# 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.

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: Making Sense of Modeling (8-12)

APRIL 16 – MAY 4

In this 3-week non-facilitated module (see end of document for details) you will investigate standards-based mathematical modeling at the secondary level through the lenses of instruction and assessment. Specific goals and activities include the following:

Examine competing conceptions of modeling; study the CCSS definition of modeling and six components of the modeling cycle; rate modeling prompts on a scale from weak to strong.

Engage in a mathematical modeling activity designed for Algebra I, Geometry, or Algebra II.

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

Registration will open on March 26, 2018 and close on April 16, 2018.

Developing Fraction Sense (3-5) Formerly titled All About Fractions (3-5)

APRIL 16 – MAY 4

This 3-week module examines learning progressions related to fractions with a focus on foundational ideas that promote fraction sense and understanding. Specific goals and activities include the following:

● Examine ways to develop “fraction sense.”

● Discover how learning progressions for K-2 geometry support the development of fraction knowledge in grades 3-5.

● Explore fraction equivalence and comparing and ordering fractions using a variety of models and manipulatives.

Registration will open on March 26, 2018 and close on April 16, 2018.

Ratio and Proportion (6-7)

APRIL 16 – MAY 4

This 3-week module explores how a solid understanding of fraction concepts lays the foundation for students to successfully work with ratios and proportions. Specific goals and activities include the following:

● Recognize how learning progressions for fractions prepare students to successfully work with ratios and proportions.

● Solve fraction, ratio, and proportion problems in multiple ways.

● Develop an awareness of student misconceptions related to fraction/ratio/proportions and examine teacher strategies to resolve these misconceptions.

Registration will open on March 26, 2018 and close on April 16, 2018.

Functions as Objects (HS)

APRIL 16 – MAY 4

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 March 26, 2018 and close on April 16, 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

*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.

# STREAM Online Math Courses

*NEW! Non-Facilitated Module: You Decide How to Divide (3-5)

FEBRUARY 19 – MARCH 9

This 3-week non-facilitated module (see end of document for details) examines the prior knowledge and mathematical foundations that support students’ conceptual understanding of division. Specific goals and activities include the following:

● Investigate different models for multiplication and how they contribute to a multi-grade learning progression; analyze student work using these models.

● Explore a variety of models and concepual frameworks for division; analyze aspects of a student-centered classroom using several of these methods.

● Apply newly acquired knowledge of division models and methods in a teaching situation.

Registration will open on January 29, 2018 and close on February 19, 2018.

Mathematical Practices (K-8)

FEBRUARY 19 – MARCH 9

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.

Number Systems and Operations (K-3)

FEBRUARY 19 – MARCH 9

This 3-week module is designed for grades K-3 teachers. Participants in this module will examine learning progressions in Number and Operations with a focus on active engagement strategies that promote understanding of number sense. Specific goals include:

● Discover the “why” behind the importance of helping students meet standards.

● Recognize the differences and different uses of strategies vs. algorithms.

● Use learning progressions and standards to sort student work.

● Develop precise mathematics vocabulary.

Registration will open on January 29, 2018 and close on February 19, 2018.

Number Systems and Operations (4-7)

FEBRUARY 19 – MARCH 9

This 3-week module is designed for grades 4-7 teachers. Participants in this module will examine learning progressions in Number Systems and Operations, with a focus on active engagement strategies that promote understanding of number sense. Specific goals include:

● Examine how learning progressions build knowledge of number and operations.

● Align rich tasks to the Number and Operations content standards.

● Read how other teachers introduce big ideas about number.

● Create an “ideal” standards-based lesson plan.

Registration will open on January 29, 2018 and close on February 19, 2018.

# Montana Math Matters: Growth Mindset and Productive Struggle (Reed Point, MT)

Participants will learn how a growth mindset affects achievement in mathematics; learn instructional strategies to promote student perseverance and productive struggle and increase student math skills and knowledge; engage in math activities; and discuss strategies that can increase all students enjoyment and learning of mathematics.

All K-12 Math teachers and administration invited to attend.

Hardin: Saturday, January 20th with Brooke Taylor

Reed Point: Saturday, February 17th with Becky Berg

9:00am-3:30pm

Sign up at goo.gl/NEVX2E

# Lewistown Regional EdReady Montana Training

Virg Hale, EdReady Montana Ambassador, will help teachers and administrators learn how the EdReady Montana FREE Math program can enhance your classroom, providing tools from remediation & acceleration to class-room supplemental math materials.

Topics covered will include:

- creating and managing student and teacher accounts
- Genius SIS system
- assessment options
- reports
- case use

Training will benefit new schools and schools already using the program, and will include time to discuss implementation.

For

# EdReady Montana Math Program- Box Elder, MT Regional Training (make up for weather related cancellation of Box Elder training)

Virg Hale, EdReady Montana Ambassador, will help teachers and administrators learn how the EdReady Montana FREE Math program can enhance your classroom, providing tools from remediation & acceleration to class-room supplemental math materials.

Topics covered will include:

- creating and managing student and teacher accounts
- Genius SIS system
- assessment options
- reports
- case use

Training will benefit new schools and schools already using the program, and will include time to discuss implementation.

# 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

# ONLINE – STEM-Centric Mathematics (K-8)

This four week course, running from April 11 – May 6, will examine the learning processes in Mathematics, Science and Engineering with a focus on foundational ideas that promote mathematical understanding.

Specific goals and activities include the following:

- Develop an understanding of key attributes for an effective STEM learning environment
- Analyze and experience STEM-centric lesson components
- Examine and consider STEM resources
- Design STEM lessons aligned to the MCCSM

Register by April 15, 2016 on the Teacher Learning Hub.

# ONLINE – Number Systems & Operations (K-3)

This 3-week modules from April 11 – April 29 examines learning progressions in Number and Operations with a focus on active engagement strategies that promote understanding of number sense.

Specific goals include:

- Recognize the differences and different uses of strategies v. algorithms
- Examine learning progressions related to Number and Operations Incorporate models for active learning
- Develop precise mathematics vocabulary

Register by April 15, 2016 on the Teacher Learning Hub.