visual tools for teaching college readiness math standards

Visual Tools for Teaching College- and Career-Readiness Standards

Edwin Ellis, Ph.D. Professor, Special Education, The University of Alabama [email protected] (205) 394-5512

Craig Henden, BAMath Teacher Oakman Middle School

Elizabeth Long, MARTI Coordinator Hartselle High School

© 2013 Edwin S. Ellis All Rights Reserved [email protected] 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 [email protected] (205) 394-5512

Craig Henden, BAMath Teacher Oakman Middle SchoolPART 3: Math Standards

Elizabeth Long, MARTI Coordinator Hartselle High School


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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


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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…


Teacher version

Student version


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 [email protected] 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!!”


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


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.


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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


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MATH CONCEPTSHIERARCHIC (Main Ideas & Details)

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COMPARE / CONTRAST

ConclusionsMATH CONCEPTS

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COMPARE / CONTRAST

Double ConclusionsMATH CONCEPTS

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HIERARCHIC (Main Ideas & Details)MATH PROCESSES / CALCULATION PROCEDURES

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MATH CONCEPTSHIERARCHIC (Main Ideas & Details)

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SEQUENCEMATH PROCESSES / COMPUTATIONS

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MATH PROCESSES / CALCULATION PROCEDURES HIERARCHIC (Main Ideas & Details)

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HIERARCHIC (Main Ideas & Details)MATH PROCESSES / CALCULATION PROCEDURES

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CAUSE / EFFECTMATH PROCESSES / CALCULATION PROCEDURES

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MATH RULES

visual tools for teaching college readiness math standards

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