The document provides examples of different types of graphic organizers including hierarchical graphic organizers, Venn diagrams, four-square graphic organizers, and matching activities. It also includes sample problems and possible solutions using different graphic organizers to organize relationships between mathematical concepts such as numbers, operations, shapes, and other topics.

1. Hierarchical Graphic Organizer Category Subcategory Subcategory Subcategory List examples of each type

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

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

4. 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, -4000 6, 17, 25, 100 0

5. Comparing and Contrasting Double Bubble Map

6. Compare and contrast Double bubble map . Here there is a student answer Make a double bubble map and compare the two equations and

7. Square Rectangle Must have parallel lines Straight lines Plane Figure Right angle All around One set of Parallel lines Longer than the other 4 Equal Sides Make a double bubble map and compare a Square and a Rectangle

8. Multiple Meanings

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

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

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

12. Venn Diagram

13. Quadrilateral Trapezoid Parallelogram Rhombus Square Rectangle

14. Flow maps

15. Student Example

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

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

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

19. 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

20. 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

21. 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.

22. 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

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

24. 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______

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