# Deepen Learning

## Content Standards

k-5

### Number & Operations—Base Ten

This three-day course focuses on Number and Operations in Base Ten for students in grades K–5. The emphasis of this course is on developing a foundation of understanding of multiplication and division, and on extending understanding of place value with whole numbers to decimals. Experiences and discussions help participants discern the role that place-value understanding and properties of operations.

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3-5

### Strategies for Supporting Fraction Sense

Course 1 of 2.  This two-day course focuses on the priority domain of Number and Operations–Fractions for students in Grades 3-5. The emphasis of the course is on building understanding of fractions as numbers and connections between whole number knowledge and fraction knowledge. The strategies and foundation developed in this course are prerequisites for the further work with fraction computation that is developed in Course 2, Making Sense of Fraction Computation.

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3-5

### Making Sense of Fraction Computation

Course 2 of 2.  This two-day course focuses on the priority domain of Number and Operations–Fractions for students in Grades 3-5. The emphasis of the course is on building understanding of fraction computation. In this course, participants learn to build on students’ understanding of whole number operations to make sense of fraction computation. Strategies that support the development of fraction operation sense are highlighted.

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6-8

### Ratios & Proportional Relationships

This two-day course explores proportionality, proportional relationships, and proportional reasoning, acknowledging that the ability to reason proportionally is at the forefront of the middle school mathematics curriculum. The course supports teachers with strategies to help make this content accessible to all students.

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6-8

### Expressions, Equations, and Functions

This course focuses on how students develop algebraic reasoning and an understanding of the different representations for functions. Teachers and coaches explore the progression of middle school content that develops an understanding of expressions, equations, and functions and prepares students for success in high school and beyond.

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k-5

### Measurement and Data

This two-day course focuses on the domain of Measurement and Data for students in grades K–5. The emphasis of this course is on developing understanding of the natural progressions in thinking that children pass through as they develop basic concepts of measurement. Experiences and discussions help participants understand the importance of providing students with many and varied measurement tasks. The tasks must be meaningful and require students to gather measurement data for a purpose or in connection with clarifying important ideas. Data investigations provide the opportunity to consider the components and skills involved with collecting, representing, and interpreting data.

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k-5

### Geometry – Elementary School

This course focuses on content from the domain of Geometry and connects to expectations in the geometric measurement content cluster from the domain of Measurement and Data. Participants gain an understanding of the levels of geometric thinking, the important measurement decisions students need opportunities to make, and types of learning experiences that promote rigorous thinking.

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6-8

### Geometry – Middle School

This course focuses on content from the domain of Geometry and connects to expectations in the geometric measurement content cluster from the domain of Measurement and Data. Participants gain an understanding of the levels of geometric thinking, the important measurement decisions students need opportunities to make, and types of learning experiences that promote rigorous thinking.

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9-12

### Geometry – High School

This course focuses on geometry experiences that formalize high school students’ geometry work in elementary and middle school by utilizing more precise definitions and developing careful proofs. During the course participants engage in activities devoted to plane Euclidean geometry, both synthetically (without coordinates) and analytically (with coordinates).

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9-12

### Connecting High School Content Using an Integrated Approach

This high school course focuses on math experiences that connect algebra, geometry, and statistics. Participants explore content designed to deepen and extend understanding of linear relationships.  This includes engaging in experiences that contrast linear and exponential functions as well as applying linear models to data that exhibit a linear trend.  During this course, participants also investigate how emphasizing properties and theorems about congruent shapes deepen students’ geometric understanding and examine the connection between geometry and algebra through the lens of analytic geometry.

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9-12

### High School Algebra and Functions

This two-day course focuses on the conceptual aspects of Algebra and Functions for students in high school with an emphasis on strategies and tools to help leverage students’ ways of thinking so they can approach any type of function, work with it, and understand how it behaves.

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## Instructional Strategies

k-5

### Math Workshop: Structures and Practices for Student Learning

Standards and student needs drive mathematics instruction. This course highlights Math Workshop, a model for organizing standards-based instruction to support all learners in the mathematics classroom. Participants engage in the Math Workshop model of instruction, reflect on how the structures and learning environment leverage increased learning for all students, and create a plan to implement Math Workshop in the classroom.

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k-8

### Supporting English Learners in Math

English learners need ongoing and explicit language instruction to access mathematical content. This course focuses on the types of support needed for English learners to be successful in mathematics. Participants gain the understanding and skills required to design lessons that increase English proficiency while simultaneously developing mathematical understanding as they analyze lessons designed for English learners. As the sessions build, participants learn how to use, and experience the benefits of, a lesson design process that supports differentiation for the varied levels of English learners in classrooms.

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### Number Talks: Fractions, Decimals, and Percentages

This full-day course focuses on number talks that build conceptual understanding of fractions, decimals, and percentages. Participants learn how to use this routine as a vehicle to focus on the essential understandings of rational numbers and develop a robust fluency.

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k-5

### Using Formative Assessment to Impact Student Learning – K-5

Merging ongoing assessment with instruction engages teachers and students in becoming partners to support student learning. Using ideas from INFORMative Assessment: Formative Assessment to Improve Mathematics Achievement, by Jeane M. Joyner and Mari Muri, this course supports participants’ extension and application of a fundamental understanding of formative assessment for the purpose of promoting student learning.

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6-12

### Using Formative Assessment to Impact Student Learning–6-12

Based on Math Solutions’ experience with the Gates Foundation Mathematics Design
Collaborative, this course helps high school teachers engage students in the rigorous mathematics called for in the Common Core State Standards. Using formative assessment lessons, produced by the Shell Centre in England and the University of California at Berkeley, participants extend and apply a fundamental understanding of formative assessment for the purpose of promoting student learning.

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k-5

### Number Talks: Whole Number Computation

This full-day course introduces educators to the theory, structure and focus of Number Talks. As participants interact throughout the day, they reflect on their current practices and target essential understandings about numbers and operations.

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pre-k-k

### Teaching Pre-School and Kindergarten Math

This course offers teachers of young children hands-on experiences with instructional strategies that promote the thinking and reasoning. Video clips are used to bring teachers into the young child’s classroom to see students grapple with counting and building and dealing with data. Participants have multiple and varied opportunities to consider instructional decisions, differentiation, and assessment.

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k-8

### Teaching Math through Problem Solving

This full-day course provides teachers with a firsthand experience of learning mathematics through problem solving. Through this experience, participants are introduced to approaches and strategies to help students build new mathematical knowledge and use a range of problem-solving strategies. Throughout the course, teachers experience and learn how to provide a classroom environment that encourages students to explore, take risks, and share their thinking.

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k-5

### Developing Number Sense

Number sense is a broad concept that covers a range of numerical thinking. This course helps teachers gain an understanding of what number sense is, why it is important, and what strategies they can use to help promote their students’ number sense. Through firsthand experiences, teachers explore their own number sense and are introduced to instructional approaches that promote thinking and communicating about numbers. Samples of student work help connect course investigations to teachers’ classroom needs.

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k-5

### Differentiating Mathematics Instruction

This course helps teachers understand what it means to support all students by differentiating three aspects of the math curriculum—content, process, and product. Teachers examine a variety of approaches that help them make instructional adjustments to content, provide activities that address how different students learn, and offer a variety of ways for students to demonstrate what they’ve learned.