7th Grade Math

Students begin the course by developing a strong understanding of ratios and proportional relationships. They solve unit rate problems in a variety of settings, including cases involving fractions and mixed numbers, and they learn to interpret proportional relationships from tables, graphs, and verbal descriptions. This work then expands into percentages, where students analyze percent increase, percent decrease, percentage change, successive percentage changes, and applications in commerce and finance, including simple interest.

The course then broadens students' understanding of number through a sustained study of rational numbers. Students add, subtract, multiply, and divide positive and negative integers, fractions, and decimals, while also interpreting opposites, absolute value, reciprocals, and decimal representations of rational numbers. They evaluate numerical expressions involving rational numbers and positive integer exponents, building a more flexible and abstract understanding of arithmetic structure.

A substantial portion of the course is devoted to algebraic reasoning. Students simplify and factor linear expressions, solve one-step and multi-step linear equations, and work with equations involving fractions, decimals, and variables on both sides. They also study two-variable equations in the coordinate plane, graph linear relationships, solve introductory systems of equations, and analyze and solve linear inequalities. Throughout this work, students interpret expressions, equations, and inequalities in context and use them to model real-world situations.

Students then apply their reasoning skills in geometry. They study segments, angles, polygons, area, perimeter, scale drawings, circles, and solid figures. Along the way, they classify shapes, solve geometric measurement problems, and connect numerical and algebraic reasoning to geometric contexts, including composite shapes and scaled figures.

Finally, students develop their understanding of statistics and probability. They examine sampling methods, estimation, bias, and margin of error, and they represent and compare data using frequency tables, histograms, and measures of center and spread. The course concludes with probability, where students analyze sample spaces, calculate probabilities of simple and compound events, use simulations, and apply probability models to make predictions.

After successfully completing the 7th Grade Math course, students will be well prepared for more advanced work in algebra, geometry, and mathematical modeling.

• Solving unit rate problems, including unit prices and cases involving fractions and mixed numbers.
• Interpreting and analyzing proportional relationships from tables, graphs, and verbal descriptions.
• Applying percentages in a wide range of contexts, including percent increase, percent decrease, percentage change, successive percentages, commerce and finance, and simple interest.
• Addition and subtraction of rational numbers, including interpreting opposites, additive inverses, and absolute value.
• Multiplication and division of rational numbers, including working with negative fractions and decimals, reciprocals, zero, and multi-step problems.
• Understanding rational numbers as finite or repeating decimals and evaluating rational-number expressions.
• Evaluating expressions with positive integer exponents and rational bases, including squares and cubes of rational numbers.
• Simplifying and factoring linear expressions using like terms, the distributive law, negative signs, fractions, and greatest common factors.
• Solving one-step and multi-step linear equations, including equations with fractional coefficients, decimal coefficients, variables on both sides, and rational expressions.
• Working with two-variable linear equations in the coordinate plane, including identifying solutions and graphing lines.
• Solving introductory systems of linear equations by substitution.
• Solving, verifying, and graphing linear and compound inequalities, and representing their solutions on number lines.
• Modeling real-world situations using linear expressions, linear equations, and one-step and two-step inequalities.
• Evaluating and simplifying rational expressions and solving rational equations containing a fractional term.
• Geometry fundamentals, including parallel and perpendicular lines, segment relationships, angle relationships, polygons, and congruent figures.
• Solving problems involving perimeter, area, composite shapes, scale drawings, circles, and parts of circles.
• Calculating surface areas and volumes of selected three-dimensional figures and interpreting cross-sections of solids.
• Understanding sampling, estimation, bias, survey interpretation, and margin of error.
• Representing and comparing data using joint and cumulative frequency tables, histograms, measures of center, range, quartiles, mean absolute deviation, and standard deviation.
• Analyzing probability models, calculating probabilities of simple and compound events, using simulations, and applying probability to make predictions.