# STREAM Online Math Courses

Geometric Thinking (K-3)

JUNE 11 – JUNE 29

This 3-week module investigates conceptually related and interdependent ideas about geometric shapes, geometric structure, and spatial relationships. Geometry is a particularly relevant area of mathematics for young children, who are naturally curious about their physical world. Specific goals and activities including the following:

● Examine properties [attributes] and categorization of two-dimensional shapes.

● Explore composition and decomposition of geometric shapes.

● Develop deeper understanding of spatial relations and spatial structuring.

Registration will open on May 21, 2018 and close on June 11, 2018.

Geometric Thinking (4-7)

JUNE 11 – JUNE 29

This 3-week module examines learning progressions in geometry with a focus on foundational ideas that promote geometric understanding. Specific goals and activities include the following:

● Recognize geometric shapes and their components (e.g., sides, angles, faces)

● Learn properties of geometric figures and categorization based on those properties

● Develop strategies for composing and decomposing geometric shapes

● Engage in spatial relations and spatial structuring

Registration will open on May 21, 2018 and close on June 11, 2018.

Exploring Transformations (7-9) Formerly titled: Movin’ Around: Transformations (grades 7-9)

JUNE 11 – JUNE 29

This 3-week module is based on Montana’s Common Core Standards for 8th grade geometry with a focus on transformations (translations, rotations, reflections, and dilations). We will examine students’ perceptions about transformations, explore and justify relationships between figures, and discover geometric connections to similarity, proportion, and slope. Specific goals and activities include the following:

● Identify and analyze common misconceptions in students’ understanding of transformations.

● Investigate model lessons dealing with important concepts related to rigid transformations and congruence versus similarity.

● Explore how to support students’ use of the Mathematical Practices through informal geometric proof and modeling.

Registration will open on May 21, 2018 and close on June 11, 2018.

Transformations and Proof (HS) Formerly titled Geometry: Transformations (HS)

JUNE 11 – JUNE 29

The introduction of the Common Core standards inspired a change in the mindset of “basing transformations on congruence” to the more intuitive approach of “basing congruence on transformations.” In modern geometry, the traditional arguments justifying congruence and similarity are more effectively supported by rigid transformations and dilations. In this 3-week module, we examine how transformations are applied to justify congruence and similarity. Specific goals and activities include the following:

● Examine and connect properties of transformations through constructions using GeoGebra.

● Experience the shift to justifying congruence and similarity through transformations.

● Revisit fundamental geometric theorems and prove them through transformations.

Registration will open on May 21, 2018 and close on June 11, 2018.

Making Sense of Modeling (8-12)

June 11- June 29

During this module, you will learn about facets of mathematical modeling instruction and assessment in high school. Specific goals and activities include the following:

● Recognize competing conceptions for the term “modeling”, understand the MCSM definition of modeling and the six components of the modeling cycle, and rate modeling prompts on a scale from weak to strong;

● Engage in a mathematical modeling activity in Algebra I, Geometry, or Algebra II; and,

● Understand best practices for assessment in mathematical modeling and apply an assessment rubric to student work.

Register for all courses at the OPI Teacher Learning Hub, http://learninghub.mrooms.net

Successful completion of each STREAM module earns 15 OPI renewal units.

# STREAM Online Math Courses

*NEW! Non-Facilitated Module: Fraction Models and Operations (3-5)

JANUARY 22 – FEBRUARY 9

This 3-week non-facilitated module (see end of document for details) examines learning progressions and models related to operations on fractions. Another module, Developing Fraction Concepts 3-5, explores the meaning of “fraction” and fundamental concepts of equivalence and comparison. This module goes a step further to examine conceptual understanding of fraction operations and the models used to develop these concepts. Specific goals and activities include the following:

Examine different types of conceptual models used to represent fraction operations.

Discover how learning progression guide students’ developing knowledge of fraction operations in grades 3-5.

Explore and apply fraction operations in real world contexts.

Registration will open on January 1, 2018 and close on January 22, 2018.

Measurement (K-3)

This 3-week module primarily focuses on measurement, the K-3 learning progressions related to measurement, and foundational ideas that promote deeper understanding of measurement concepts. Specific goals and activities include the following:

● Develop enduring understandings of measurement attributes, processes, and tools.

● Explore relationships among units, attributes, and measures within a system of measurement.

● Engage in authentic problem-solving using tools that can be applied in the classroom.

Registration will open on January 1, 2018 and close on January 22, 2018.

Describing Data (4-7)

JANUARY 22 – FEBRUARY 9

This 3-week module explores how data and statistics concepts are developed in grades 4 through 7. Specific goals and activities include the following:

Standards-Based Teaching

Renewing Educators Across Montana

Gain familiarity with the data and statistics standards and learning progressions.

● Identify statistical vs. non-statistical questions and scenarios.

● Learn how to select appropriate representations for data and appropriate statistical measure to describe a data set.

● Practice data analysis and statistical summary on a real data set drawn from an elementary school setting.

Registration will open on January 1, 2018 and close on January 22, 2018.

Statistics: Inferences (HS)

JANUARY 22 – FEBRUARY 9

Statistics and Probability do not appear as stand-alone topics in Montana’s Common Core State Standards. These concepts are dispersed throughout all high school mathematics courses with an emphasis on informed decision making. The power of statistics and probability to understand the world we live in is some of the most applicable knowledge students can acquire in our classrooms. Specific goals and activities include for this 3-week module include:

● Understand how key concepts in statistics and probability develop along a learning progression.

● Discover how knowledge of statistics and probability leads into making inferences, predictions, and decisions.

● Explore how mathematical modeling enhances teaching probability and statistics – or do statistics and probability enhance the teaching of modeling?

Registration will open on January 1, 2018 and close on January 22, 2018.

Register for all courses at the OPI Teacher Learning Hub, http://learninghub.mrooms.net

Successful completion of each STREAM module earns 15 OPI renewal units