visual tools for teaching college readiness math standards
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Visual Tools for Teaching College- and Career-Readiness Standards
Edwin Ellis, Ph.D. Professor, Special Education, The University of Alabama edwinellis1@gmail.com (205) 394-5512
Craig Henden, BAMath Teacher Oakman Middle School
Elizabeth Long, MARTI Coordinator Hartselle High School
© 2013 Edwin S. Ellis All Rights Reserved edwinellis1@gmail.com www.GraphicOrganizers.com
For information about how to access Smart Visual software featured in this presentation or professional development for your school, please contact Dr. Edwin Ellis
Visual Tools for Teaching College- and Career-Readiness Standards
Edwin Ellis, Ph.D. Professor, Special Education, The University of Alabama edwinellis1@gmail.com (205) 394-5512
Craig Henden, BAMath Teacher Oakman Middle SchoolPART 3: Math Standards
Elizabeth Long, MARTI Coordinator Hartselle High School
© 2013 Edwin S. Ellis All Rights Reserved edwinellis1@gmail.com www.GraphicOrganizers.com
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
TM
Makes Sense Strategies Toolkit © Edwin Ellis, PhD (205) 394-5512
Math competencies in which visual tools are particularly useful….Math concepts / terms / definitions
Math processes / calculation procedures
Math rules
Rhombus TrapezoidMonomial Binomial Trinomial Polynomial
When to apply different systems of linear inequalitiesPythagorean Theorem – when it applies
Steps to computing unknown angles Steps to computing DOTS (Differences in Two Squares)
For example…
For example…
For example…
© 2013 Edwin S. Ellis All Rights Reserved edwinellis1@gmail.com www.GraphicOrganizers.com
© 2013 Edwin S. Ellis All Rights Reserved edwinellis1@gmail.com www.GraphicOrganizers.com
© 2013 Edwin S. Ellis All Rights Reserved edwinellis1@gmail.com www.GraphicOrganizers.com
Teacher version
Student version
© 2013 Edwin S. Ellis All Rights Reserved edwinellis1@gmail.com www.GraphicOrganizers.com
© 2013 Edwin S. Ellis All Rights Reserved edwinellis1@gmail.com www.GraphicOrganizers.com
© 2013 Edwin S. Ellis All Rights Reserved edwinellis1@gmail.com www.GraphicOrganizers.com
Teacher version
Student version
© 2013 Edwin S. Ellis All Rights Reserved edwinellis1@gmail.com www.GraphicOrganizers.com
© 2013 Edwin S. Ellis All Rights Reserved edwinellis1@gmail.com www.GraphicOrganizers.com
Adjacent Angles: linked. Share a vertex and a side.Vertical Angles: formed by intersecting lines (opposite each other).Congruent Angles: angles with equal measure.
“VERTICAL ANGLES ARE CONGRUENT”
Adjacent, Vertical,
Congruent
So what? What is important to understand about this?
Learning Geometry has 2 Main Ideas: Vocabulary and Pictures.
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.(each angle would be the “supplement” of the other)
Complements&
Supplements
Parallel Lines: in the same plane, but never intersect.
Perpendicular Lines: lines that intersect forming 4 right angles.
Parallel&
Perpendicular
Is about …
Angle Relationships
Lesson 7.1 ANGLES © 2013 Edwin S. Ellis All Rights Reserved edwinellis1@gmail.com www.GraphicOrganizers.com
So what? What is important to understand about this?
Learning Geometry has 2 Main Ideas: Vocabulary and Pictures.
Lesson 7.2 - ANGLES Is about …
Identifying and Classifying Angles
Main idea
Identifying Angles
Angle – formed by two rays or segments with a common endpoint
Vertex – the common endpoint (vertices)
Acute – between 0 and 90 degrees
Right – 90 degrees
Obtuse – between 90 and 180 degrees
Straight – 180 degrees
Main idea
Finding Complements and Supplements
Complementary Angles – two angles whose sum equals 90 degrees.
(each angle would be the “complement” of the other)
Supplementary Angles – two angles whose sum equals 180 degrees.
(each angle would be the “supplement” of the other)
Main idea
Finding Angle Measures(using angle relationships)
Adjacent Angles – linked, share a side and a vertex
Vertical Angles – (formed by intersecting lines) opposite from each other
Congruent Angles – angles with equal measures
BIG PHRASE:
“Vertical Angles are Congruent!!”
© 2013 Edwin S. Ellis All Rights Reserved edwinellis1@gmail.com www.GraphicOrganizers.com
© 2013 Edwin S. Ellis All Rights Reserved edwinellis1@gmail.com www.GraphicOrganizers.com
Don’t Forget About The Test Next Wednesday
will be about
Order of Operations, Distributive Property, Mean, Median, Mode, and Range
Wednesday, August 29th
Order of Operations
1) Work Grouping Symbols – ( ), [ ], fractions
2) Work out exponents
3) Multiply or Divide
4) Add or Subtract
Distributive Property
9(4+5) = 9(4) + 9(5)(8-2)5 = 5(8) – 5(2)
a(b+c) = ab + ac(b-c)a = ab - ac
Mean
The AVERAGE woman is mean….
-add up all of the numbers-divide by the number of numbers
Median
The median of a highway is the MIDDLE of the road….
-put the numbers in order-if there are two middle numbers, find their average-if there is only one, it is the median
Mode
MOST = Mode….
-the number or numbers that repeat the most times (can be more than one mode or no mode)
Range
The difference in the largest and smallest numbers in the data….
-once in order, subtract the first number from the last
© 2013 Edwin S. Ellis All Rights Reserved edwinellis1@gmail.com www.GraphicOrganizers.com
Volume
Ex. 1:
Ex. 2:
Prisms/Cylinders
V = Bh
B is the area of the base.
Ex. 5:
Ex. 6:
SpheresV = 4πr³
3
Ex. 3:
Ex. 4:
Pyramids/ConesV = 1Bh
3B is the area of the base.
© 2013 Edwin S. Ellis All Rights Reserved edwinellis1@gmail.com www.GraphicOrganizers.com
© 2013 Edwin S. Ellis All Rights Reserved edwinellis1@gmail.com www.GraphicOrganizers.com
TM
Makes Sense Strategies Toolkit © Edwin Ellis, PhD (205) 394-5512
MATH CONCEPTS
I know this word. It means…
I have never seen or heard this word before
I have seen or heard this word before, but I'm not sure what it means
CCS: A-CED 1, A-CED 3Systems of equations and inequalities
WORDInequalityGreater thanLess thanEqual toGraph (verb)SolutionComplementNotationIntegersAll real #s
© 2013 Edwin S. Ellis All Rights Reserved edwinellis1@gmail.com www.GraphicOrganizers.com
TM
Makes Sense Strategies Toolkit © Edwin Ellis, PhD (205) 394-5512
MATH CONCEPTSHIERARCHIC (Main Ideas & Details)
TM
Makes Sense Strategies Toolkit © Edwin Ellis, PhD (205) 394-5512
MATH CONCEPTSHIERARCHIC (Main Ideas & Details)
TM
Makes Sense Strategies Toolkit © Edwin Ellis, PhD (205) 394-5512
MATH CONCEPTSHIERARCHIC (Main Ideas & Details)
TM
Makes Sense Strategies Toolkit © Edwin Ellis, PhD (205) 394-5512
MATH CONCEPTSHIERARCHIC (Main Ideas & Details)
TM
Makes Sense Strategies Toolkit © Edwin Ellis, PhD (205) 394-5512
MATH CONCEPTSHIERARCHIC (Main Ideas & Details)
TM
Makes Sense Strategies Toolkit © Edwin Ellis, PhD (205) 394-5512
MATH CONCEPTSHIERARCHIC (Main Ideas & Details)
TM
Makes Sense Strategies Toolkit © Edwin Ellis, PhD (205) 394-5512
MATH CONCEPTSHIERARCHIC (Main Ideas & Details)
TM
Makes Sense Strategies Toolkit © Edwin Ellis, PhD (205) 394-5512
MATH CONCEPTSHIERARCHIC (Main Ideas & Details)
TM
Makes Sense Strategies Toolkit © Edwin Ellis, PhD (205) 394-5512
COMPARE / CONTRAST
ConclusionsMATH CONCEPTS
TM
Makes Sense Strategies Toolkit © Edwin Ellis, PhD (205) 394-5512
COMPARE / CONTRAST
Double ConclusionsMATH CONCEPTS
TM
Makes Sense Strategies Toolkit © Edwin Ellis, PhD (205) 394-5512
HIERARCHIC (Main Ideas & Details)MATH PROCESSES / CALCULATION PROCEDURES
TM
Makes Sense Strategies Toolkit © Edwin Ellis, PhD (205) 394-5512
MATH CONCEPTSHIERARCHIC (Main Ideas & Details)
TM
Makes Sense Strategies Toolkit © Edwin Ellis, PhD (205) 394-5512
TM
Makes Sense Strategies Toolkit © Edwin Ellis, PhD (205) 394-5512
SEQUENCEMATH PROCESSES / COMPUTATIONS
TM
Makes Sense Strategies Toolkit © Edwin Ellis, PhD (205) 394-5512
MATH PROCESSES / CALCULATION PROCEDURES HIERARCHIC (Main Ideas & Details)
TM
Makes Sense Strategies Toolkit © Edwin Ellis, PhD (205) 394-5512
HIERARCHIC (Main Ideas & Details)MATH PROCESSES / CALCULATION PROCEDURES
TM
Makes Sense Strategies Toolkit © Edwin Ellis, PhD (205) 394-5512
HIERARCHIC (Main Ideas & Details)MATH PROCESSES / CALCULATION PROCEDURES
TM
Makes Sense Strategies Toolkit © Edwin Ellis, PhD (205) 394-5512
HIERARCHIC (Main Ideas & Details)MATH PROCESSES / CALCULATION PROCEDURES
TM
Makes Sense Strategies Toolkit © Edwin Ellis, PhD (205) 394-5512
HIERARCHIC (Main Ideas & Details)MATH PROCESSES / CALCULATION PROCEDURES
TM
Makes Sense Strategies Toolkit © Edwin Ellis, PhD (205) 394-5512
HIERARCHIC (Main Ideas & Details)MATH PROCESSES / CALCULATION PROCEDURES
TM
Makes Sense Strategies Toolkit © Edwin Ellis, PhD (205) 394-5512
HIERARCHIC (Main Ideas & Details)MATH PROCESSES / CALCULATION PROCEDURES
TM
Makes Sense Strategies Toolkit © Edwin Ellis, PhD (205) 394-5512
HIERARCHIC (Main Ideas & Details)MATH PROCESSES / CALCULATION PROCEDURES
TM
Makes Sense Strategies Toolkit © Edwin Ellis, PhD (205) 394-5512
HIERARCHIC (Main Ideas & Details)MATH PROCESSES / CALCULATION PROCEDURES
TM
Makes Sense Strategies Toolkit © Edwin Ellis, PhD (205) 394-5512
HIERARCHIC (Main Ideas & Details)MATH PROCESSES / CALCULATION PROCEDURES
TM
Makes Sense Strategies Toolkit © Edwin Ellis, PhD (205) 394-5512
HIERARCHIC (Main Ideas & Details)MATH PROCESSES / CALCULATION PROCEDURES
TM
Makes Sense Strategies Toolkit © Edwin Ellis, PhD (205) 394-5512
HIERARCHIC (Main Ideas & Details)MATH PROCESSES / CALCULATION PROCEDURES
TM
Makes Sense Strategies Toolkit © Edwin Ellis, PhD (205) 394-5512
CAUSE / EFFECTMATH PROCESSES / CALCULATION PROCEDURES
TM
Makes Sense Strategies Toolkit © Edwin Ellis, PhD (205) 394-5512
MATH RULES
TM
Makes Sense Strategies Toolkit © Edwin Ellis, PhD (205) 394-5512
MATH RULES
TM
Makes Sense Strategies Toolkit © Edwin Ellis, PhD (205) 394-5512
MATH RULES
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