Philosophy of Mathematics
Mathematics is a universal language that establishes a foundation for analytical reasoning, making connections, solving authentic problems, and using representations to communicate abstract concepts. Developing mathematical literacy requires students to engage in the Standards for Mathematical Practice and to acquire the skills necessary for a productive life in a dynamic, information-based society.
We further believe:
- Mathematics is critical for all students.
- Students must use various representations and models as thinking tools to help build an understanding of abstract concepts.
- Mathematics provides order to abstract concepts.
- Mathematics trains the mind to be analytic, providing the foundation for intelligent and precise thinking.
- Computational and procedural fluency, conceptual understanding, and problem solving are mutually reinforcing components of mathematics instruction.
- Problem solving and application experiences are foundational and should be embedded throughout each student's mathematics education.
- Students must know when, how, and why they should apply strategies in mathematics.
- Students must develop the capacity to evaluate the reasonableness of solutions.
- Students must apply their mathematical thinking to justify their ideas and critique the reasoning of others.
- Perseverance in mathematics is an essential skill that all students must develop.
The curriculum communicates high standards and expectations for students to routinely apply the CCSS Mathematical Practices:
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Make sense of problems and persevere in solving them
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Reason abstractly and quantitatively
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Construct viable arguments and critique the reasoning of others
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Model with mathematics
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Use appropriate tools strategically
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Attend to precision
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Look for and make use of structure
Grade 5
Students focus intensively on the three critical areas specified by the Common Core State Standards for Mathematics in Grade Five:
- Developing fluency with addition and subtraction of fractions, and developing understanding of the multiplication of fractions and of division of fractions in limited cases (unit fractions divided by whole numbers and whole numbers divided by unit fractions).
- Extending division to 2-digit divisors, integrating decimal fractions into the place-value system, developing understanding of operations with decimals to hundredths, and developing fluency with whole number and decimal operations.
- Developing understanding of volume
Grade 6
- Connecting ratio and rate to whole number multiplication and division and using concepts of ratio and rate to solve problems.
- Completing understanding of division of fractions and extending the notion of number to the system of rational numbers, which includes negative numbers
- Writing, interpreting, and using expressions and equation
- Developing understanding of statistical thinking
Grade 7
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Developing understanding of and applying proportional relationships
- Developing understanding of operations with rational numbers and working with expressions and linear equations
- Solving problems involving scale drawings and informal geometric constructions, and working with two- and three-dimensional shapes to solve problems involving area, surface area, and volume
- Drawing inferences about populations based on samples
Grade 8, Pre-Algebra
- Formulating and reasoning about expressions and equations, including modeling an association in bivariate data with a linear equation, and solving linear equations and systems of linear equations
- Grasping the concept of a function and using functions to describe quantitative relationships
- Analyzing two - and three-dimensional space and figures using distance, angle, similarity, and congruence, and understanding and applying the Pythagorean Theorem
Grade 8, Algebra
- Relationships between quantities and reasoning with equations
- Linear and exponential relationships
- Descriptive statistics
- Expressions and equations
- Quadratic functions and modeling
