# STREAM: Geometric Thinking (K-3)

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. Participants will: examine properties and categorization of two-dimensional shapes; explore composition and decomposition of geometric shapes; develop deeper understanding of spatial relations and spatial structuring.

15 Renewal Units

Enrollment opens – March 17, 2018

# STREAM: Geometric Thinking (4-7)

This 3-week module examines learning progressions in geometry with a focus on foundational ideas that promote geometric understanding. Participants will:

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.

15 Renewal Units

Enrollment opens – March 17, 2018

# STREAM: Exploring Transformations (7-9)

This 3-week module is based on Montana’s Content Standards for 8th-grade geometry with a focus on 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.

15 Renewal Units

Enrollment Opens – March 17, 2108

# STREAM: Developing Fraction Sense (3-5)

This course examines learning progressions related to fractions, with a focus on foundational ideas that promote fraction sense and understanding. Participants will: examine ways to develop “fraction sense.”; discover how learning progressions for K-2 geometry support the development of fraction knowledge in 3-5; explore fraction equivalence, comparing and ordering fractions using models and manipulatives.

15 Renewal Units

Enrollment Opens – December 17, 2018

# STREAM: Transformations and Proofs (HS)

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.

15 Renewal Units

Enrollment opens – December 17, 2018

# 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: Geometric Measurement (K-5)

MARCH 19 – APRIL 6

This 3-week non-facilitated module (see end of document for details) elaborates learning steps that students follow to acquire conceptual understanding of linear measurement, perimeter, area, and volume. Only after the conceptual knowledge is solidly developed are students able to accurately apply formulas and choose appropriate tools. Specific goals include:

● Recognize how to incorporate the eight Mathematical Practices into lessons and activities.

● Develop conceptual progressions for learning perimeter, area, and volume in grades K-5.

● Analyze conceptually taught lessons to identify learning progressions within the lesson and identify student misconceptions.

● Solve, share and defend solutions for perimeter, area, and volume problems.

Registration will open on February 26, 2018 and close on March 19, 2018.

Mathematical Practices (K-8)

MARCH 19 – APRIL 6

This 3-week module provides teachers with strategies for embedding the Mathematical Practices into everyday instruction and for incorporating modeling and other STEM-focused activities into lessons and activities. Specific goals and activities include the following:

Recognize the eight Mathematical Practices and how to incorporate them into lessons and activities.

● Analyze videos of exemplary teaching and identify the Mathematical Practices in use.

● Revise existing lessons to engage students in specific Mathematical Practices.

Registration will open on February 26, 2018 and close on March 19, 2018.

Algebraic Thinking (K-5)

MARCH 19 – APRIL 6

This 3-week module will examine learning progressions that illuminate early stages of algebraic thinking and develop the foundation for later success in algebra. Specific goals and activities include the following:

● Explore how addition, subtraction, multiplication, and division operate under the same properties in algebra as they do in arithmetic.

● Recognize variables as tools that are used to describe mathematical ideas in a variety of ways.

Develop strategies for describing relationships among quantities to determine equivalence or inequality.

Registration will open on February 26, 2018 and close on March 19, 2018.

Algebraic Thinking (6-7)

MARCH 19 – APRIL 6

This 3-week module is designed to draw out high-level algebraic thinking from middle grades students. The focus is on using the 6th and 7th grade standards for expressions and equations as a vehicle to examine teacher practice and improve students’ algebraic thinking. Specific goals and activities include the following:

● Define algebraic thinking and reasoning through the “Habits of Mind” framework.

● Evaluate the way teachers talk to and question students about expressions, equations, and inequalities.

● Explore the standards for expressions and equations and the Mathematical Practices through engaging problems.

● Apply algebraic thinking to STEM and real-world problem solving lessons.

Registration will open on February 26, 2018 and close on March 19, 2018.

Linear Relationships (7-9) Formerly titled: Straight Talk: Linearity (7-9)

MARCH 19 – APRIL 6

In this 3-week module we will examine how the concept of proportionality is related to the study of linear equations. We will explore Montana’s Common Core Standards for Probability and Statistics in the 8th grade, focusing on the study of bivariate data. Finally, we will extend our investigation to a study of functions using time versus distance as a context. Specific goals and activities include the following:

● Examine student work and create activities to strengthen students’ understanding of linearity and proportion.

● Use GeoGebra (free, downloadable software) to “dive into data” and ultimately create a standards-based lesson for probability and statistics.

● Study, create, and compare three principal representations of functions.

Registration will open on February 26, 2018 and close on March 19, 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.