• # Grades 6-8: A Story of Ratios

• ## Grade 6: Sixth grade mathematics is about (1) connecting ratio and rate to whole number multiplication and division and using concepts of ratio and rate to solve problems; (2) completing understanding of division of fractions and extending the notion of number to the system of rational numbers, which includes negative numbers; (3) writing, interpreting, and using expressions and equations; and (4) developing understanding of statistical thinking.

• Fluency: Multi-digit division
• Fluency: Multi-digit decimal operations
• Understand ratio concepts and use ratio reasoning to solve problems.
• Apply and extend previous understandings of multiplication and division to divide fractions by fractions.
• Apply and extend previous understandings of numbers to the system of rational numbers (positives & negatives, fractions & whole numbers)
• Apply and extend previous understandings of arithmetic to algebraic expressions.
• Reason about and solve one-variable equations and inequalities.
• Represent and analyze quantitative relationships between dependent and independent variables.

## Grade 7: Seventh grade mathematics is about (1) developing understanding of and applying proportional relationships; (2) developing understanding of operations with rational numbers and working with expressions and linear equations; (3) 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; and (4) drawing inferences about populations based on samples.

• Analyze proportional relationships and use them to solve real-world and mathematical problems.
• Apply and extend previous understandings of operations with fractions to add, subtract, multiply, and divide rational numbers.
• Use properties of operations to generage equivalent expressions.
• Solve real-life and mathematical problems using numerical and algebraic expressions and equations.

## Grade 8: Eighth grade mathematics is about (1) 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; (2) grasping the concept of a function and using functions to describe quantitative relationships; (3) analyzing two- and three-dimensional space and figures using distance, angle, similarity, and congruence, and understanding and applying the Pythagorean Theorem.

• Work with radicals and integer exponents.
• Understand the connections between proportional relationships, lines, and linear equations.
• Analyze and solve linear equations and pairs of simultaneous linear equations.
• Define, evaluate, and compare functions.
• Understand congruence and similarity using physical models, transparencies, or geometry software.
• Understand and apply the Pythagorean Theorem (at the end of year ~ May)

Source: A Story of Ratios: A Curriculum Overview for grades 6-8