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- 1. Visual Tools for Teaching College- and Career-Readiness StandardsEdwin Ellis, Ph.D. Craig Henden, BA Professor, Special Education, Math Teacher The University of Alabama Oakman Middle edwinellis1@gmail.com School (205) 394-5512 For information about how to access Smart Visual software featured in this presentation or professional development for your school, pleaseElizabeth Long, MA contact Dr. Edwin Ellis RTI Coordinator Hartselle High School © 2013 Edwin S. Ellis All Rights Reserved edwinellis1@gmail.com www.GraphicOrganizers.com
- 2. Visual Tools for Teaching College- and Career-Readiness StandardsEdwin Ellis, Ph.D. Craig Henden, BA Professor, Special Education, Math Teacher The University of Alabama Oakman Middle edwinellis1@gmail.com School (205) 394-5512 PART 3: Math StandardsElizabeth Long, MA RTI Coordinator Hartselle High School © 2013 Edwin S. Ellis All Rights Reserved edwinellis1@gmail.com www.GraphicOrganizers.com
- 3. TM Makes Sense Strategies Toolkit © Edwin Ellis, PhD (205) 394-5512Why use visual tools when teachingMATH? * Makes critical information more explicit * Helps students focus on critical features * Provides an alternative (visual) format for remembering semantic math information * Organizes students’ thinking * Reveals structures that may not seem obvious to some students © 2013 Edwin S. Ellis All Rights Reserved edwinellis1@gmail.com www.GraphicOrganizers.com
- 4. TM Makes Sense Strategies Toolkit © Edwin Ellis, PhD (205) 394-5512Math competencies in which visual tools areparticularly useful….Math concepts / terms / definitions For example… Rhombus Trapezoid Monomial Binomial Trinomial PolynomialMath rules For example… When to apply different systems of linear inequalities Pythagorean Theorem – when it appliesMath processes / calculation procedures For example… Steps to computing unknown angles Steps to computing DOTS (Differences in Two Squares) © 2013 Edwin S. Ellis All Rights Reserved edwinellis1@gmail.com www.GraphicOrganizers.com
- 5. © 2013 Edwin S. Ellis All Rights Reserved edwinellis1@gmail.com www.GraphicOrganizers.com
- 6. © 2013 Edwin S. Ellis All Rights Reserved edwinellis1@gmail.com www.GraphicOrganizers.com
- 7. © 2013 Edwin S. Ellis All Rights Reserved edwinellis1@gmail.com www.GraphicOrganizers.com Teacher versionStudent version
- 8. © 2013 Edwin S. Ellis All Rights Reserved edwinellis1@gmail.com www.GraphicOrganizers.com
- 9. © 2013 Edwin S. Ellis All Rights Reserved edwinellis1@gmail.com www.GraphicOrganizers.com
- 10. © 2013 Edwin S. Ellis All Rights Reserved edwinellis1@gmail.com www.GraphicOrganizers.com Teacher version Student version
- 11. © 2013 Edwin S. Ellis All Rights Reserved edwinellis1@gmail.com www.GraphicOrganizers.com
- 12. © 2013 Edwin S. Ellis All Rights Reserved edwinellis1@gmail.com www.GraphicOrganizers.comLesson 7.1 ANGLES Is about … Angle Relationships Adjacent, Adjacent Angles: linked. Share a vertex and a side. Vertical, Vertical Angles: formed by intersecting lines (opposite each other). Congruent Angles: angles with equal measure. Congruent “VERTICAL ANGLES ARE CONGRUENT” Complements Complementary Angles: two angles whose measures’ sum is 90 degrees. & (each angle would be the “complement” of the other) “right for each other” Supplementary Angles: two angles whose measures’ sum is 180 degrees. Supplements (each angle would be the “supplement” of the other) Parallel Parallel Lines: in the same plane, but never intersect. & Perpendicular Perpendicular Lines: lines that intersect forming 4 right angles. So what? What is important to understand about this?Learning Geometry has 2 Main Ideas: Vocabulary and Pictures.
- 13. © 2013 Edwin S. Ellis All Rights Reserved edwinellis1@gmail.com www.GraphicOrganizers.comLesson 7.2 - ANGLES Is about …Identifying and Classifying Angles Main idea Main idea Main idea Identifying Angles Finding Complements and Finding Angle Measures Supplements (using angle relationships) Angle – formed by two rays or Complementary Angles – two angles Adjacent Angles – linked, share a side segments with a common endpoint whose sum equals 90 degrees. and a vertex Vertex – the common endpoint (each angle would be the Vertical Angles – (formed by (vertices) “complement” of the other) intersecting lines) opposite from each other Congruent Angles – angles with Acute – between 0 and 90 degrees equal measures Right – 90 degrees Supplementary Angles – two angles whose sum equals 180 degrees. BIG PHRASE: Obtuse – between 90 and 180 degrees (each angle would be the “Vertical Angles are Congruent!!” “supplement” of the other) Straight – 180 degrees So what? What is important to understand about this? Learning Geometry has 2 Main Ideas: Vocabulary and Pictures.
- 14. © 2013 Edwin S. Ellis All Rights Reserved edwinellis1@gmail.com www.GraphicOrganizers.com
- 15. © 2013 Edwin S. Ellis All Rights Reserved edwinellis1@gmail.com www.GraphicOrganizers.comWednesday, August 29th will be aboutOrder of Operations, Distributive Property, Mean, Median, Mode, and Range Order of Operations Distributive Property Mean 1) Work Grouping Symbols – ( ), [ ], fractions 9(4+5) = 9(4) + 9(5) The AVERAGE woman is mean…. (8-2)5 = 5(8) – 5(2) 2) Work out exponents -add up all of the numbers 3) Multiply or Divide a(b+c) = ab + ac -divide by the number of numbers (b-c)a = ab - ac 4) Add or Subtract Median Mode Range The median of a highway is the MOST = Mode…. The difference in the largest and MIDDLE of the road…. smallest numbers in the data…. -the number or numbers that repeat -put the numbers in order the most times (can be more than -once in order, subtract the first -if there are two middle numbers, one mode or no mode) number from the last find their average -if there is only one, it is the medianDon’t Forget About The Test Next Wednesday
- 16. © 2013 Edwin S. Ellis All Rights Reserved edwinellis1@gmail.com www.GraphicOrganizers.com Prisms/Cylinders Spheres V = Bh Volume V = 4πr³ 3 B is the area of the base.Ex. 1: Ex. 5: Pyramids/Cones V = 1BhEx. 2: 3 Ex. 6: B is the area of the base. Ex. 3: Ex. 4:
- 17. © 2013 Edwin S. Ellis All Rights Reserved edwinellis1@gmail.com www.GraphicOrganizers.com
- 18. TM Makes Sense Strategies Toolkit © Edwin Ellis, PhD (205) 394-5512MATH CONCEPTS
- 19. © 2013 Edwin S. Ellis All Rights Reserved edwinellis1@gmail.com www.GraphicOrganizers.com I have seen or heard this I have never seen or I know this word. word before, but Im not sure heard this word WORD It means… what it means beforeInequalityGreater thanLess thanEqual toGraph (verb)SolutionComplementNotationIntegersAll real #s
- 20. TM Makes Sense Strategies Toolkit © Edwin Ellis, PhD (205) 394-5512MATH CONCEPTSHIERARCHIC (Main Ideas & Details)
- 21. TM Makes Sense Strategies Toolkit © Edwin Ellis, PhD (205) 394-5512MATH CONCEPTSHIERARCHIC (Main Ideas & Details)
- 22. TM Makes Sense Strategies Toolkit © Edwin Ellis, PhD (205) 394-5512MATH CONCEPTSHIERARCHIC (Main Ideas & Details)
- 23. TM Makes Sense Strategies Toolkit © Edwin Ellis, PhD (205) 394-5512MATH CONCEPTSHIERARCHIC (Main Ideas & Details)
- 24. TM Makes Sense Strategies Toolkit © Edwin Ellis, PhD (205) 394-5512MATH CONCEPTSHIERARCHIC (Main Ideas & Details)
- 25. TM Makes Sense Strategies Toolkit © Edwin Ellis, PhD (205) 394-5512MATH CONCEPTSHIERARCHIC (Main Ideas & Details)
- 26. TM Makes Sense Strategies Toolkit © Edwin Ellis, PhD (205) 394-5512MATH CONCEPTSHIERARCHIC (Main Ideas & Details)
- 27. TM Makes Sense Strategies Toolkit © Edwin Ellis, PhD (205) 394-5512MATH CONCEPTSHIERARCHIC (Main Ideas & Details)
- 28. TM Makes Sense Strategies Toolkit © Edwin Ellis, PhD (205) 394-5512MATH CONCEPTSCOMPARE / CONTRAST
- 29. TM Makes Sense Strategies Toolkit © Edwin Ellis, PhD (205) 394-5512MATH CONCEPTSCOMPARE / CONTRAST
- 30. TM Makes Sense Strategies Toolkit © Edwin Ellis, PhD (205) 394-5512MATH PROCESSES / CALCULATION PROCEDURESHIERARCHIC (Main Ideas & Details)
- 31. TM Makes Sense Strategies Toolkit © Edwin Ellis, PhD (205) 394-5512MATH CONCEPTSHIERARCHIC (Main Ideas & Details)
- 32. TM Makes Sense Strategies Toolkit © Edwin Ellis, PhD (205) 394-5512
- 33. TM Makes Sense Strategies Toolkit © Edwin Ellis, PhD (205) 394-5512MATH PROCESSES / COMPUTATIONSSEQUENCE
- 34. TM Makes Sense Strategies Toolkit © Edwin Ellis, PhD (205) 394-5512MATH PROCESSES / CALCULATION PROCEDURESHIERARCHIC (Main Ideas & Details)
- 35. TM Makes Sense Strategies Toolkit © Edwin Ellis, PhD (205) 394-5512MATH PROCESSES / CALCULATION PROCEDURESHIERARCHIC (Main Ideas & Details)
- 36. TM Makes Sense Strategies Toolkit © Edwin Ellis, PhD (205) 394-5512MATH PROCESSES / CALCULATION PROCEDURESHIERARCHIC (Main Ideas & Details)
- 37. TM Makes Sense Strategies Toolkit © Edwin Ellis, PhD (205) 394-5512MATH PROCESSES / CALCULATION PROCEDURESHIERARCHIC (Main Ideas & Details)
- 38. TM Makes Sense Strategies Toolkit © Edwin Ellis, PhD (205) 394-5512MATH PROCESSES / CALCULATION PROCEDURESHIERARCHIC (Main Ideas & Details)
- 39. TM Makes Sense Strategies Toolkit © Edwin Ellis, PhD (205) 394-5512MATH PROCESSES / CALCULATION PROCEDURESHIERARCHIC (Main Ideas & Details)
- 40. TM Makes Sense Strategies Toolkit © Edwin Ellis, PhD (205) 394-5512MATH PROCESSES / CALCULATION PROCEDURESHIERARCHIC (Main Ideas & Details)
- 41. TM Makes Sense Strategies Toolkit © Edwin Ellis, PhD (205) 394-5512MATH PROCESSES / CALCULATION PROCEDURESHIERARCHIC (Main Ideas & Details)
- 42. TM Makes Sense Strategies Toolkit © Edwin Ellis, PhD (205) 394-5512MATH PROCESSES / CALCULATION PROCEDURESHIERARCHIC (Main Ideas & Details)
- 43. TM Makes Sense Strategies Toolkit © Edwin Ellis, PhD (205) 394-5512MATH PROCESSES / CALCULATION PROCEDURESHIERARCHIC (Main Ideas & Details)
- 44. TM Makes Sense Strategies Toolkit © Edwin Ellis, PhD (205) 394-5512MATH PROCESSES / CALCULATION PROCEDURESHIERARCHIC (Main Ideas & Details)
- 45. TM Makes Sense Strategies Toolkit © Edwin Ellis, PhD (205) 394-5512MATH PROCESSES / CALCULATION PROCEDURESHIERARCHIC (Main Ideas & Details)
- 46. TM Makes Sense Strategies Toolkit © Edwin Ellis, PhD (205) 394-5512MATH PROCESSES / CALCULATION PROCEDURESCAUSE / EFFECT
- 47. TM Makes Sense Strategies Toolkit © Edwin Ellis, PhD (205) 394-5512MATH RULES
- 48. TM Makes Sense Strategies Toolkit © Edwin Ellis, PhD (205) 394-5512MATH RULES
- 49. TM Makes Sense Strategies Toolkit © Edwin Ellis, PhD (205) 394-5512MATH RULES

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