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## Mathematics 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.

• 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

• 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