Mathematics

At AVS, students develop a strong, flexible number sense in order to provide the fundamentals needed for problem-solving.

By providing students with a variety of meaningful tasks and activities, students gain the capacity to flexibly work with number systems and build conceptual understanding of the different math domains. From here, procedural fluency is developed through classroom activities, such as number talks, games, and puzzles. By way of independent, partner, small group, and whole class learning, students engage in integrated projects to explore problems in depth and discover numerous methods to solve these problems. In addition, students construct viable arguments for solutions with efficiency, accuracy, and flexibility.

Students investigate and explore mathematics within hands-on experiences, such as designing and measuring animal play areas and learning coordinate planes through playing Battleship. Through mathematically rich activities, students expand their problem-solving skills by developing their abilities to recognize patterns, creating representations, making generalizations, and learning to choose tools and strategies to support their reasoning. Critical-thinking and communication skills are strengthened as students collaborate with teammates to share their own mathematical reasoning and constructively critique the arguments of others.

 

LS Mathematics 

Lower School students develop a rich conceptual understanding, procedural fluency, and real-world application of the following domains: 

• Number sense 
• Algebraic thinking 
• Measurement and geometry 
• Statistics, data analysis, and probability 
• Mathematical reasoning 

Students investigate and explore mathematics through hands-on experiences, such as designing and measuring animal play areas or creating factories to deepen their understanding of place value. These mathematically rich activities help students enhance their problem-solving skills by recognizing patterns, creating representations, making generalizations, and learning to select the appropriate tools and strategies to support their reasoning. Critical-thinking and communication skills are strengthened as students collaborate with teammates to share their own mathematical reasoning and constructively critique the arguments of others. 

Our students develop a strong, flexible number sense, which serves as the foundation for effective problem-solving. By engaging in a variety of meaningful tasks and activities, students learn to work flexibly with number systems and build a conceptual understanding across different math domains. Procedural fluency is then developed through engaging classroom activities, such as number strings, games, and puzzles. Whether working independently, in pairs, small groups, or as a whole class, students engage in integrated projects that allow them to explore problems in depth and discover multiple methods for solving them. Additionally, students learn to construct viable arguments for their solutions, demonstrating efficiency, accuracy, and flexibility.

From Junior Kindergarten through fifth grade, our math curriculum is designed to maintain understanding through continuous, spiraling review, ensuring that students progress along a continuum that prevents gaps in learning and fosters an appreciation of math in real-world applications. The following key areas form the core of our math instruction:

• The Number System and Place Value 
• Fractions/Decimals/Percents 
• Addition and Subtraction 
• Multiplication/Division 
• Patterns and Algebraic Thinking 
• Time and Money 
• Measurement Comparison 
• Graphing/Charts/Data Analysis 
• Perimeter/Area/Volume 
• Two and Three Dimensional Shapes and Angles 
• The Coordinate Plane 

At Alta Vista the emphasis of mathematics. is to develop a strong, flexible number sense in order to provide the fundamentals for problem solving.

By providing students with a variety of meaningful tasks and activities, students gain the capacity to flexibly work with number systems and build conceptual understanding of the different mathematical domains. From here, procedural fluency is developed through classroom activities such as problems of the month, interactive online simulations, and rich tasks.

 

Alta Vista Middle School 

MS Math Curriculum Overview

Mathematics

At AVS, the emphasis in middle school mathematics is on developing a robust and flexible number sense, which provides the foundation for effective problem-solving. Students are engaged with a variety of meaningful tasks and activities that enable them to work flexibly with number systems and build conceptual understandings across different mathematical domains. Procedural fluency is developed through activities such as problem strings, interactive online simulations, and rich, context-based tasks.

Through independent work, partner work, small group collaborations, and whole-class learning, students participate in integrated projects that allow them to delve deeply into complex problems, crafting efficient and effective strategies for solving them. They are also encouraged to construct viable arguments for their solutions, demonstrating logical thinking, accuracy, and flexibility.

The curriculum reinforces big ideas to cultivate lifelong mathematicians who continuously develop, utilize, and reflect upon a repertoire of strategies during the problem-solving process. Through mathematically rich activities, students expand their problem-solving abilities by recognizing patterns, creating representations, making generalizations, and learning to select appropriate tools and strategies to support their reasoning. Critical thinking and communication skills are strengthened as students collaborate with peers to share mathematical reasoning and constructively critique each other's arguments.

Courses Include

• Ratio and Rationals

Ratios & Rationals acts as a fundamental step into middle school mathematics with a heavy emphasis on fractions, ratios, and rates. These concepts are fundamental to understanding relationships in everyday life and understanding the behavior of linear functions. Continuing the strong foundation of rational numbers laid in the lower school AVS math courses, R&R extends these concepts and makes connections between operations with rational numbers to algebraic expressions and equations. Students also further develop their understanding of three dimensional geometric figures as they apply to surface area and volume. Data collection and analysis plays an important role as students begin working with spreadsheets to summarize and analyze data sets.

• Probability and Proportions

In this 7th grade course, students develop the fundamental tools one needs to be prepared for Algebra by focusing on core understandings needed to think algebraically. After mastering integer operations, we work calculating percentage change of real numbers. Students then spend time developing an understanding of ratios, proportionality and scale factor. From there we move into geometry, with an in depth study on circles, triangles, and angle relationship theorems. We then use these theorems to build students’ understanding of expressions, equations, and inequalities. Students then move on to data analysis, statistics, and probability. Here students investigate conditional probability given fair and unfair conditions, measures of variability, and best representations of a given data set.

• Algebra 1

This high school level Algebra 1 course follows standards set in the California Mathematics Framework for High School Algebra 1 and is intended to develop fluency with linear, quadratic, and exponential functions. The critical areas of instruction involve deepening and extending students’ understanding of linear and exponential relationships by comparing and contrasting those relationships and by applying linear models to data that exhibit a linear trend. In addition, students engage in methods for analyzing, solving, and using exponential and quadratic functions.

• Data Analysis (8th Grade Math Elective)

Data Analysis is designed to introduce students to the exciting opportunities available at the intersection of data analysis, computing, mathematics, and the humanities through interdisciplinary projects and rigorous discussion. Data is everywhere, and this course will help prepare students to live in a world of data. DA focuses on practical applications of data collection, interpretation, and communication, to give students concrete and applicable skills. Instead of using small, tailored, curated data sets as in a traditional statistics curriculum, this curriculum engages students with a wider world of information that falls into the "Big Data" paradigm and is derived from students' lived experiences. In contrast to the traditional formula-based approach, statistical principles are taught by inference built from using automated randomization and simulations. Students will practice visualizing and communicating their findings from the data in verbal, visual, and multimedia formats. By the end of this course, students should find themselves with a transformed understanding of the many ways data and bias shape how one processes the world.