled branch and sub branches. 2.Have numbers, arrows, or lines to show the connections or sequence of events. 3.Relate similarities. 4.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 Algebra Calculus Trigonometry Geometry MATH

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

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

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

12 Positive Integers Numbers What is it? Illustration/Example What are some examples? Properties/Attributes What is it like? Fractions Compare and Contrast - example Whole Numbers Negative Integers Zero -3, -8, , 17, 25, 100 0

13 Venn Diagram

14 Venn Diagram - example Prime Numbers Even Numbers Multiples of

15 Multiple Meanings

16 Multiple Meanings – example TRI- ANGLES RightEquiangular AcuteObtuse 3 sides 3 angles 1 angle = 90° 3 sides 3 angles 3 angles < 90° 3 sides 3 angles 3 angles = 60° 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. Square Quadrilateral 4 equal sides & 4 equal angles (90°)

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

20 Four-Square Graphic Organizer – example 1. Word: semicircle 2. Example: 3. Non-example:4. Definition 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 ParallelogramRhombus SquareQuadrilateral PolygonKite Irregular polygonTrapezoid Isosceles TrapezoidRectangle

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 AdditionMultiplication a + ba times b a plus ba x b sum of a and ba(b) ab SubtractionDivision a – ba/b a minus ba divided by b a less bb) 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 Possible Solution to PS #1 POLYGON Parallelogram: has 2 pairs of parallel sides Kite Square, rectangle, rhombus Kite: has 0 sets of parallel sides Irregular: 4 sides w/irregular shape Quadrilateral Trapezoid: has 1 set of parallel sides Trapezoid, isosceles trapezoid

28 Possible Solution to PS #2 REAL NUMBERS

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

30 Possible Solution to PS #4 Numbers Operations RulesSymbols Geometric Figures Mathematics Triangle Quadrilateral Hexagon Integer Prime Rational Irrational Whole Composite Addition Subtraction Multiplication Division Corollary Postulatem║n √4 {1,2,3…}

31 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.

32 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 hicOrg.pdf Visual mapping software: Inspiration and Kidspiration (for lower grades) at Math Matrix from the Center for Implementing Technology in Education. Available at

33 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 /udl/GraphicOrganizersHTML.asp

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

35 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.

36 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.

37 Wrap-Up Questions

38 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

39 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