# STREAM: Fraction Models and Operations (3-5)

This 3-week STREAM module 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.

15 Renewal Units

Enrollment opens – May 12, 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: Ratios & Proportions (6-7)

This course explores how a solid understanding of fraction concepts lays the foundation for students to successfully work with ratios and proportions. Participants will: recognize how learning fraction progressions prepare students to work with ratios/proportions; solve fraction, ratio, and proportion problems in multiple ways; develop an awareness of misconceptions related to fractions, ratios, proportions and examine strategies to resolve them.

15 Renewal units

Enrollment opens – October 14, 2018

# 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