2018
Teacher Resource
Guide for
Alternate Math
Elements I & II
Effective Date: 2018-2019 School Year
Page | 2 13-Jun-18
2018
Teacher Resource Guide for
Alternate Math Elements I & II
Carey M. Wright, EdD, State Superintendent of Education
Kim S. Benton, EdD, Chief Academic Officer
Gretchen Cagle, State Director of Special Education
Margaret Ellmer, PhD, Bureau Director, Office of Special Education
Sharon Strong Coon, Office Director, Office of Special Education
Bobby L. Richardson, Office Director, Office of Special Education
Allison Paige Pigott, Instructional Support Specialist, Office of Special Education
Page | 3 13-Jun-18
Mississippi Department of Education
Post Office Box 771
Jackson, Mississippi
39205-0771
Office of Special Education
601-359-3498
www.mdek12.org/ose
The Mississippi State Board of Education, the Mississippi Department of Education, the
Mississippi School for the Arts, the Mississippi School for the Blind, the Mississippi School for the
Deaf, and the Mississippi School for Mathematics and Science do not discriminate on the basis of
race, sex, color, religion, national origin, age, or disability in the provision of educational programs
and services or employment opportunities and benefits. The following office has been designated to
handle inquiries and complaints regarding the nondiscrimination policies of the above-mentioned
entities:
Director, Office of Human Resources
Mississippi Department of Education
Page | 4 13-Jun-18
Table of Contents
Acknowledgements .......................................................................................................................... 5
Introduction ..................................................................................................................................... 7
Support Documents and Resources ................................................................................................. 8
Structure of the Teacher Resource Guide for Alternate Math Elements I & II ................................. 9
Structure of the Teacher Resource Guide for Alternate Math Elements I & II (Graphic) ............... 10
Levels of Support (LOS) ................................................................................................................ 11
Teacher Resource Guide for Alternate Math Elements I & II ........................................................ 12
APPENDIX A: Additional Resources ............................................................................................ 25
APPENDIX B: Glossary ............................................................................................................... 26
References ...................................................................................................................................... 29
Page | 5 13-Jun-18
Acknowledgements
The Mississippi Department of Education gratefully acknowledges the hard work of the following
individuals for their involvement in developing the Teacher Resource Guide Alternate Math Elements I &
II.
Gretchen Cagle Mississippi Department of Education
Dayna Clark Pass Christian School District
Sharon Strong Coon Mississippi Department of Education
Alicia Dunigan Senatobia School District
Margaret Ellmer, PhD Mississippi Department of Education
Doris Flettrich Pass Christian School District
Kellie Fondren Mississippi State University
Pasteia Garth Nettleton School District
Madelyn Harris Mississippi Department of Education
Jordan Helton Madison School District
Jan Houston Starkville Oktibbeha School District
Teressa Hovious University of Mississippi
Karen John Petal School District
Lydia Lankford Madison School District
Misty McMahon Ocean Springs School District
Roslyn Miller, PhD Mississippi State University
Myra Pannell, PhD Mississippi State University
Allison Paige Pigott Mississippi Department of Education
Bobby L. Richardson Mississippi Department of Education
Amye Rowan Pearl School District
Denise Sibley Mississippi State University
Connie Smith Laurel School District
Susan Stampley Senatobia School District
Elizabeth Testa Vicksburg-Warren School District
Jaicia Thomas Lamar County School District
Stacey Todd Ocean Springs School District
Tiffany Withers Rankin County School District
Page | 6 13-Jun-18
The Standards:
The Dynamic Learning Maps Essential Elements are copyrighted by the University of Kansas
Center for Research. They are based substantially on an earlier version that was copyrighted by
Edvantia. The Essential Elements may be reprinted or used, with appropriate citation, in part or
entirety by anyone in the DLM Consortium states. However, no text in the document may be
modified. Comments, explanations, or other additional materials may be interspersed as long as they
clearly indicate that they are not part of the Essential Elements and are not the opinions of the DLM
Consortium or the University of Kansas Center for Research. Others may use the contents with
written permission from the Center for Educational Testing and Evaluation. Appropriate citation
follows.
Dynamic Learning Maps Consortium. (2013). Dynamic Learning Maps Essential Elements for Mathematics.
Lawrence, KS: University of Kansas.
Remaining Material in the Teacher Resource Guide:
The remaining materials in the teacher resource guide (performance objectives, I can statements, real world
connections, vocabulary, and resources) were developed through a collaboration of Mississippi teachers,
administrators, MDE Office of Special Education staff, and Mississippi State University Research and
Curriculum Unit staff. The information is not part of the Essential Elements and are not the opinions of the
DLM Consortium or the University of Kansas Center for Research.
Page | 7 13-Jun-18
Introduction
Mission Statement
The Mississippi Department of Education (MDE) is dedicated to student success, which includes
improving student achievement in mathematics and establishing communication skills within a
technological environment. The Mississippi Alternate Academic Achievement Standards (MS AAAS) for
Math Elements I & II (DLM Essential Elements) provide a consistent, clear understanding of what
students are expected to know and be able to do by the end of the course. The purpose of the MS
AAAS for Math Elements I & II (DLM Essential Elements) is to build a bridge from the content in the
general education mathematics framework to academic expectations for students with the most
significant cognitive disabilities. The standards are designed to be rigorous and relevant to the real
world, reflecting the knowledge and skills that students need for success in postsecondary settings.
Purpose
In an effort to closely align instruction for students with significant cognitive disabilities who are
progressing toward postsecondary settings, the MS AAAS for Math Elements I & II (DLM Essential
Elements) include course-specific standards for mathematics. This document is designed to provide a
resource for 9-12 special education teachers with a basis for curriculum development and
instructional delivery.
The Teacher Resource Guide for Alternate Math Elements I & II contains prioritized content, which is
presented as a matrix to show the continuum of the concept across complexity levels. The matrix
shows varying access points to the prioritized content. A student’s progression through content
contained in the matrix is intended to be fluid. It is not the intent, nor should it be practice, for a
student to be exposed to content in a straight vertical line through one of the columns. Every
student, regardless of disability, comes to the learning environment with a different set of prior
knowledge and experience. For this reason, a student may be able to access some content from the
middle complexity level and access other concepts at the more complex level. Teachers should
evaluate a student’s ability in relation to the content and select the entry point based on that
evaluation. Students should not be locked into receiving exposure to all content at the same entry
point.
Page | 8 13-Jun-18
Support Documents and Resources
The MDE Office of Special Education aims to provide local districts, schools, and teachers
supporting documents to construct standards-based instruction and lessons, allowing them to
customize content and delivery methods to fit each student’s needs. The teacher resource guide
includes suggested resources, instructional strategies, sample lessons, and activities. Additional
sample activities and resources for selected standards may be added; this shall be a living document
with ongoing updates based on educator feedback. The intent of these resources is to assist teachers
in linking their instruction to the prioritized content. The teacher resource guide includes activity
adaptations for students with a varying range of abilities within the classroom. The activities and
adaptations provided are intended to serve as a model of how students participating in the
Mississippi Academic Assessment Program-Alternate (MAAP-A) may receive academic instruction
in mathematics. There are many ways in which skills and concepts can be incorporated based on
student’s individual learning styles and needs. Professional development efforts are aligned to the
MS AAAS for Math Elements I & II (DLM Essential Elements) and delivered in accord with teacher
resources to help expand expertise in delivering student-centered lessons.
Page | 9 13-Jun-18
Structure of the Teacher Resource Guide for Alternate Math Elements I & II
Mississippi Alternate Academic Achievement Standards for Math Elements I & II (DLM Essential Elements): A
general statement of what students with significant cognitive disabilities should know and be able to
do because of instruction.
Performance Objectives: Statements that describe in precise, measurable terms what learners will be
able to do at the end of an instructional sequence.
I Can Statement(s): Includes the Performance Objective(s) as the Most Complex and scaffolds the
performance objectives two additional levels (B) and (C) to Least Complex. This matrix demonstrates
the continuum of the concept across complexity levels. The purpose is to assist teachers in
modifying to meet the unique diverse needs of learners with significant cognitive disabilities.
Real-World Connections: One way to facilitate learning that is meaningful to students and prepares
them for their professional lives outside of school. When teachers move beyond textbook or
curricular examples and connect content learned in the classroom to real people, places and events,
students are able to see a greater relevance to their learning. Real-world connections are used to help
students see that learning is not confined to the school, allow them to apply knowledge and skills in
real-world situations, and personalize learning to increase and sustain student engagement.
Vocabulary: Includes a list of difficult or unfamiliar words.
Resources: Includes suggested resources, instructional strategies, lessons, and activities. Additional
sample activities and resources for selected standards may be added; this shall be a living document
with ongoing updates based on educator feedback. The intent of these activities is to assist teachers
in linking their instruction to the prioritized content.
Page | 10 13-Jun-18
Structure of the Teacher Resource Guide for Alternate Math Elements I & II (Graphic)
Vocabulary
Mississippi Alternate Academic
Achievement Standards for Math
Elements I & II (DLM Essential
Elements)
Performance Objective(s)
Resources
I Can Statements
Page | 11 13-Jun-18
Levels of Support (LOS)
Students with significant cognitive disabilities require varying LOS to engage in academic content.
The goal is to move the student along the continuum of assistance toward independence by
decreasing the LOS provided and increasing student accuracy within the context of content to
demonstrate progress.
The following chart describes the continuum of LOS. Appropriate LOS are important to increase
student engagement and student independence and to track student achievement and progress.
Level of
Assistance
Definition
Example
Non-Example
Non-
Engagement (N)
The student requires assistance
from the teacher to initiate,
engage, or perform; however, the
student actively refuses or is
unable to accept teacher
assistance.
The student resists the teacher’s
physical assistance toward the correct
answer.
The student does not look at the
activity.
Physical
Assistance (P)
The student requires physical
contact from the teacher to
initiate, engage, or perform.
The teacher physically moves the
student’s hand to the correct answer.
The teacher taps the correct answer
and expects the student to touch
where he/she tapped.
Gestural
Assistance (G)
The student requires the teacher
to point to the specific answer.
When presenting a choice of three
pictures and asking the student which
picture is a triangle, the teacher will
point to or tap on the correct picture
to prompt the student to indicate
that picture.
The teacher moves the student’s
hand to gesture toward the right
answer.
Verbal
Assistance (V)
The student requires the teacher
to verbally provide the correct
answer to a specific item.
The teacher says, “Remember, the
main character was George. Point to
the picture of the main character.”
The teacher says “Who is the main
character?” without providing the
information verbally.
Model
Assistance (M)
The student requires the teacher
to model a similar
problem/opportunity and answer
prior to performance.
The teacher models one-to-one
correspondence using manipulatives
and then asks the student to perform a
similar item.
The teacher completes the exact
same activity as the student is
expected to perform.
Independent (I)
The student requires no assistance
to initiate, engage, or perform.
The student may still require other
supports and accommodations to
meaningfully engage in the
content but does not require
assistance to participate and
respond.
The teacher asks the student, “Who is
the main character of the book?” and
the student meaningfully responds
without any prompting or assistance.
The teacher asks the student, “Who
is the main character?” and points to
the picture of the main character.
Page | 12 13-Jun-18
Teacher Resource Guide for Alternate Math Elements I & II
COURSE: Alternate Math Elements I and II
DOMAIN: Statistics and Probability – Making Inferences and Justifying Conclusions
CLUSTER: Understand and evaluate random processes underlying statistical experiments.
Page | 13 13-Jun-18
Standard:
EE.N-CN.2.a. Use the commutative, associative, and distributive
properties to add, subtract, and multiply whole numbers.
Performance Objectives:
EE.N-CN.2.a.1 Apply the operations of addition, subtraction, and
multiplication in real-world problems using money.
EE.N-CN.2.a.2 Use the operations of addition, subtraction, and
multiplication with whole numbers less than 20.
I Can Statements
MOST COMPLEX LEAST COMPLEX
EE.N-CN.2.a.1 (A) Apply the operations of
addition, subtraction, and multiplication in real-
world problems using money.
EE.N-CN.2.a.1 (B) Identify when to add,
subtract, or multiply using money in real-world
problems.
EE.N-CN.2.a.1 (C) Identify coins and bills and
their value.
EE.N-CN.2.a.2 (A) Use the operations of
addition, subtraction, and multiplication with
whole numbers less than 20.
EE.N-CN.2.a.2 (B) Use the correct operation
(i.e., addition, subtraction, or multiplication) for
numbers less than 20 in given problems and
manipulatives.
EE.N-CN.2.a.2 (C) Recognize numbers to 20.
Real-World Connections:
• Shopping, such as totaling single items and totaling identical items or
groups of items
• Finding totals of items or money by grouping or ordering in different
ways
• Job skills
Vocabulary:
• Add
• Subtract
• Multiply
• Group
• Sort
• Commutative
• Associative
• Distributive
Resources:
• Purplemath -- Associative, Commutative, and Distributive Properties
• The World of Math Online -- Properties of Integers
• Khan Academy -- Distributive Property Over Addition
• Menu Math: Teaching Algebra to Everyone [Free]
• Teachers Pay Teachers -- Area Multiplication: Teaching Multiplication with Understanding
• Horses, Pigs, and Cows -- [PDF for Purchase, but free teaching videos and sample worksheet on https://www.tttpress.com/free-videos.html]
• VNPS -- Student thinking / The learning Kaleidoscope -- MTBoS Mod: 3 Act Edition
• Robert Kaplinsky -- Description of Calories / Robert Kaplinsky -- Collected Money to Buy a Game
COURSE: Alternate Math Elements I and II
DOMAIN: Statistics and Probability – Making Inferences and Justifying Conclusions
CLUSTER: Understand and evaluate random processes underlying statistical experiments.
Page | 14 13-Jun-18
Standard:
EE.N-CN.2.b. Solve real-world problems involving addition and
subtraction of decimals, using models when needed.
Performance Objectives:
EE.N-CN.2.b.1 Use the operations of addition and subtraction up to the
tenths place with decimals
EE.N-CN.2.b.2 Use the operations of addition and subtraction with
decimals in real‐world situations
EE.N-CN.2.b.3 Apply the operations of addition and subtraction in real-
world situations
I Can Statements
MOST COMPLEX LEAST COMPLEX
EE.N-CN.2.b.1 (A) Use the operations of
addition and subtraction up to the tenths place
with decimals.
EE.N-CN.2.b.1 (B) Identify numbers in the
tenths and hundredths place.
EE.N-CN.2.b.1 (C) Identify decimal numbers.
EE.N-CN.2.b.2 (A) Use the operations of
addition and subtraction with decimals in real‐
world situations.
EE.N-CN.2.b.2 (B) Add and subtract with
money.
EE.N-CN.2.b.2 (C) Add and subtract decimal
numbers.
EE.N-CN.2.b.3 (A) Apply the operations of
addition and subtraction in real-world situations.
EE.N-CN.2.b.3 (B) Solve real-world problems
involving addition and subtraction of decimals.
EE.N-CN.2.b.3 (C) Model real-world problems
involving addition and subtraction of decimals.
Real-World Connections:
• Money
• Budgeting
• Meal preparation
• Shopping
Vocabulary:
• Decimals
• Tenths
• Hundredths
• Place value
• Add
• Subtract
Resources:
• LearnZillion -- Addition and Subtraction Involving Decimals
• Alabama Learning Exchange -- Lesson Plan
• Bluehost -- Math Worksheets, Lessons, Charts, Learning, Equations, Formulas and Tricks
• Menu Math: Teaching Algebra to Everyone [Free]
• Horses, Pigs, and Cows -- [PDF for Purchase, but free teaching videos on https://www.tttpress.com/free-videos.html ]
• Robert Kaplinsky -- Chinese Food Coupon / Pennies value
• Robert Kaplinsky -- Coins Worth / Collected Money to Buy a Game / Monthly or Annual Payments
• VNPS -- Student Thinking
• The Learning Kaleidoscope -- MTBoS Mod: 3 Act Edition
COURSE: Alternate Math Elements I and II
DOMAIN: Statistics and Probability – Making Inferences and Justifying Conclusions
CLUSTER: Understand and evaluate random processes underlying statistical experiments.
Page | 15 13-Jun-18
Standard:
EE.N-CN.2.c. Solve real-world problems involving multiplication of
decimals and whole numbers, using models when needed.
Performance Objectives:
EE.N-CN.2.c.1 Use the operation of multiplication with decimals and
whole numbers in real-world situations.
EE.N-CN.2.c.2 Use the operation of multiplication with decimals up to
the hundredths place
I Can Statements
MOST COMPLEX LEAST COMPLEX
EE.N-CN.2.c.1 (A) Use the operation of
multiplication with decimals and whole numbers
in real-world situations.
EE.N-CN.2.c.1 (B) Follow multiplication
procedures to multiply decimals.
EE.N-CN.2.c.1 (C) Identify decimal numbers.
EE.N-CN.2.c.2 (A) Use the operation of
multiplication with decimals up to the hundredths
place.
EE.N-CN.2.c.2 (B) Given a real-world problem
and a model, multiply with decimals to the
hundredths position.
EE.N-CN.2.c.2 (C) Identify tenth and
hundredth decimal place values.
Real-World Connections:
• Money
• Meal preparation
• Shopping
• Budgeting
Vocabulary:
• Decimals
• Tenths
• Hundredths
• Place Value
• Multiply
Resources:
• CK-12 Multiplication and Division of Decimals
• Margaret B. Pollard Middle -- Pollard Announcements
• Newfoundland Multiplication and Division of Decimals
• Menu Math: Teaching Algebra to Everyone [Free]
• Optical Art Task
• Robert Kaplinsky -- Chinese Coupon / Pennies value
• Robert Kaplinsky -- Coins Worth / Collected Money to Buy a Game
• VNPS - Student Thinking / The Learning Kaleidoscope -- MTBoS Mod: 3 Act Edition
COURSE: Alternate Math Elements I and II
DOMAIN: Statistics and Probability – Making Inferences and Justifying Conclusions
CLUSTER: Understand and evaluate random processes underlying statistical experiments.
Page | 16 13-Jun-18
Standard:
EE.S-IC.1-2. Determine the likelihood of an event occurring when the
outcomes are equally likely to occur.
Performance Objectives:
EE.S-IC.1-2.a Determine the likelihood of an event occurring when the
outcomes are not equally likely to occur.
EE.S-IC.1-2.b Determine the likelihood of an event occurring when the
outcomes are equally likely to occur.
EE.S-IC.1-2.c Determine the possible outcomes of an event occurring.
I Can Statements
MOST COMPLEX LEAST COMPLEX
EE.S-IC.1-2.a (A) Determine the likelihood of
an event occurring when the outcomes are not
equally likely to occur.
EE.S-IC.1-2.c (B) Given an event and the
possibilities, identify the outcome that is most
likely to occur.
EE.S-IC.1-2.c (C) Given an event and its
outcome, identify the outcome.
EE.S-IC.1-2.b (A) Determine the likelihood of
an event occurring when the outcomes are
equally likely to occur.
EE.S-IC.1-2.b (B) Using a graphic organizer or
chart, demonstrate understanding of the
likelihood of an event occurring when the
outcomes are equally likely to occur.
EE.S-IC.1-2.b (C) Given an event in which the
outcomes are equally likely to occur, identify the
outcome.
EE.S-IC.1-2.c (C) Determine the possible
outcomes of an event occurring.
EE.S-IC.1-2.c (B) Using a graphic organizer or
chart, identify the possible outcomes of an event
occurring.
EE.S-IC.1-2.c (C) Given an event, identify the
outcome of the event.
Real-World Connections:
• Random selection
• Games
• Populations
• Samples
Vocabulary:
• Probability
• Event
• Occur
• Outcome
• Population
• Sample
Resources:
• Math Goodies
• IXL Experimental Probability
• Stat Trek Probability
COURSE: Alternate Math Elements I and II
DOMAIN: Statistics and Probability – Making Inferences and Justifying Conclusions
CLUSTER: Understand independence and conditional probability, and use them to interpret data.
Page | 17 13-Jun-18
Standard:
EE.S-CP.1-5. Identify when events are independent or dependent.
Performance Objectives:
EE.S-CP.1-5.a Find the probability of an event after another event has
occurred.
EE.S-CP.1-5.b Identify when events are independent or dependent.
I Can Statements
MOST COMPLEX LEAST COMPLEX
EE.S-CP.1-5.a (A) Find the probability of an
event after another event has occurred.
EE.S-CP.1-5.a (B) Using a graphic organizer or
chart, demonstrate understanding of the
likelihood of an event after another event has
occurred.
EE.S-CP.1-5.a (C) Given a choice of
probabilities, identify the probability of an event
after another event has occurred.
EE.S-CP.1-5.b (A) Identify when events are
independent or dependent.
EE.S-CP.1-5.b (B) Identify the outcomes of an
event.
EE.S-CP.1-5.b (C) Determine which event
occurs first in a sequence.
Real-World Connections:
• Counting
• Risk management
• Risk analysis
Vocabulary:
• Probability
• Event
• Occur
• Outcome
• Replace
• Independent
• Dependent
Resources:
• Teaching Channel – Grade6 – Math Probability
• Probability of Independent and Dependent Events
• Lesson – Introduction to Probability and Difference Between Independent and Dependent Events
• Robert Kaplinsky – Stronger Passwords
COURSE: Alternate Math Elements I and II
DOMAIN: Geometry – Congruence
CLUSTER: Experiment with transformation in the plane.
Page | 18 13-Jun-18
Standard:
EE.G-CO.1. Know the attributes of perpendicular lines, parallel lines, and
line segments; angles; and circles.
Performance Objectives:
EE.G-CO.1.a Name two attributes for angles and circles.
EE.G-CO.1.b Draw perpendicular lines, parallel lines, and line segments.
I Can Statements
MOST COMPLEX LEAST COMPLEX
EE.G-CO.1.a (A) Name two attributes for
angles and circles.
EE.G-CO.1.a (B) Given a list, choose two
attributes of angles and circles.
EE.G-CO.1.a (C) Choose the correct picture to
identify an angle and a circle.
EE.G-CO.1.b (A) Draw perpendicular lines,
parallel lines, and line segments.
EE.G-CO.1.b (B) From an array, choose a
perpendicular line, parallel line, and line segment.
EE.G-CO.1.b (C) Choose an example of a
perpendicular line, parallel line, and line segment.
Real-World Connections:
• Street directions, bus routes, maps
• Clockwise and counter-clockwise directions
• Architecture and drafting
• Design
• Construction
• Drawing
• Career Preparation
Vocabulary:
• Perpendicular
• Parallel
• Line
• Segment
• Angle
• Circle
Resources:
• GeoGebra -- Equations, Graph Functions, Data analysis, and 3D Math
• Gizmos -- Simulations
• Math Solutions – Fourth- and Fifth-Grade Lesson
• Optical Art Task
COURSE: Alternate Math Elements I and II
DOMAIN: Geometry – Congruence
CLUSTER: Experiment with transformation in the plane.
Page | 19 13-Jun-18
Standard:
EE.G-CO.4-5. Given a geometric figure and a rotation, reflection, or
translation of that figure, identify the components of the two figures that
are congruent.
Performance Objectives:
EE.G-CO.4-5.a Given geometric figures, identify two figures that are
congruent.
EE.G-CO.4-5.b Identify rotations, reflections, and slides of a geometric
figure.
I Can Statements
MOST COMPLEX LEAST COMPLEX
EE.G-CO.4-5.a (A) Given geometric figures,
identify two figures that are congruent.
EE.G-CO.4-5.a (B) From an array of figures,
choose two figures that are congruent.
EE.G-CO.4-5.a (C) Choose a picture of a
geometric figure.
EE.G-CO.4-5.b (A) Identify rotations,
reflections, and slides of a geometric figure.
EE.G-CO.4-5.b (B) From an array of figures,
choose examples of rotations, reflections, and
slides.
EE.G-CO.4-5.b (C) Attend to movement,
demonstrating rotations, reflections, and slides.
Real-World Connections:
• Mirror image
• Graphic design
• Career preparation
Vocabulary:
• Rotation
• Reflection
• Slide
• Translation
• Congruent
Resources:
• EduGains -- Guides to Effective Instruction Math Grades 4-6 Geometry and Spatial Sense
• Desmos -- Des-Patterns, Transformation Golf: Rigid Motion
• Youcubed -- Optical Art Task
COURSE: Alternate Math Elements I and II
DOMAIN: Geometry – Congruence
CLUSTER: Understand congruence in terms of rigid motions.
Page | 20 13-Jun-18
Standard:
EE.G-CO.6-8. Identify corresponding congruent and similar parts of
shapes.
Performance Objectives:
EE.G-CO.6-8.a Identify parts of shapes (e.g., sides, angles) and the
corresponding (the same) congruent parts.
I Can Statements
MOST COMPLEX LEAST COMPLEX
EE.G-CO.6-8.a (A) Identify parts of shapes
(e.g., sides, angles) and the corresponding (the
same) congruent parts.
EE.G-CO.6-8.a (B) Given a model, locate a
side, angle, and congruent parts of a shape.
EE.G-CO.6-8.a (C) Choose a picture of a
geometric shape with angles.
Real-World Connections:
• Sorting
• Drawing
• Architecture and drafting
• Design
• Construction
Vocabulary:
• Congruent
• Corresponding
• Sides
• Angles
Resources:
• Inspire K12 Lesson Plans
• Explore Learning
• Math Solutions -- Line Segments
COURSE: Alternate Math Elements I and II
DOMAIN: Geometry – Expressing Geometric Properties with Equations
CLUSTER: Use coordinates to prove simple geometric theorems algebraically.
Page | 21 13-Jun-18
Standard:
EE.G-GPE.7 Find perimeters and areas of squares to solve real-world
problems.
Performance Objectives:
EE.G-GPE.7.a Find perimeter of squares and rectangles to solve real-
world problems.
EE.G-GPE.7.b Find the area of squares and rectangles to solve real-world
problems.
I Can Statements
MOST COMPLEX LEAST COMPLEX
EE.G-GPE.7.a (A) Find perimeter of squares
and rectangles to solve real-world problems.
EE.G-GPE.7.a (B) Given the formula, find the
perimeter of squares and rectangles.
EE.G-GPE.7.a (C) Identify a square and
rectangle.
EE.G-GPE.7.b (A) Find the area of squares and
rectangles to solve real-world problems.
EE.G-GPE.7.b (B) Find the area of a rectangle
of square by counting on a grid.
EE.G-GPE.7.b (C) Identify the interior space of
a rectangle or square.
Real-World Connections:
• Measure lengths and spaces
• Drafting and architecture
• Design
• Drawing
Vocabulary:
• Perimeter
• Area
• Square
• Rectangle
• Length
• Space
Resources:
• CPM Area and Perimeter Tiles
• LearnZillion -- Rectangles (Perimeters With Different Area)
• IXL -- Algebra1: Perimeter
• Robert Kaplinsky -- Paint a Handball Wall
COURSE: Alternate Math Elements I and II
DOMAIN: Geometry – Geometric Measurement and Dimension
CLUSTER: Explain volume formulas, and use them to solve problems.
Page | 22 13-Jun-18
Standard:
EE.G-GMD.1-3. Make a prediction about the volume of a container, the
area of a figure, and the perimeter of a figure, and then test the prediction
using formulas or models.
Performance Objectives:
EE.G-GMD.1-3.a Make a prediction about the volume of a container and
test it to solve real-world problems.
EE.G-GMD.1-3.b Make a prediction about the area of a figure and test it
to solve real-world problems.
EE.G-GMD.1-3.c Make a prediction about the perimeter of a figure and
test it to solve real-world problems.
I Can Statements
MOST COMPLEX LEAST COMPLEX
EE.G-GMD.1-3.a (A) Make a prediction about
the volume of a container and test it to solve
real-world problems.
EE.G-GMD.1-3.a (B) Determine the volume
of a container using a grid.
EE.G-GMD.1-3.a (C) Choose the container
with the largest volume capacity.
EE.G-GMD.1-3.b (A) Make a prediction about
the area of a figure and test it to solve real-world
problems.
EE.G-GMD.1-3.b (B) Determine the area of a
figure using a grid.
EE.G-GMD.1-3.b (C) Choose the shape with
the largest area.
EE.G-GMD.1-3.c (A) Make a prediction about
the perimeter of a figure and test it to solve real-
world problems.
EE.G-GMD.1-3.c (B) Determine the perimeter
of a figure using a grid.
EE.G-GMD.1-3.c (C) Choose the shape with
the largest perimeter.
Real-World Connections:
• Measure lengths and spaces
• Drafting and architecture
• Design
• Drawing
• Measurement
• Weight
• Volume
• Counting
Vocabulary:
• Perimeter
• Area
• Volume
• Prediction
• Grid
• Formula
Resources:
• Gizmos: Balancing Blocks / Perimeters and Areas of Similar Figures
• Gizmos: Surface and Lateral Areas of Prisms and Cylinders / Prisms and Cylinders
• Teacher to Teacher Press: 3-D Name Project
• Robert Kaplinsky How Much Money is That?! / Do We Have Enough Paint?
• Robert Kaplinsky How Big is the 2010 Guatemalan Sinkhole? / How Many Gumballs Fit in the Gumball Machine
• Tap Into Teen Minds: Prisms and Pyramids
• Fawn Nguyen: I Am a Doughnut / From Listerine to Fuji Water
• Dan Meyer: You Pour, I Choose
COURSE: Alternate Math Elements I and II
DOMAIN: Geometry – Geometric Measurement and Dimension
CLUSTER: Visualize relationships between two-dimensional and three-dimensional objects.
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Standard:
EE.G-GMD.4. Identify the shapes of two-dimensional cross-sections of
three-dimensional objects.
Performance Objectives:
EE.G-GMD.4.a Identify a cross section of a three-dimensional cube,
pyramid, and cylinder.
EE.G-GMD.4.b Distinguish between two- and three-dimensional shapes.
I Can Statements
MOST COMPLEX LEAST COMPLEX
EE.G-GMD.4.a (A) Identify a cross section of a
three-dimensional cube, pyramid, and cylinder.
EE.G-GMD.4.a (B) Given an array of three-
dimensional objects, choose the object named
(e.g., cube, pyramid, cylinder).
EE.G-GMD.4.a (C) Identify a square, rectangle,
and circle using pictures or objects.
EE.G-GMD.4.b (A) Distinguish between two
and three-dimensional shapes.
EE.G-GMD.4.b (B) Given two examples,
determine which is a two-dimensional shape.
EE.G-GMD.4.b (C) Given pictures, sort two-
and three-dimensional shapes.
Real-World Connections:
• Spatial visualization
• Design
• Drawing
• Architecture and drafting
Vocabulary:
• Cube
• Pyramid
• Cylinder
• Two-dimensional
• Three-dimensional
• Square
• Rectangle
• Circle
Resources:
• Gizmos: Surface and Lateral Areas of Prisms and Cylinders / Prisms and Cylinders
• Gizmos: Surface and Lateral Areas of Pyramids and Cones / Pyramids and Cones / 3D and Orthographic Views
• Geogebra: Cross-Sections and Solids
COURSE: Alternate Math Elements I and II
DOMAIN: Geometry – Modeling with Geometry
CLUSTER: Apply geometric concepts in modeling situations.
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Standard:
EE.G-MG.1-3. Use properties of geometric shapes to describe real-life
objects.
Performance Objectives:
EE.G-MG.1-3.a Identify geometric shapes and match them to real-world
examples.
I Can Statements
MOST COMPLEX LEAST COMPLEX
EE.G-MG.1-3.a (A) Identify geometric shapes
and match them to real-world examples.
EE.G-MG.1-3.a (B) Name basic geometric
shapes (e.g., circle, square, triangle, rectangle,
etc.).
EE.G-MG.1-3.a (C) Match geometric shapes
with real-world objects.
Real-World Connections:
• Drawing
• Architecture and drafting
• Construction
• Design
• Street signs
Vocabulary:
• Sides
• Angles
• Regular
• Irregular
• Base
• Vertex/vertices
Resources:
• Chapter 10: Identify and Describe Geometric Figures [Pdf]
• NCTM Illuminations Shape Tool
• Teachnology -- Shapes Lesson Plans
• New Visions For Public Schools -- Building Shapes
• New Visions For Public Schools -- Net Cutouts
• Which One Doesn't Belong -- Shapes
• Robert Kaplinsky -- Money Count / Robert Kaplinsky -- Paint a Handball Wall
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APPENDIX A: Additional Resources
Other Resources for Teaching Mathematics to Students with Significant Cognitive Disabilities
Title
Keywords
URL
Students With Disabilities CAN Do
Math!
Universal Design for Learning,
Standards for Mathematical Practice
Instructional Routines
I notice/I wonder
Counting Collections
Contemplate Then Calculate
Universal Design for Learning
Contemplate Then Calculate
Teacher Education by Design
Mathematical Practices
Look for and Make Use of Structure
Teacher Education by Design -- Mathematics Instructional Activities
I Notice / I Wonder
Notice and Wonder
Problem Solving
NCTM -- The Math Forum -- Notice and Wonder (Problems &
Puzzles)
New Visions for Public Schools
Curriculum Resources
Algebra
Geometry
Filter by Types Connecting Representations and Contemplate Then
Calculate
DUDAMATH
Interactive exploration of mathematics
DUDAMATH -- Arithmetic
The Itty Bitty Book of the CIF
Instructional Resources
Protocols
The Little Itty Bitty Book of The CIF [PDF]
Which One Doesn’t Belong?
Patterns, Shapes, Similarities, Differences
Numbers, Graphs
Which One Doesn't Belong -- Shapes
Robert Kaplinsky
Real world,
Low entry, high ceiling
Robert Kaplinsky -- Lessons
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APPENDIX B: Glossary
Angle. A shape formed by two lines or rays that diverge from a common point or vertex.
Algebra. The part of mathematics in which letters and other general symbols are used to represent numbers
and quantities in formulae and equations.
Area. The amount of space a two‐dimensional shape occupies, measured in squares.
Associative property for addition. The sum of three or more numbers, which is always the same when
added together, no matter what order they are in. This is illustrated by a + (b + c) = (a + b) + c; 2 + (3 + 4) =
(2 + 3) + 4.
Associative property for multiplication. The product of three or more numbers, which is always the same
when multiplied together, regardless of their grouping. This is illustrated by a(bc) = (ab)c; 2(3×4) = (2×3)4.
Attributes. Characteristics of an object or geometric shape. These include qualities of shape, color, size, side,
length, and so forth.
Base. The surface a solid object stands on, or the bottom line of a shape, such as a triangle or rectangle.
Categorical data. Types of data, which may be divided into groups, such as race, sex, age group, and
educational level, when categorized into a small number of groups.
Circle. A round plane figure with a boundary (i.e., circumference) that consists of points equidistant from a
fixed point (i.e., center).
Commutative property of addition. The sum of numbers is always the same when added together, no
matter if the order of the addends is changed. This is illustrated by a + b = b + a (2 + 1 = 1 + 2).
Commutative property of multiplication. The product of numbers is always the same when multiplied
together, even if the order of factors is changed (i.e., if a and b are two real numbers, then a × b = b × a.)
Compose numbers. To combine parts/components to form a number (adding parts to obtain a number).
Congruent figures. Figures that have the same size and shape.
Congruent. The same.
Cubed. A number multiplied by itself three times.
Decompose numbers. The process of separating numbers into their components (i.e., to divide a number
into smaller parts). Example: 456 can be decomposed as 456 = 400 + 50 + 6.
Denominator. The “bottom” number of a fraction; the number that represents the total number of parts
into which one whole is divided (e.g., in 3/4, the 4 is the denominator and indicates that one whole is divided
into 4 parts).
Decimal. A number with a decimal point in it
Dependent event. Two events are dependent if the outcome or occurrence of the first affects the outcome
or occurrence of the second so that the probability is changed.
Distributive property. The distributive property lets you multiply a sum by multiplying each addend
separately and then add the products.
Equation. A mathematical sentence of equality between two expressions; equations have an equal sign (e.g.,
n + 50 = 75 or 75 = n + 50 means that n + 50 must have the same value as 75).
Event. A set of possible outcomes resulting from a particular experiment.
Exponent. A quantity representing the power to which a given number or expression is to be raised, usually
expressed as a raised symbol beside the number or expression.
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Expression. An operation between numbers that represents a single numeric quantity; expressions do not
have an equal sign (e.g., 4r, x+2, y
‐
1).
Fraction. A mathematical expression representing the division of one whole number by another.
Frequency table. A table that lists items and uses tally marks to record and show the number of times they
occur.
Functions. A special kind of relation where each x‐value has one and only one y‐value.
Inequality. A mathematical sentence in which the value of the expressions on either side of the relationship
symbol are unequal; relation symbols used in inequalities include > (greater than) and < (less than) symbols
(e.g., 7 > 3, x < y).
Irregular shape. A polygon that does not have all sides equal and all angles equal.
Line graph. A graphical representation using points connected by line segments to show how something
changes over time.
Line segment. The part of a line that connects two points. It has definite end points.
Mean. The “average” – To find the mean, add up all the numbers and then divide by the number of
numbers.
Models. Pictorial or tactile aids used to explore mathematical ideas and solve mathematical problems –
Manipulatives can be used to model situations.
Numerator. The top number in a fraction.
Operations. Addition, subtraction, multiplication, and division.
Parallel Lines. Lines that are the same distance apart and that never intersect. Lines that have the same slope
are parallel.
Perpendicular lines. Lines that intersect, forming right angles.
Place value. The value of a digit depending on its place in a number.
Ratios. A comparison between two things. For instance, someone can look at a group of people and refer to
the “ratio of boys to girls” in the class. Suppose there are 35 students, 15 of whom are boys; the ratio of boys
to girls is 15 to 20.
Rectangle. A four‐sided polygon (i.e., a flat shape with straight sides) where every angle is a right angle (90°);
opposite sides are parallel and of equal length.
Regular shape. A polygon is regular when all angles are equal and all sides are equal.
Set. A group or collection of things that go together (e.g., a group of four stars).
Side. In most general terms, a line segment that is part of the figure. It is connected at either end to another
line segment, which, in turn, may or may not be connected to still other line segments.
Similar shapes. Objects of the same shape but different sizes in which the corresponding angles are the
same.
Slope. The steepness/incline/grade of a line.
Square. A four‐sided polygon (e.g., a flat shape with straight sides) where all sides have equal length and
every angle is a right angle (90°).
Three‐dimensional geometric shape. The study of solid figures in three‐dimensional space: cube,
rectangular prism, sphere, cone, cylinder, and pyramid.
Two‐dimensional shape. The study of two‐dimensional figures in a plane; drawings of square, rectangle,
Page | 28 13-Jun-18
circle, triangle, pentagon, hexagon, and octagon.
Variable. A symbol for an unknown number to be solved; it is usually a letter like x or y (e.g., in x + 3 = 7, x
is the variable).
Vertex. The common endpoint of two or more rays or line segments.
Volume. The amount of space a three‐dimensional shape occupies, measured in cubes.
Page | 29 13-Jun-18
References
Center for Literacy and Disability Studies. (2015). DLM Essential Elements in Mathematics
Unpacking High School. Retrieved from https://www.dlmpd.com/instructional-resources/
Dynamic Learning Maps Consortium. (n.d.). Mathematics glossary. Lawrence, KS: University of
Kansas. Retrieved from https://dynamiclearningmaps.org/erp_ye
Dynamic Learning Maps Consortium. (2014). Essential Elements, Linkage Levels, and Mini-Map.
Lawrence, KS: University of Kansas. Retrieved from
https://dynamiclearningmaps.org/essential-elements/math
Dynamic Learning Maps Consortium. (2013). Dynamic Learning Maps Essential Elements for
mathematics. Lawrence, KS: University of Kansas. Retrieved from
https://dynamiclearningmaps.org/erp_ye
Florida Department of Education, Special Education. (2016). FSAA Datafolio Teacher Resource Guide.
FL: Florida Department of Education.
Mississippi Department of Education. (2018). 2018 Mississippi college- and career-readiness standards for
mathematics. Jackson, MS: Author.
North Dakota Department of Public Instruction. (2013). Common Core Instructional Tools:
Mathematics. Retrieved from
https://www.nd.gov/dpi/SchoolStaff/SpecialEd/NDAlternateAssessmentELAMath/Toolsf
orTeachers/
South Carolina Alternate Mathematics Support Guide. (2018, April 26). Retrieved from https://sc-
alt.portal.airast.org/core/fileparse.php/3982/urlt/SC-MATH-Support-Guide_042618.pdf
Wayne County Regional Educational Service Agency Special Education Centers. (2014). Grades HS
Mathematics Essential Elements “I Can” Statements. Retrieved from
http://www.resa.net/downloads/teaching_tools/grades_hs_math_i_can_20140725_130421_
12.pdf