# 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: Statistical Inferences (HS)

Statistics and Probability do not appear as stand-alone topics in Montana’s Content 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.

15 Renewal Units

Enrollment Opens – February 10, 2018

# EdReady Montana Sidney Regional Training- Math

September 14th: 4th—12th Grade Math 8:30—11:30 AM,

Fairview High School 713 Western Ave, Fairview MT. Renewal Units available; please bring your laptop. Learn how EdReady Montana, a FREE math & English program can enhance your classroom, providing tools from remediation & acceleration to classroom supplemental math & English materials. Topics covered will include: creating and managing student and teacher accounts, Genius SIS system, assessment options, reports, and case use. Training will benefit new schools and schools already using the program, and will include time to discuss implementation.

# Implementing the Standards for Mathematical Practices Workshop – Patterns and Algebraic Thinking

What does a classroom environment look like in which the Standards for Mathematical Practices are really alive?

Join us this summer to experience first -hand such an environment. The mathematical content focus will be *Patterns and Algebraic Thinking*.

**Together with other K-20 teachers of math in your area:**

- Solve challenging and engaging problems both collaboratively and as independent problem solvers.
- Live and learn mathematics within an environment that models optimal classroom practice.
- Deepen your own mathematical understanding while learning how to support students as powerful users of mathematics.
- Learn how to support a range of student needs from struggling students to advanced learners – within one classroom and without labeling students.

So put the dates on the calendar and get ready for a fun and challenging five days of math with some of the most amazing teachers you will come to know.

**When**: August 13 – 17 from 8:30 to 4:00 at Salish Kootenai College, Pablo, MT

**Cost**: Free of charge – lunch will not be provide

**Credit**: Graduate level continuing education credits will be offered through the University of Montana. Information regarding these credits will be included in a follow-up email once you have registered. OPI Renewal Units will also be available.

**On-Line Registration**: **http://blogs.polson.k12.mt.us/fraction Please provide your summer contact information.**

**Registration**** Deadline: **June 1, 2018

**More Information**: contact Polly Dupuis at pdupuis@polson.k12.mt.us

# 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.

# Virtual Math Community – Planning Math Lessons with CHAMPS

CHAMPS – Have you ever created an amazing lesson plan with activities and groupings that completed flopped? Come learn about CHAMPS behavior “management” outline. CHAMPS is both a planning tool for teachers as well as wording you can use with your students to help bring clear expectations to allow your lesson plans to thrive.

Join the GoTo Meeting at 3:45 on Tuesday, April 25.

# 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: 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 – Number Systems & Operations (4-7)

This 3-week module running from April 11 – 29 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 learning progressions related to Number Systems and Operations (4-7)
- Align tasks to the Number and Operations content standards
- Read professional articles
- Create a learning plan

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