STREAM Online Math Courses

Algebraic Thinking (K-5)
JULY 9 – JULY 27
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 June 18, 2018 and close on July 9, 2018.

Algebraic Thinking (6-7)
JULY 9 – JULY 27
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 June 18, 2018 and close on July 9, 2018.

Linear Relationships (7-9) Formerly titled: Straight Talk: Linearity (7-9)
JULY 9 – JULY 27
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 the8th 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 June 18, 2018 and close on July 9, 2018.

Functions as Objects (HS)
JULY 9 – JULY 27
It’s time to fight back against the “function machine”! In this 3-week module we examine functions as objects in their own right, rather than treating them as rules, algorithms, or machines. We will explore Montana’s Common Core Standards for functions in high school with a focus on building functions. Finally, we will extend and complete our investigation with a modeling activity. Specific goals and activities include the following:
● Redefine it! Develop a fresh understanding of functions as objects that can be represented and manipulated mathematically.
● Move it! Use Desmos (free online software) effectively to discover and investigate function movement.
● Represent it! Study relationship between the four representations of functions: verbal, tabular, algebraic, and graphical.
Registration will open on June 18, 2018 and close on July 9, 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.

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.

EdReady for the Math Classroom Online Chat

EdReady Math- Join Ryan Schrenk to learn about all that EdReady has to offer, for free, to your class this spring! Learn best practices on using EdReady and how to best prepare your students for the next grade, or college! Log in through the Teacher Learning Hub and enroll in the Virtual Math Community to earn 1 renewal unit. Or paste this link into your browser (https://global.gotomeeting.com/join/804885669%20) to join the meeting!

American Indian Literature (for use in grades K-8) Indian Education for All Online Book Club Course

April 2 – May 22, 2018
This course serves as an opportunity for participants to explore OPI developed instructional units based on literature sent to all Montana elementary and middle school libraries alongside additional primarily fiction texts for use in grades K-8. The course will be divided into three parts: literature for K-2, literature for 3-5, and literature for 6-8. Many resources are place-based, either focused on Montana tribes or created by Montana Indian authors. Participants will read texts, engage in discussions, complete instructional activities, and examine accurate and authentic Native American fiction and nonfiction texts. Ultimately, participants will select texts and instructional units for immediate integration of IEFA into their classrooms. This course is rigorous and requires the participant complete extensive reading and access a number of texts through their school or public library or purchase said materials from WM-PLC or booksellers.
Objectives
Participants will:
1. Develop background knowledge of Indian Education for All (IEFA).
2. Read American Indian literature and explore the background and perspective of the authors.
3. Explore literature units developed by the Montana Office of Public Instruction, and examine ways to integrate them into their classroom setting.
4. Explore several instructional strategies to use with the anchor texts.
5. Discuss with colleagues ideas for implementing the Essential Understandings
Regarding Montana Indians and IEFA literature across grade levels and content areas.
6. Create a final project which integrates the materials and concepts covered.

Instructor: Erin Lipkind (erinlipkind@gmail.com)

Registration fee: $175

Credit: 30 OPI Renewal Units or 2 Semester Credits (semester credit is offered through the University of Montana and is an additional fee of $155. The course instructor will provide a separate registration form and instructions for submitting payment).
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The Boarding School Era Online Book Club

The WM-PLC is offering an online “book club” during the fall of 2016, October 24 – December 11. The book club course focuses on Indian Education for All content. Read and explore books focusing on the Boarding School Era including My Name is Seepeetza by Shirley Sterling, Shi-Shi-Etko by Nicola L. Campbell, Away from Home: American Indian Boarding School Experiences, 1879-2000 by Margaret L. Archuleta, Brenda J. Child, and K Tsianina Lomawaima, and Sweetgrass Basket by Marlene Carvell. Sindie Kennedy is the course facilitator.

The course begins on October 24 and concludes on December 11, 2016.