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MATH220 Count on It: Number Sense for Grades K-5
Description: This module, designed for elementary school teachers, will help answer such questions. In the course of this module, we will learn more about number sense by exploring lesson plans, Web resources, and NCTM Standards dedicated to helping students develop a richer and deeper understanding of numbers.

Objective(s)	Virginia Standards of Learning Alignment
Develop an understanding of the student expectations that NCTM promotes for learning about Number and Operations in grades K - 5	Math K.1; K.2; K.3; K.4; K.5; 1.1; 1.2; 1.3; 1.4; 1.5; 1.6; 2.1; 2.2; 2.3; 2.4; 2.5; 3.1; 3.2; 3.3; 3.4; 3.5; 3.6; 3.7; 4.2; 4.3; 4.4; 5.1; 5.2;
Gain increased understanding of how students develop number sense	No Direct Alignment
Gain increased understanding of how to assess students' number sense	Math K.7; K.8; K.9; K.10; 1.7; 1.8; 1.9; 2.6; 2.7; 2.8; 2.9; 2.10; 3.8; 3.9; 3.10; 3.11; 3.12; 4.1; 4.5; 4.6; 4.7; 4.8; 4.9; 5.3; 5.4; 5.5; 5.6; 5.7
Integrate technology, manipulatives and effective pedagogical strategies to create a lesson that promotes the vision of the NCTM Number and Operations Standard.	C/T 5.2; 5.3; 5.4

MATH205 Data Analysis and Probability for Grades K-5
Description: This online course is designed to bring you up to date on the most effective ways to integrate technology into your teaching of these topics, which are so important in today's information-rich world. Through the use of two classroom technologies-the Internet and computer software-you will discover ways to provide students with a richly engaging and instructive learning environment.

Objective(s)	Virginia Standards of Learning Alignment
Develop an understanding of the student expectations that NCTM promotes for Data Analysis and Probability in grades K-5	Math K.6; K.14; K.15; K.16; 2.6; 2.7; 2.8; 3.9; 3.10; 3.11; 3.12; 4.5; 4.6; 4.7; 4.8; 4.9; 5.4; 5.5; 5.6; 5.7
Understand the importance of studying Data Analysis and Probability	No Direct Alignment
Learn about different spreadsheet applications that can be used to represent data	No Direct Alignment
Learn about different spreadsheet applications that can be used to represent data	No Direct Alignment
integrate and evaluate Web-based activities focusing on data analysis and probability	I C/T5.2; C/T5.4; C/T8.1; C/T8.2; C/T8.3
Integrate into classroom practice strategies to teach data analysis and probability	Math 1.7; 1.8; 1.9; 1.18; 1.20; 2.9; 2.10; 2.23; 2.24; 3.8; 3.21; 3.22; 3.23; 4.19; 4.20; 5.3; 5.17; 5.18; 5.19

MATH175 Developing Algebraic Thinking in Grades K-2
Description: "Algebra is frequently described as "generalized arithmetic" and indeed algebraic thinking is a natural extension of arithmetical thinking. Both arithmetic and algebra are useful for describing important relationships in the world. But although arithmetic is effective in describing static pictures of the world, algebra is dynamic and a necessary vehicle for describing a changing world."

Greenes, C., M. Cavanagh, et al. Navigating through Algebra in prekindergarten - grade 2. Reston, VA: NCTM, 2001.

As adults, we recognize how the world is constantly changing; children are no different. Their natural play involves changes that they make themselves and ones that they do not initiate. The world is full of situations that are slight variants of other situations. Walking to school may be pretty routine for a child, but the time he or she leaves might vary from day to day. One purpose of this course is to help you identify the ways in which change and variation arise in the early elementary curriculum and how they may provide opportunities for your students to engage in algebraic thinking. In this course, you will do a few of these kinds of problems yourself, but, because the mathematics is often relatively easy for adults, you will spend considerable time thinking about how you would work with your students on these kinds of problems. You don't need to know or teach formal algebra yourself, since the focus of this course is on discovering and taking advantage of the potential for algebraic thinking that is already present in the mathematics your students encounter.
 

Objective(s)	Virginia Standards of Learning Alignment
A deeper understanding of the connections between algebraic thinking and arithmetic as students learn it in grades K-2;	Math K.17, K.181.20; 1.21
Experience using variables in several different ways in the K-2 curriculum;	Math 2.25; 2.26
The ability to diagnose the potential misconceptions in children's uses of the "=" sign;	No Direct Alignment
Strategies for providing students with a solid foundation for algebra through the study of arithmetic.	No Direct Alignment

 
Math 120 Fostering Cooperative Learning, Discussion, and Critical Thinking in Elementary Math (Grades 1-5)
Description: Examine and implement exemplary elementary math lessons and activities that incorporate cooperative learning, critical thinking, and problem-solving, while addressing state mathematics and technology standards…..

Taken from the narrative of the math Standards:
“While learning mathematics, students will be actively engaged, using concrete materials and appropriate technologies such as calculators and computers.”

“Problem solving has been integrated throughout the six content strands. The development of problem-solving skills should be a major goal of the mathematics program at every grade level. Instruction in the process of problem solving will need to be integrated early and continuously into each student’s mathematics education. Students must be helped to develop a wide range of skills and strategies for solving a variety of problem types.”

Objective(s)	Virginia Standards of Learning Alignment
Understand how cooperative learning, communication, and critical thinking can increase student learning of mathematics.	Cooperative learning, discussion, and critical thinking are integrated throughout the math standards.
Be able to analyze math lessons to identify the critical-thinking skills and strategies developed.	Cooperative learning, discussion, and critical thinking are integrated throughout the math standards.
Be able to incorporate higher-level thinking questions into math discussions.	Cooperative learning, discussion, and critical thinking are integrated throughout the math standards.
Use technology to teach mathematics lessons incorporating cooperative learning, discussion, and critical thinking.	Cooperative learning, discussion, and critical thinking are integrated throughout the math standards.
Develop lessons which incorporate features of successful cooperative learning and problem solving in context.	Cooperative learning, discussion, and critical thinking are integrated throughout the math standards.

Cooperative learning, discussion, and critical thinking are integrated throughout the math standards.

MATH180 Math in Everyday Life for Grades K-5
Description: We have created this course to help teachers easily and effectively incorporate real-world problem solving into their teaching. Through the use of two classroom technologies—the Internet and calculators—participants will experience ways that regular life activities can help teach problem solving skills to students.

Objective(s)	Virginia Standards of Learning Alignment
Read and discuss issues related to NCTM standards, problem solving, and the use of calculators in the classroom.	Can support ALL mathematics standards of learning.
Examine and critique lesson plans that involve using calculators to help students solve real world math problems.	Can support ALL mathematics standards of learning.
Explore Web resources that help enable teachers to introduce problem solving methods and concepts.	Can support ALL mathematics standards of learning.
Search for and evaluate other related Web resources and math lesson plans.	Can support ALL mathematics standards of learning.
Complete a final project that fits in with their personal teaching goals.	Can support ALL mathematics standards of learning.

Because this course addresses teaching strategies that integrate math with technology, it can be correlated to all math and technology standards.

MATH315 Nonstandard Measurement in Grades K-2
Description: In this course, you will learn the value of progressing from nonstandard to standard units during the early study of measurement. You will deepen your understanding of nonstandard and standard measurement, the role of estimation in measurement, and the best practices used in teaching measurement to elementary-level students. In addition, you will analyze common misconceptions experienced by children and adults and develop intervention strategies to clarify such misconceptions.

Objective(s)	Virginia Standards of Learning Alignment
deepen your understanding of using nonstandard tools to measure length, area, and volume;	Math 1.12
study and apply the practice of estimation to develop measurement skills;	Math 1.9; 2.12; 2.13; 2.14; 2.15
identify the similarities and differences between nonstandard and standard measuring tools;	Math K.8; K.10; 1.13; 1.14; 2.17
study the evolution of systems of measurement and examine how the units within some systems are interrelated;	No Direct Alignment
strengthen your ability to observe and clarify students' misconceptions and understandings about measurement;	No Direct Alignment
reflect on your own thinking and the thinking of students	No Direct Alignment
synthesize your ideas about measurement into a final project; and	No Direct Alignment
provide suggestions for various instructional strategies to meet the needs of a range of students.	No Direct Alignment

 
MATH235 Patterns and Relations: Algebra Concepts for Grades 1-5
This course is designed to help elementary school educators better understand the role and importance of patterns and relations in mathematics and the NCTM expectations for students. In this course, they will learn more about algebraic thinking with patterns and relations by studying NCTM standards and articles, by exploring lesson plans, by investigating in problem situations, by solving problems, and by examining Web resources. Learners will examine different types of patterns using manipulative and technology experiences that involve constructing and describing patterns, conjecturing, and generalizing. Activities that introduce and use a pictorial language of arrows for relations will be incorporated to picture problem-solving strategies, pose problems involving numerical relations, use patterns in problem solving, and further develop algebraic thinking concepts.


MATH310 Progressing from Nonstandard to Standard Measurement in Grades 1-4
In this course, you will learn the value of progressing from nonstandard to standard units during the early study of measurement. You will deepen your understanding of nonstandard and standard measurement, the role of estimation in measurement, and the best practices used in teaching measurement to elementary-level students. In addition, you will analyze common misconceptions experienced by children and adults and develop intervention strategies to clarify such misconceptions.

MATH190 Shaping Up: Teaching Geometry in Grades K-2
Description: This online course is designed to bring you up to date on the most effective ways to teach geometry using technology. Through the use of two classroom technologies—the Internet and computer software—you will discover ways to provide students with a richly engaging and instructive geometry learning environment.

Objective(s)	Virginia Standards of Learning Alignment
Integrate into unit planning the NCTM standards for teaching geometry	Math K.11; K.12; K.13; 1.15; 1.16; 1.17; 2.20; 2.21; 2.22
Use knowledge of lesson planning to connect geometry and technology in a mini-unit	No Direct Alignment
Use software and Web-based interactive activities to generate resources for students to use as they explore geometry concepts	C/T5.2; C/T5.4
Use Internet resources to enhance students' knowledge of geometry concepts	No Direct Alignment
Apply knowledge of NCTM standards and unit planning in the creation and field-testing of a mini-unit that integrates technology into the teaching of geometry.	No Direct Alignment

MATH280 Understanding Counting and Numbers (Grades K-2)
Description: In this course, you will learn about topics in counting and numbers based on the National Council of Teachers of Mathematics (NCTM) Standards for grades K-2. You will gain knowledge about specific expectations that can help you give children a solid foundation in mathematics. The Counting and Numbers course will help you support your students to learn numbers and their relationships, and make connections among mathematical ideas. As a result, you can offer your students a strong foundation in counting and the understanding of quantity, number relationships, and place value. You will also learn multiple teaching strategies that will enable you to reach a wide range of students. Through participation in peer discussions, you will become part of an online community. You will gain knowledge and pedagogy about teaching counting and numbers as you share experiences and exchange ideas and opinions. As a final task, you will create an original lesson plan that integrates literature with mathematics for use in your instructional program.

Objective(s)	Virginia Standards of Learning Alignment
count with understanding and recognize 'how many' in sets of objects;	Math K.1; K.2; K.3; K.4; K.5; 1.1; 2.5
use multiple models to develop initial understanding of place value and the base-ten number system;	Math 1.2; 1.3; 1.4; 1.5; 2.1
develop understanding of the relative position and magnitude of whole numbers and of ordinal and cardinal numbers and their connections;	Math 2.3
develop a sense of whole numbers and represent and use them in flexible ways, including relating, composing, and decomposing numbers;	No Direct Alignment
connect number words and numerals to the quantities they represent, using various physical models and representations;	Math K.6
understand and represent commonly used fractions, such as 1/4, 1/3, and 1/2.	Math 1.6; 2.4

MATH255 Understanding Geometric Shapes and Spatial Sense in Grades 1-4
Description: This course explores how to broaden and deepen elementary school students' understanding of and experiences with geometry. The activities in the course go beyond identifying shapes; they explore the interconnection between geometry and spatial relationships by looking at shapes and how they relate to each other and by looking at examples of geometry found in architecture, art, and nature. The spatial sense and flexible thinking that is required to generalize how shapes are connected in two- and three- dimensional forms is important not only in geometry, but in other math topics. For example, students will need a good spatial sense to understand proportional reasoning, fractions, and properties of algebra, including commutative and associative properties.

Objective(s)	Virginia Standards of Learning Alignment
A deeper understanding of geometry and spatial relations and how these concepts enrich the development of problem solving skills;	Math 1.15; 1.16; 1.17;
A stronger knowledge of how elementary students make sense of geometric principals and spatial relations;	No Direct Alignment
Strategies for improving your own teaching of geometry and spatial relationships.	Math 2.20; 2.21; 2.22; 3.18; 3.19; 3.20; 4.14; 4.15; 4.16; 4.17; 4.18

MATH250 Understanding Numbers and Operations: Addition and Subtraction in Grades PreK-3
Description: This course, designed for elementary school teachers, will help you better understand the role and importance of computation strategies in mathematics. In the course of this course, you will learn more about addition and subtraction strategies by studying NCTM Standards, by examining many types of strategies and student work, by exploring lesson plans, by investigating in problem situations, and by examining Web resources.

The course addresses Number and Operations Standards as described in the National Council of Teachers of Mathematics (NCTM) Principles and Standards for School Mathematics (PSSM 2000):

Instructional programs from Prekindergarten through grade 12 should enable all students to:

• Understand numbers, ways of representing numbers, relationships among numbers, and number systems;
• Understand meanings of operations and how they relate to one another;
• Compute fluently and make reasonable estimates.

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Grades 3-5

MATH295 Applying the NCTM Principles to Grades 3-5
Applying the NCTM Principles to Grades 3-5 is an introduction to the six principles identified in the National Council of Teachers of Mathematics' Standards and Principles for School Mathematics. These principles are Equity, Curriculum, Teaching, Learning, Assessment, and Technology. Through a combination of text, video, and discussion features, the course presents key concepts and strategies for applying these principles in grades 3-5. As you move through the course, you will have opportunities to individualize your learning experience and design a plan to help you put what you've learned into practice.


MATH220 Count On It!: Number Sense for Grades K-5
This course will explore the meaning of number sense, why it is important for elementary school students, and how we assess the type of number sense that students possess. It will show effective and exciting ways to use technology, manipulatives, and the Internet to teach number sense to students while meeting national educational standards.


MATH205 Data Analysis and Probability for Grades K-5
This course is designed to bring participants up to date on the most effective ways to teach these important mathematics topics. After examining the latest recommendations from the NCTM, the course presents sample lessons created by math experts. It goes on to explore ways that educators can use the Internet and computer software to enrich students' learning environment.


MATH270 Developing Algebraic Thinking in Grades 3-5
Number sense activities allow students to think algebraically. This course focuses on understanding patterns, analyzing situations using algebra, and representing relationships with mathematical models. Learners will discuss strategies for bringing out algebra in the classroom and explore the algebraic content present in the activities they currently use. As a final project, learners design problems for a teacher’s guide on algebraic thinking.


MATH165 Enabling Students with Special Needs to Succeed in Math Class (Grades 4-8)
The Individuals with Disabilities Education Act of 1997 creates new challenges for educators. The requirement that students do more reading and writing and other elements of these new mathematics curricula presents extra challenges for students with attention, language, sensory and other disabilities. This course helps educators develop ways to adapt their curricula, provide supportive scaffolds and collaborate with special needs teachers to help all students succeed in their classrooms.


MATH120 Fostering Cooperative Learning, Discussion, and Critical Thinking in Elementary Math (Grades 1-5)
This course presents proven critical thinking and cooperative learning strategies for teaching mathematics that can be enhanced by today's classroom technology. Learners will explore both software and Web activities specifically designed to support collaboration and problem solving within the curriculum and to help students meet national standards. Please note: this course requires educators to work with students in order to complete some assignments.


MATH160 Gender Equity in the Mathematics Classroom (Grades 4-8)
This course explores ways of creating classroom environments in middle school that are supportive of girls' success in math. Building on what educators already know about good instructional practice, this course attends to the unique social and academic needs of girls at this point in their development, with an eye towards encouraging pursuit of mathematics in high school and beyond.


MATH180 Math in Everyday Life for Grades K-5
By exploring valuable Web resources and considering student use of the calculator, learners will discover exciting and effective ways to enrich their math curriculum to incorporate real-world math into their elementary school classrooms while meeting national educational standards.


MATH275 Measurement: Perimeter and Area in Grades 3-5
This course builds upon a general understanding of measuring the length of objects, including identifying measurable attributes and selecting appropriate units. It is intended to deepen and expand your conceptual understandings of measurement and the application of measurement in real situations. Particular emphasis will be placed on understanding the concepts of perimeter and area. Learners will solidify their understanding of these concepts by engaging in multiple investigations and by using concrete and virtual (or online) manipulatives. From these investigations, learners will develop strategies and discuss the formulas to calculate perimeters and areas more efficiently.


MATH260 Number and Operation Sense in Grades 3-5
In this course, learners will do activities that develop students' number sense. Learners will solve rich mathematical problems and use those experiences to consider what students do and do not know about numbers and to develop strategies to support them in deepening their understanding of the structure of numbers. The final project includes the creation of a case study about the development of one student's number sense and understandings of operations. Please note: this course requires educators to work with students in order to complete some assignments.


MATH235 Patterns and Relations: Algebra Concepts for Grades 1-5
This course is designed to help elementary school educators better understand the role and importance of patterns and relations in mathematics and the NCTM expectations for students. In this course, they will learn more about algebraic thinking with patterns and relations by studying NCTM standards and articles, by exploring lesson plans, by investigating in problem situations, by solving problems, and by examining Web resources. Learners will examine different types of patterns using manipulative and technology experiences that involve constructing and describing patterns, conjecturing, and generalizing. Activities that introduce and use a pictorial language of arrows for relations will be incorporated to picture problem-solving strategies, pose problems involving numerical relations, use patterns in problem solving, and further develop algebraic thinking concepts.


MATH310 Progressing from Nonstandard to Standard Measurement in Grades 1-4
In this course, you will learn the value of progressing from nonstandard to standard units during the early study of measurement. You will deepen your understanding of nonstandard and standard measurement, the role of estimation in measurement, and the best practices used in teaching measurement to elementary-level students. In addition, you will analyze common misconceptions experienced by children and adults and develop intervention strategies to clarify such misconceptions.


MATH245 Rational Numbers, Fractions, Decimals and Percents in Grades 5-8
This course is about the meanings of fractions, decimals, and percents, and the difficulties that students have understanding these numbers. The activities in this course serve to deepen the learners’ knowledge of rational numbers, particularly with fractions, decimals and percents, and the interrelation among the three forms, and the difficulties these forms pose for students and teachers alike, especially if the students have not progressed from viewing fractions as portions to fractions as quantities. Readings provide background information on content and pedagogy. Video clips provide opportunities for the learners to observe students’ mathematical understanding and teacher-lead questioning techniques. The final project includes writing a short unit reviewing rational numbers that focuses on the number sense that students need to have before moving onto a unit where they are introduced to operations.


MATH325 Real Life Measurement in Grades 3-5
This course asks learners to reflect upon how measurement is used in real-life situations, and it then provides strategies for making those connections in mathematical classrooms. To strengthen their understandings of measurement, learners will review the core concepts involved in taking measurements to find perimeter, area, surface area, and volume. Learners will also refine their strategies for teaching angle measurement to children. Using nonstandard and standard units to measure regular shapes, learners will deepen their understandings of what tools, units, and techniques are required for measuring different attributes. Learners also become familiar with strategies to interpret and communicate the results of their measurements. Using web-based applets, hands-on activities, concrete manipulatives, and online videos, learners will explore ways to provide experiences in discovery, estimation, and problem-solving inside the classroom that mirror the use of measurement outside the classroom.


MATH195 Shaping Up: Teaching Geometry Using Technology in Grades 3-5
This course is designed to bring participants up to date on the most effective ways to teach geometry. After presenting the latest recommendations from the NCTM, the course looks at some sample lessons created by math experts. It goes on to explore ways that educators can take advantage of the Internet and computer software to help provide students with a rich learning environment.


MATH265 Spatial Reasoning in Grades 5-8
This course is about visualization and spatial reasoning and the importance these activities play in students' problem solving in many areas of grade 5-8 mathematics, including—but not restricted to—geometry. Learners will use online tools and paper cut-outs as they work to identify three-dimensional objects represented in two-dimensional forms, learn some techniques of perspective drawing, and derive formulas for the areas and volumes of various two- and three-dimensional objects. Readings and video clips encourage discussion about the importance of spatial reasoning and visualization, students' geometric concepts and common misconceptions, and classroom practices that could help students develop their spatial reasoning and visualization skills.


MATH255 Understanding Geometric Shapes and Spatial Sense in Grades 1-4
This course explores how to broaden and deepen elementary school students' understanding of and experiences with geometry. The activities in the course go beyond identifying shapes; they explore the interconnection between geometry and spatial relationships by looking at shapes and how they relate to each other and by looking at examples of geometry found in architecture, art, and nature. As a final task, learners will assess how well their current math textbook approaches geometry and create two lesson plans that they can use to enrich students' understandings of spatial relationships and visualizations.


MATH250 Understanding Numbers and Operations: Addition and Subtraction in Grades preK-3
This course is designed to help elementary school educators better understand how students learn addition and subtraction and the role and importance of computation strategies in mathematics. In this course, they will learn more about students’ development of addition and subtraction concepts and strategies by studying NCTM standards and articles on learning with understanding, by reviewing various strategies and students’ use of strategies, by exploring lesson plans, and by examining Web resources. A variety of methods will be used to engage participants and to expand their knowledge base of approaches that improve student understanding of number and operations. Activities that examine varied addition and subtraction strategies and that reinforce addition and subtraction as inverse operations will be incorporated to help develop conceptual understanding.


MATH320 Understanding Probability in Grades 4-6
This course explores the concepts of probability, the intuition and problem solving skills related to probability, and the importance of being able to analyze probability and statistics used in the media. The learners will work through activities that will stretch their understanding of probability and data analysis. They will also consider how students understand these concepts through an examination of student work. This course emphasizes intuition, experimentation, and probabilistic reasoning.


MATH285 Understanding the Number System (Grades 3-5)
This course is designed for teachers of students in grades 3–5. Its goal is to deepen the understanding of our base-ten number system while acquiring activities and strategies for teaching this material to upper elementary students of all abilities. The methods presented in the course incorporate constructivist theory, allowing the students to create meaning and understanding of new topics by building upon previous knowledge and using interactive, hands-on methods.

MATH295 Applying the NCTM Principles in Grades 3-5
Description: In this course, you learn about the NCTM’s Principles and Standards for School Mathematics and explore implementation strategies for grades 3-5.

Because this course addresses aligning curriculum with standards, it correlates to ALL standards.

MATH220 Count on It: Number Sense for Grades K-5
Description: This module, designed for elementary school teachers, will help answer such questions. In the course of this module, we will learn more about number sense by exploring lesson plans, Web resources, and NCTM Standards dedicated to helping students develop a richer and deeper understanding of numbers.

Objective(s)	Virginia Standards of Learning Alignment
Develop an understanding of the student expectations that NCTM promotes for learning about Number and Operations in grades K - 5	Math K.1; K.2; K.3; K.4; K.5; 1.1; 1.2; 1.3; 1.4; 1.5; 1.6; 2.1; 2.2; 2.3; 2.4; 2.5; 3.1; 3.2; 3.3; 3.4; 3.5; 3.6; 3.7; 4.2; 4.3; 4.4; 5.1; 5.2;
Gain increased understanding of how students develop number sense	No Direct Alignment
Gain increased understanding of how to assess students' number sense	Math K.7; K.8; K.9; K.10; 1.7; 1.8; 1.9; 2.6; 2.7; 2.8; 2.9; 2.10; 3.8; 3.9; 3.10; 3.11; 3.12; 4.1; 4.5; 4.6; 4.7; 4.8; 4.9; 5.3; 5.4; 5.5; 5.6; 5.7
Integrate technology, manipulatives and effective pedagogical strategies to create a lesson that promotes the vision of the NCTM Number and Operations Standard.	C/T 5.2; 5.3; 5.4

MATH205 Data Analysis and Probability for Grades K-5
Description: This online course is designed to bring you up to date on the most effective ways to integrate technology into your teaching of these topics, which are so important in today's information-rich world. Through the use of two classroom technologies-the Internet and computer software-you will discover ways to provide students with a richly engaging and instructive learning environment.

Objective(s)	Virginia Standards of Learning Alignment
Develop an understanding of the student expectations that NCTM promotes for Data Analysis and Probability in grades K-5	Math K.6; K.14; K.15; K.16; 2.6; 2.7; 2.8; 3.9; 3.10; 3.11; 3.12; 4.5; 4.6; 4.7; 4.8; 4.9; 5.4; 5.5; 5.6; 5.7
Understand the importance of studying Data Analysis and Probability	No Direct Alignment
Learn about different spreadsheet applications that can be used to represent data	No Direct Alignment
Learn about different spreadsheet applications that can be used to represent data	No Direct Alignment
integrate and evaluate Web-based activities focusing on data analysis and probability	I C/T5.2; C/T5.4; C/T8.1; C/T8.2; C/T8.3
Integrate into classroom practice strategies to teach data analysis and probability	Math 1.7; 1.8; 1.9; 1.18; 1.20; 2.9; 2.10; 2.23; 2.24; 3.8; 3.21; 3.22; 3.23; 4.19; 4.20; 5.3; 5.17; 5.18; 5.19

Math 270 Developing Algebraic Thinking in Grades 3-5
Description: Teachers and researchers have long recognized that the transition from learning arithmetic to learning algebra is one of the major hurdles students face in learning mathematics. Researchers are finding, however, that elementary students can learn to think about arithmetic in ways that both enhance their early learning of arithmetic and provide a foundation for learning algebra. Research results show that young students can learn to make and justify generalizations about the underlying structure and properties of arithmetic - generalizations that form the basis for much of algebra.

This course addresses the mathematics of algebraic thinking as described in the National Council of Teachers of Mathematics' (NCTM) Principles and Standards for School Mathematics (PSSM 2000), focusing on the ways in which students in grades 3-5 can be prepared for algebra by:

• Understanding patterns, relations, and functions;
• Representing and analyzing mathematical situations and structures using algebraic symbols;
• Using mathematical models to represent and understand quantitative relationships.

• high expectations and worthwhile opportunities for all.
• accommodating differences to help everyone learn mathematics.
• resources and support for all classrooms and all students."

Math 120 Fostering Cooperative Learning, Discussion, and Critical Thinking in Elementary Math (Grades 1-5)
Description: Examine and implement exemplary elementary math lessons and activities that incorporate cooperative learning, critical thinking, and problem-solving, while addressing state mathematics and technology standards…

Taken from the narrative of the math Standards:
“While learning mathematics, students will be actively engaged, using concrete materials and appropriate technologies such as calculators and computers.”

“Problem solving has been integrated throughout the six content strands. The development of problem-solving skills should be a major goal of the mathematics program at every grade level. Instruction in the process of problem solving will need to be integrated early and continuously into each student’s mathematics education. Students must be helped to develop a wide range of skills and strategies for solving a variety of problem types.”

Objective(s)	Virginia Standards of Learning Alignment
Understand how cooperative learning, communication, and critical thinking can increase student learning of mathematics.	Can support ALL mathematics standards of learning.
Be able to analyze math lessons to identify the critical-thinking skills and strategies developed.	Can support ALL mathematics standards of learning.
Be able to incorporate higher-level thinking questions into math discussions.	Can support ALL mathematics standards of learning.
Use technology to teach mathematics lessons incorporating cooperative learning, discussion, and critical thinking.	Can support ALL mathematics standards of learning.
Develop lessons which incorporate features of successful cooperative learning and problem solving in context.	Can support ALL mathematics standards of learning.

Cooperative learning, discussion, and critical thinking are integrated throughout the math standards.

MATH160 Gender Equity in the Mathematics Classroom (Grades 4-8)
Description: Educators and parents frequently hear ideals such as "education for all" and "leave no child behind," but what do those ideals really mean and what actions are required by math educators to fulfill them? Since the 1970s, reports and education discussions have pointed to gender inequities in mathematics learning. In response to gender inequity, as well as inequities because of race, poverty, disability, and limited English proficiency, the National Council of Teachers of Mathematics' (NCTM) Principles and Standards for School Mathematics has identified an "Equity Principle" that states: "excellence in mathematics education requires equity - high expectations and strong support for all students."

In this course, learners will look at the current research on gender equity in mathematics education from a variety of areas: curricula, classroom interactions, assessment, and the education climate. Learners will identify the progress that has been made towards eliminating gender gaps and investigate areas in which gender differences still occur. Learners will also explore some concrete strategies that mathematics educators can use to create a classroom in which girls and boys are equally motivated to perform to their highest abilities.

Objective(s)	Virginia Standards of Learning Alignment
Be able to communicate what gender equity means in the mathematics classroom;	This is not a standards-based course.
Have a basic understanding of the current research on this topic and how it applies to their teaching;	This is not a standards-based course.
Identify some of the main areas in which they can work to increase gender equity in their classrooms, as well as specific educational practices and strategies they can use;	This is not a standards-based course.
Develop a gender equity action plan they can implement in their classrooms.	This is not a standards-based course.

This is not a standards-based course.

MATH180 Math in Everyday Life for Grades K-5
Description: We have created this course to help teachers easily and effectively incorporate real-world problem solving into their teaching. Through the use of two classroom technologies—the Internet and calculators—participants will experience ways that regular life activities can help teach problem solving skills to students.

Objective(s)	Virginia Standards of Learning Alignment
Read and discuss issues related to NCTM standards, problem solving, and the use of calculators in the classroom.	Can support ALL mathematics standards of learning.
Examine and critique lesson plans that involve using calculators to help students solve real world math problems.	Can support ALL mathematics standards of learning.
Explore Web resources that help enable teachers to introduce problem solving methods and concepts.	Can support ALL mathematics standards of learning.
Search for and evaluate other related Web resources and math lesson plans.	Can support ALL mathematics standards of learning.
Complete a final project that fits in with their personal teaching goals.	Can support ALL mathematics standards of learning.

MATH275 Measurement: Perimeter and Area in Grades 3-5
Description: This course is intended to deepen and expand your conceptual understandings of measurement and the application of measurement in real situations. Particular emphasis will be placed on understanding the concepts of perimeter and area. You will solidify your understanding of these concepts by engaging in multiple investigations and by using concrete and virtual (or online) manipulatives. From these investigations, you will develop strategies and discuss the formulas to calculate perimeters and areas more efficiently. Although unit selection and conversion will be incorporated into the course content and examples, they will not be primary topics.

Objective(s)	Virginia Standards of Learning Alignment
Strengthened your understanding of measurement in general and of perimeter and area in particular;	Math 5.10
Gained a deeper understanding of how the concept of measurement can be developed in real-life situations and how that awareness can enhance your teaching of perimeter and area;	Math 3.14; 3.15; 3.16; 3.17; 4.10; 4.11; 4.12; 4.13 5.8; 5.9; 5.11; 5.12; 5.13
Developed strategies to apply the research findings on student understanding of measurement in your classroom.	Math 3.14; 3.15; 3.16; 3.174.10; 4.11; 4.12; 4.13 5.8; 5.9; 5.11; 5.12; 5.13

MATH260 Number and Operation Sense in Grades 3-5
Description: In grades 3-5, students consolidate and extend their knowledge of addition and subtraction, develop thorough understandings of multiplication and division, and build solid foundations for efficiently and flexibly computing with all four operations. This requires students to build rich models of our number system for many purposes. In this course, you will do activities that develop students' number sense. You will do the activities yourself, reflect on how you might use the activities with your students, and work with a student on these activities several times during the course.

Objective(s)	Virginia Standards of Learning Alignment
A better understanding of multiplication and division and their relationships to one another;	Math 3.4; 3.5; 3.9; 4.8; 5.3; 5.4; 5.5; 5.6; 5.7
Experience using activities that require number sense with at least one student in grade 3, 4, or 5;	No Direct Alignment
Strategies for developing your students' number sense.	Math 3.1; 3.2; 3.3; 3.6; 3.7; 3.8; 3.11; 3.12; 4.1; 4.2; 4.3; 4.4; 4.5; 4.6; 4.7; 4.9; 5.1; 5.2;

The sessions will increase your knowledge about the structure of our number system. You will begin the course with an addition and subtraction activity that emphasizes place value. Sessions 2 and 3 explore a variety of ways to find and use the factors and multiples of numbers. Session 4 connects all four math operations. In Sessions 5 and 6, you will use the distributive property to solve problems. In Session 6, you will write a case study about the development of one student's number sense and understandings of operations.

MATH235 Patterns and Relations: Algebra Concepts for Grades 1-5
This course is designed to help elementary school educators better understand the role and importance of patterns and relations in mathematics and the NCTM expectations for students. In this course, they will learn more about algebraic thinking with patterns and relations by studying NCTM standards and articles, by exploring lesson plans, by investigating in problem situations, by solving problems, and by examining Web resources. Learners will examine different types of patterns using manipulative and technology experiences that involve constructing and describing patterns, conjecturing, and generalizing. Activities that introduce and use a pictorial language of arrows for relations will be incorporated to picture problem-solving strategies, pose problems involving numerical relations, use patterns in problem solving, and further develop algebraic thinking concepts.


MATH310 Progressing from Nonstandard to Standard Measurement in Grades 1-4
In this course, you will learn the value of progressing from nonstandard to standard units during the early study of measurement. You will deepen your understanding of nonstandard and standard measurement, the role of estimation in measurement, and the best practices used in teaching measurement to elementary-level students. In addition, you will analyze common misconceptions experienced by children and adults and develop intervention strategies to clarify such misconceptions.

MATH245 Rational Numbers, Fractions, Decimals, and Percents in Grades 5-8
Description: This course is about the meanings of fractions, decimals, and percents, and the difficulties that students have understanding these numbers. Rational numbers are numbers that can be expressed as a ratio of two integers. They first came into being as fractions in response to a need to indicate quantities less than one---for example, in fair-sharing contexts such as sharing three loaves of bread among seven people. This is partitioning, in which the whole numbers that are the denominator (number of equal parts required) and the numerator (how many of those equal parts are collected into a group) are combined in a meaningful way. This use of fractions eventually led to a more general development of rational numbers as quantities, numbers that need not relate contextually to the whole numbers that are used to express them. A conceptual leap is required to see rational numbers (in fractional or other forms) as a single quantity and not some combination of whole numbers. Similar difficulties arise for decimals and percents. The interrelation among the three forms pose difficulties for students and teachers alike, especially if the students have not progressed from viewing fractions as portions to fractions as quantities.

Objective(s)	Virginia Standards of Learning Alignment
A deeper understanding of what rational numbers are;	Math 5.1; 5.2; 6.1; 6.2; 8.1; 8.2
A greater appreciation for and understanding of the difficulties students have learning about rational numbers;	No Direct Alignment
Strategies to address students' difficulties and to strengthen students' understanding about rational numbers.	Math 5.3; 5.4; 5.5; 5.6; 5.7; 6.3; 6.4; 6.5; 6.6; 6.7; 6.8; 7.1; 7.2; 7.3; 7.4; 7.5; 7.6; 8.3; 8.4; 8.5

MATH325 Real Life Measurement in Grades 3-5
This course asks learners to reflect upon how measurement is used in real-life situations, and it then provides strategies for making those connections in mathematical classrooms. To strengthen their understandings of measurement, learners will review the core concepts involved in taking measurements to find perimeter, area, surface area, and volume. Learners will also refine their strategies for teaching angle measurement to children. Using nonstandard and standard units to measure regular shapes, learners will deepen their understandings of what tools, units, and techniques are required for measuring different attributes. Learners also become familiar with strategies to interpret and communicate the results of their measurements. Using web-based applets, hands-on activities, concrete manipulatives, and online videos, learners will explore ways to provide experiences in discovery, estimation, and problem-solving inside the classroom that mirror the use of measurement outside the classroom.

MATH195 Shaping Up: Teaching Geometry in Grades 3-5
Description: This online course is designed to bring you up to date on the most effective ways to teach geometry using technology. Through the use of two classroom technologies—the Internet and computer software—you will discover ways to provide students with a richly engaging and instructive geometry learning environment.

Objective(s)	Virginia Standards of Learning Alignment
Integrate into unit planning the NCTM standards for teaching geometry	Math 3.18; 3.19; 3.20; 4.14; 4.15; 4.16; 4.17; 4.18; 5.14; 5.15; 5.16
Use knowledge of lesson planning to connect geometry and technology in a mini-unit	No Direct Alignment
Use software and Web-based interactive activities to generate resources for students to use as they explore geometry concepts	C/T5.2; C/T5.4; C/T8.1; C/T8.2; C/T8.3
Use Internet resources to enhance students' knowledge of geometry concepts	No Direct Alignment
Apply knowledge of NCTM standards and unit planning in the creation and field-testing of a mini-unit that integrates technology into the teaching of geometry.	No Direct Alignment

MATH265 Spatial Reasoning in Grades 5-8
Description: This course is about visualization and spatial reasoning and the importance these activities play in students' problem solving in many areas of grade 5-8 mathematics, including---but not restricted to---geometry. Learners will use online tools and paper cut-outs as they work to identify three-dimensional objects represented in two-dimensional forms, learn some techniques of perspective drawing, and derive formulas for the areas and volumes of various two- and three-dimensional objects. Readings and video clips encourage discussion about the importance of spatial reasoning and visualization, students' geometric concepts and common misconceptions, and classroom practices that could help students develop their spatial reasoning and visualization skills.

Objective(s)	Virginia Standards of Learning Alignment
Improved your skills in visualizing 3-D objects from 2-D representations;	Math 5.15; 5.16; 6.14; 6.15; 6.17; 7.9;
Improved your understanding of area, volume, and other properties of common 2-D and 3-D figures;	No Direct Alignment
Increased your understanding of spatial reasoning, and be able to explain its importance in solving problems;	No Direct Alignment
Learn about the research regarding student learning in geometry (especially concerning spatial reasoning and visualization) and effective instructional practices for teaching these topics.	Math 6.17; 7.10; 7.11; 7.8; 8.9; 8.10

MATH255 Understanding Geometric Shapes and Spatial Sense in Grades 1-4
Description: This course explores how to broaden and deepen elementary school students' understanding of and experiences with geometry. The activities in the course go beyond identifying shapes; they explore the interconnection between geometry and spatial relationships by looking at shapes and how they relate to each other and by looking at examples of geometry found in architecture, art, and nature. The spatial sense and flexible thinking that is required to generalize how shapes are connected in two- and three- dimensional forms is important not only in geometry, but in other math topics. For example, students will need a good spatial sense to understand proportional reasoning, fractions, and properties of algebra, including commutative and associative properties.

Objective(s)	Virginia Standards of Learning Alignment
A deeper understanding of geometry and spatial relations and how these concepts enrich the development of problem solving skills;	Math 1.15; 1.16; 1.17
A stronger knowledge of how elementary students make sense of geometric principals and spatial relations;	No Direct Alignment
Strategies for improving your own teaching of geometry and spatial relationships.	Math 2.20; 2.21; 2.22; 3.18; 3.19; 3.20; 4.14; 4.15; 4.16; 4.17; 4.18

MATH250 Understanding Numbers and Operations: Addition and Subtraction in Grades PreK-3
Description: This course, designed for elementary school teachers, will help you better understand the role and importance of computation strategies in mathematics. In the course of this course, you will learn more about addition and subtraction strategies by studying NCTM Standards, by examining many types of strategies and student work, by exploring lesson plans, by investigating in problem situations, and by examining Web resources.

The course addresses Number and Operations Standards as described in the National Council of Teachers of Mathematics (NCTM) Principles and Standards for School Mathematics (PSSM 2000):

Instructional programs from Prekindergarten through grade 12 should enable all students to:

• Understand numbers, ways of representing numbers, relationships among numbers, and number systems;
• Understand meanings of operations and how they relate to one another;
• Compute fluently and make reasonable estimates.

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Grades 6-8

MATH 125 Ahead of the Curve: Exponential and Other Functions (Grades 6-8)
Understanding functions is important to the study of algebra. Aligned with the NCTM Algebra Standard, this course focuses on identifying functions as linear or nonlinear, comparing properties of linear and exponential functions, and modeling various phenomena with functions. Learners will gain an understanding of functions and growth, identify student misconceptions about these concepts, and discuss strategies for teaching exponential functions.


MATH300 Applying the NCTM Principles to Grades 6-8
Applying the NCTM Principles to Grades 6-8 is an introduction to the six principles identified in the National Council of Teachers of Mathematics' Standards and Principles for School Mathematics. These principles are Equity, Curriculum, Teaching, Learning, Assessment, and Technology. Through a combination of text, video, and discussion features, the course presents key concepts and strategies for applying these principles in grades 6-8. As you move through the course, you will have opportunities to individualize your learning experience and design a plan to help you put what you've learned into practice.


MATH145 Calculating the Mathematics of Motion (Grades 6-8)
The traditional teaching of motion uses formulas with no connection to real life. In this course, learners collect data and draw conclusions about speed based on experience. This context based approach leads to greater understanding. Learners analyze motion using algebra and measurement and identify student difficulties when calculating motion. In the final project, learners design consecutive lessons for the math of motion.


MATH165 Enabling Students with Special Needs to Succeed in Math Class (Grades 4-8)
The Individuals with Disabilities Education Act of 1997 creates new challenges for educators. The requirement that students do more reading and writing and other elements of these new mathematics curricula presents extra challenges for students with attention, language, sensory, and other disabilities. This course helps educators develop ways to adapt their curricula, provide supportive scaffolds, and collaborate with special needs teachers to help all students succeed in their classrooms.

MATH230 Fostering Collaboration, Discussion, and Critical Thinking in Middle School Math (Grades 6-8)
This course presents proven critical thinking and cooperative learning strategies for teaching mathematics that can be enhanced by today's classroom technology. Learners will explore both software and Web activities specifically designed to support collaboration and problem solving within the curriculum and help students meet the standards. Please note: this course requires educators to work with students in order to complete some assignments.

MATH160 Gender Equity in the Mathematics Classroom (Grades 4-8)
This course explores ways of creating classroom environments in middle school that are supportive of girls' success in math. Building on what educators already know about good instructional practice, this course attends to the unique social and academic needs of girls at this point in their development, with an eye towards encouraging pursuit of mathematics in high school and beyond.


MATH210 Just the Stats: Data Analysis for Grades 6-8
This course is designed to bring learners up-to-date on the most effective ways to integrate technology into the teaching of Data Analysis, which is so important in today's information-rich world. Using the calculator, the computer, and the Internet, this course will focus on ways to provide students with the background they need to responsibly display and analyze data.


MATH150 Making Comparisons with Data Analysis (Grades 6-8)
Aligned with NCTM Standards, this course focuses on making comparisons, a central concept in middle school. Learners engage in the process of statistical investigation and gain an understanding of distribution, measures of spread, and graphical representations. Participants apply their experiences to instruction, analyze student work, and research ways to address student misconceptions. Learners design a sequence of lessons as a final project.


MATH185 Math in Everyday Life for Grades 6-8
This course will explore ways that educators can incorporate real-world math into the middle school classroom. Participants will learn exciting and effective ways to enrich their math curriculum while meeting national educational standards.


MATH240 Measurement: Surface Area and Volume in Grades 6-8
Geometry and measurement are important topics in the development of content knowledge and reasoning ability of middle school mathematics. In this course, learners will study NCTM Standards and other readings, solve problems and examine student work on problem-solving activities, investigate manipulative and technology resources, and participate in discussions to expand their knowledge of concepts of volume and surface area of three-dimensional shapes and geometric relationships for the middle school classroom. Concepts will be developed as exemplified in the NCTM Geometry and Measurement Standards for grades 6–8 and van Hiele’s model of development of geometric thought. The relationships among three-dimensional solids, surface area, and volume will be investigated using numeric, algebraic, and geometric representations throughout the course.


MATH215 The Odds Are Good: Probability for Grades 6-8
This course is designed to bring participants up to date on the most effective ways to teach this fascinating mathematics topic. After examining the latest recommendations from the NCTM, the course presents sample lessons created by math experts. It goes on to explore ways that educators can use the Internet and computer software to enrich students' learning environment.


MATH135 Patterns and Relations (Grades 6-8)
Patterns and relations are the core of algebra. Aligned with the NCTM Algebra Standard, this course focuses on how to represent, analyze, and generalize a variety of patterns. Learners will gain an understanding of the mathematics of patterns, identify what middle students commonly misunderstand, and develop strategies for teaching patterns. As a final task, the learner will discuss the importance of patterns and relations in the math education.


MATH170 Proportional Reasoning (Grades 6-8)
This course explores the difficulty in developing strong proportional reasoning skills. The course activities have been used in classrooms to target misconceptions about proportionality. Learners examine different methods of comparison, various ways to solve proportion problems, and intuitive approaches that students might use. Learners prepare a student interview and complete a final project in which they respond to a classroom case study.


MATH245 Rational Numbers, Fractions, Decimals and Percents in Grades 5-8
This course is about the meanings of fractions, decimals, and percents, and the difficulties that students have understanding these numbers. The activities in this course serve to deepen the learners’ knowledge of rational numbers, particularly with fractions, decimals and percents, and the interrelation among the three forms, and the difficulties these forms pose for students and teachers alike, especially if the students have not progressed from viewing fractions as portions to fractions as quantities. Readings provide background information on content and pedagogy. Video clips provide opportunities for the learners to observe students’ mathematical understanding and teacher-lead questioning techniques. The final project includes writing a short unit reviewing rational numbers that focuses on the number sense that students need to have before moving onto a unit where they are introduced to operations.


MATH130 Representing the Mathematics of Motion (Grades 6-8)
The mathematics of motion provides a way to represent and explore problems about the position of objects. Aligned with NCTM Standards, this course explores the relationship of motion and graphs. Learners will solve problems to understand the math of motion, reflect on student misconceptions, and develop strategies for teaching these concepts. As a final task, learners will create an activity for introducing the math of motion in middle school.


MATH200 Shaping Up: Teaching Geometry Using Technology in Grades 6-8
This course is designed to bring participants up to date on the most effective ways to teach geometry. After presenting the latest recommendations from the NCTM, the course looks at some sample lessons created by math experts. It goes on to explore ways that educators can take advantage of the Internet and computer software to help provide students with a rich learning environment.


MATH265 Spatial Reasoning in Grades 5-8
This course is about visualization and spatial reasoning and the importance these activities play in students' problem solving in many areas of grade 5-8 mathematics, including—but not restricted to—geometry. Learners will use online tools and paper cut-outs as they work to identify three-dimensional objects represented in two-dimensional forms, learn some techniques of perspective drawing, and derive formulas for the areas and volumes of various two- and three-dimensional objects. Readings and video clips encourage discussion about the importance of spatial reasoning and visualization, students' geometric concepts and common misconceptions, and classroom practices that could help students develop their spatial reasoning and visualization skills.


MATH140 Understanding Linear Functions (Grades 6-8)
This course explores linear functions and their real-life connections. It focuses on representing patterns; comparing multiple representations; identifying linear functions; and using the y = mx + b form. Learners will discuss linear situations, experience tools such as student interviews to understand learning, and develop strategies for teaching linear functions. As a final project, learners write a reflection based on student work.


MATH320 Understanding Probability in Grades 4-6
This course explores the concepts of probability, the intuition and problem solving skills related to probability, and the importance of being able to analyze probability and statistics used in the media. The learners will work through activities that will stretch their understanding of probability and data analysis. They will also consider how students understand these concepts through an examination of student work. This course emphasizes intuition, experimentation, and probabilistic reasoning.

MATH125 Ahead of the Curve: Exponential and Other Functions for Grades 6-8
Description: The study of algebra involves understanding linear and nonlinear functions. Differentiating between the two and using them effectively is essential to the study of higher mathematics. In this module, you will deepen your knowledge of the underlying mathematics in exponential functions by comparing them with other functions, both linear and nonlinear, while exploring ways to enrich the classroom experience for your students.

The course is designed to address the mathematics of exponential functions and the differences between exponential functions and other functions as described in the National Council of Teachers of Mathematics' (NCTM) Principles and Standards for School Mathematics (PSSM 2000) and focuses on the expectations for middle school and high school students:

"Instructional programs from pre-kindergarten through grade 12 should enable all students to understand linear and exponential functions. In grades 6-8 all students should:

• Identify functions as linear or nonlinear and contrast their properties from tables, graphs, and equations;
• Relate and compare different forms of representation for a relationship

Math 145 Calculating the Mathematics of Motion for Grades 6-8
Description: This course is designed to address the mathematics of algebra, measurement, and problem solving as described in the National Council of Teachers of Mathematics' (NCTM) Principles and Standards for School Mathematics (PSSM 2000) and focuses on the expectations for middle school and high school students:

"Instructional programs from pre-kindergarten through grade 12 should enable all students to-use mathematical models to represent and understand quantitative relationships; analyze change in various contexts; understand measurable attributes of objects and the units, systems, and processes of measurement; apply appropriate techniques, tools, and formulas to determine measurement.

Objective(s)	Standard
A deeper understanding of the underlying mathematics for representing and analyzing motion situations and structures using algebra and measurement;	Math 6.7; 6.8; 6.9; 6.10; 6.11; 6.12; 6.13; 6.18; 6.23; 7.4; 7.5; 7.6; 7.7; 7.8; 6.16; 7.17; 7.18; 7.19; 7.22; 8.3; 8.4; 8.5; 8.6; 8.7; 8.11; 8.12; 8.14; 8.15; 8.16; 8.17
Practice in understanding what middle school students commonly understand and misunderstand about calculating motion;	No Direct Alignment
Strategies to improve the way you teach problem solving about motion.	No Direct Alignment

MATH165 Enabling Students with Special Needs to Succeed in Math Class (Grades 4-8)
Description: "Equity requires:

• high expectations and worthwhile opportunities for all.
• acc