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June 2018
Free

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. To register for this course, go to the Teacher Learning Hub. Registration will open…

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Free

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 To register for this course, go to the Teacher Learning Hub. Registration will open on May 21, 2018 and close…

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Free

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…

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Free

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: Examining and connecting properties of transformations through constructions using GeoGebra. Experiencing…

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July 2018
Free

Algebraic Thinking (K-5)

July 9 - July 27

This 3-week course 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. To register for…

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Free

Algebraic Thinking (6-7)

July 9 - July 27

This 3-week course 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…

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Free

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 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…

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Free

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…

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