Visual Tools for Teaching College Readiness Math Standards1. Visual Tools for Teaching College- and Career-
Readiness Standards
Edwin 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, please
Elizabeth 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 Standards
Edwin 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 Standards
Elizabeth 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) 394-5512
Why use visual tools when teaching
MATH?
* 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) 394-5512
Math competencies in which visual tools are
particularly useful….
Math concepts / terms / definitions
For example…
Rhombus Trapezoid
Monomial Binomial Trinomial Polynomial
Math rules
For example…
When to apply different systems of linear inequalities
Pythagorean Theorem – when it applies
Math 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 version
Student 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
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13. © 2013 Edwin S. Ellis All Rights Reserved edwinellis1@gmail.com www.GraphicOrganizers.com
Lesson 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.
14. © 2013 Edwin S. Ellis All Rights Reserved edwinellis1@gmail.com www.GraphicOrganizers.com
Lesson 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.
15. © 2013 Edwin S. Ellis All Rights Reserved edwinellis1@gmail.com www.GraphicOrganizers.com
16. © 2013 Edwin S. Ellis All Rights Reserved edwinellis1@gmail.com www.GraphicOrganizers.com
Wednesday, August 29th will be about
Order 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 median
Don’t Forget About The Test Next Wednesday
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Prisms/Cylinders Spheres
V = Bh
Volume V = 4πr³
3
B is the area of the base.
Ex. 1: Ex. 5:
Pyramids/Cones
V = 1Bh
Ex. 2: 3 Ex. 6:
B is the area of the base.
Ex. 3:
Ex. 4:
18. © 2013 Edwin S. Ellis All Rights Reserved edwinellis1@gmail.com www.GraphicOrganizers.com
19. TM
Makes Sense Strategies Toolkit
© Edwin Ellis, PhD (205) 394-5512
MATH CONCEPTS
23. © 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 I'm not sure heard this word
WORD It means… what it means before
Inequality
Greater than
Less than
Equal to
Graph (verb)
Solution
Complement
Notation
Integers
All real #s
24. TM
Makes Sense Strategies Toolkit
© Edwin Ellis, PhD (205) 394-5512
MATH CONCEPTS
HIERARCHIC (Main Ideas & Details)
25. TM
Makes Sense Strategies Toolkit
© Edwin Ellis, PhD (205) 394-5512
MATH CONCEPTS
HIERARCHIC (Main Ideas & Details)
26. TM
Makes Sense Strategies Toolkit
© Edwin Ellis, PhD (205) 394-5512
MATH CONCEPTS
HIERARCHIC (Main Ideas & Details)
27. TM
Makes Sense Strategies Toolkit
© Edwin Ellis, PhD (205) 394-5512
MATH CONCEPTS
HIERARCHIC (Main Ideas & Details)
28. TM
Makes Sense Strategies Toolkit
© Edwin Ellis, PhD (205) 394-5512
MATH CONCEPTS
HIERARCHIC (Main Ideas & Details)
29. TM
Makes Sense Strategies Toolkit
© Edwin Ellis, PhD (205) 394-5512
MATH CONCEPTS
HIERARCHIC (Main Ideas & Details)
30. TM
Makes Sense Strategies Toolkit
© Edwin Ellis, PhD (205) 394-5512
MATH CONCEPTS
HIERARCHIC (Main Ideas & Details)
31. TM
Makes Sense Strategies Toolkit
© Edwin Ellis, PhD (205) 394-5512
MATH CONCEPTS
HIERARCHIC (Main Ideas & Details)
32. TM
Makes Sense Strategies Toolkit
© Edwin Ellis, PhD (205) 394-5512
MATH CONCEPTS
COMPARE / CONTRAST
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Makes Sense Strategies Toolkit
© Edwin Ellis, PhD (205) 394-5512
MATH CONCEPTS
COMPARE / CONTRAST
34. TM
Makes Sense Strategies Toolkit
© Edwin Ellis, PhD (205) 394-5512
MATH PROCESSES / CALCULATION PROCEDURES
HIERARCHIC (Main Ideas & Details)
35. TM
Makes Sense Strategies Toolkit
© Edwin Ellis, PhD (205) 394-5512
MATH CONCEPTS
HIERARCHIC (Main Ideas & Details)
36. TM
Makes Sense Strategies Toolkit
© Edwin Ellis, PhD (205) 394-5512
37. TM
Makes Sense Strategies Toolkit
© Edwin Ellis, PhD (205) 394-5512
MATH PROCESSES / COMPUTATIONS
SEQUENCE
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Makes Sense Strategies Toolkit
© Edwin Ellis, PhD (205) 394-5512
MATH PROCESSES / CALCULATION PROCEDURES
HIERARCHIC (Main Ideas & Details)
39. TM
Makes Sense Strategies Toolkit
© Edwin Ellis, PhD (205) 394-5512
MATH PROCESSES / CALCULATION PROCEDURES
HIERARCHIC (Main Ideas & Details)
40. TM
Makes Sense Strategies Toolkit
© Edwin Ellis, PhD (205) 394-5512
MATH PROCESSES / CALCULATION PROCEDURES
HIERARCHIC (Main Ideas & Details)
41. TM
Makes Sense Strategies Toolkit
© Edwin Ellis, PhD (205) 394-5512
MATH PROCESSES / CALCULATION PROCEDURES
HIERARCHIC (Main Ideas & Details)
42. TM
Makes Sense Strategies Toolkit
© Edwin Ellis, PhD (205) 394-5512
MATH PROCESSES / CALCULATION PROCEDURES
HIERARCHIC (Main Ideas & Details)
43. TM
Makes Sense Strategies Toolkit
© Edwin Ellis, PhD (205) 394-5512
MATH PROCESSES / CALCULATION PROCEDURES
HIERARCHIC (Main Ideas & Details)
44. TM
Makes Sense Strategies Toolkit
© Edwin Ellis, PhD (205) 394-5512
MATH PROCESSES / CALCULATION PROCEDURES
HIERARCHIC (Main Ideas & Details)
45. TM
Makes Sense Strategies Toolkit
© Edwin Ellis, PhD (205) 394-5512
MATH PROCESSES / CALCULATION PROCEDURES
HIERARCHIC (Main Ideas & Details)
46. TM
Makes Sense Strategies Toolkit
© Edwin Ellis, PhD (205) 394-5512
MATH PROCESSES / CALCULATION PROCEDURES
HIERARCHIC (Main Ideas & Details)
47. TM
Makes Sense Strategies Toolkit
© Edwin Ellis, PhD (205) 394-5512
MATH PROCESSES / CALCULATION PROCEDURES
HIERARCHIC (Main Ideas & Details)
48. TM
Makes Sense Strategies Toolkit
© Edwin Ellis, PhD (205) 394-5512
MATH PROCESSES / CALCULATION PROCEDURES
HIERARCHIC (Main Ideas & Details)
49. TM
Makes Sense Strategies Toolkit
© Edwin Ellis, PhD (205) 394-5512
MATH PROCESSES / CALCULATION PROCEDURES
HIERARCHIC (Main Ideas & Details)
50. TM
Makes Sense Strategies Toolkit
© Edwin Ellis, PhD (205) 394-5512
MATH PROCESSES / CALCULATION PROCEDURES
CAUSE / EFFECT
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Makes Sense Strategies Toolkit
© Edwin Ellis, PhD (205) 394-5512
MATH RULES
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Makes Sense Strategies Toolkit
© Edwin Ellis, PhD (205) 394-5512
MATH RULES
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Makes Sense Strategies Toolkit
© Edwin Ellis, PhD (205) 394-5512
MATH RULES