## Math

The Seventh Grade mathematics program helps students develop the habits and skills necessary to practice math like real-world mathematicians.

Seventh Graders start to practice mathematics, not as a set of facts and algorithms to be memorized or imitated, but as a creative exploration and reflection of our mind’s interaction with the world.  Throughout the course, students make meaning (i.e. discover the logic) of the concepts and refine their understanding by expressing it in precise language, diagrams, and symbols that convince and teach others. Work routines are designed to develop a balance of number sense and calculational fluency, depth of understanding, consideration of multiple strategies and representations, growing self-advocacy and responsibility for one’s own learning, and increasingly higher-quality solutions. The primary curriculum for middle school math is Open Up Resources – Illustrative Mathematics, which is supplemented by rich problems, extensions, and practical assignments.

Essential Questions

• What is the difference between an answer and a solution?
• How is proportionality connected to different areas of math?
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• Scale Drawing

• Explore characteristics of scale copies and scale factors
• Interpret and use scale drawings
• Develop measurement skills and understanding of units

Introducing Proportional Relationships

• Use scale factor and constant of proportionality analyze proportional relationships
• Find the constant of proportionality in tables, equations, graphs, and verbal descriptions
• Create and interpret equations and graphs of proportional relationships
• Refine skills in using the coordinate plane system
• Recognize what types of situations give rise to proportional relationships

Measuring Circles

• Explore the relationship between circumference, radius, and diameter
• Develop a more precise understanding of the characteristics of circle
• Understand informal derivations of the area and circumference formulas
• Apply formulas to solve abstract and real-world problems

Proportional Relationships and Percentages

• Deepen understanding of ratios, scale factors, unit rates, and proportional relationships
• Write and solve proportions
• Solve problems involving percent increase and decrease
• Solve problems involving percentage and percent rate (ex: tax, % error)

Rational Number Arithmetic

• Explore opposites, absolute value, and how signed number represent real quantities
• Develop fluency in arithmetic with signed numbers
• Extend use of the fraction bar to division involving variables
• Solve problems by interpreting negative numbers in context
• Introduce linear equations in one variable and the concept of a solution

Expressions, Equations and Inequalities

• Recognize correspondences between situations, diagrams, and equations representing relationships between two quantities
• Use algebraic methods to solve equations of the form px + q =r and p(x+q) = r
• Solve inequalities and interpret the solutions in context
• Explore equivalent linear expressions using properties of operations

Angles, Triangles, and Prisms

• Investigate whether sets of angles and side measurements determine triangles
• Develop the angle concepts: complementary, supplementary, vertical, and unique
• Analyze cross sections of prisms, pyramids, and polyhedral
• Use the formula for volume of a right rectangular prism
• Solve problems involving area, surface area, and volume

Probability and Sampling

• Design and use simulations to represent probabilities of outcomes (relative frequency) of chance experiments
• Represent sample spaces with multiple representations
• Calculate the number of outcomes in a sample space to find the probability of an event
• Evaluate different methods for obtaining a representative sample from a population
• Generate samples from a population and compare the distributions of the samples and population
• Compare two populations by comparing samples from each