Unit 1: Number System Fluency
Students develop a unified understanding of number, recognizing whole numbers, fractions, decimals that terminate or repeat, and percentages as different representations of rational numbers. They perform multi-digit division and decimal operations. Students relate multiplication and division to understand and explain how to divide fractions by fractions. They divide fractions to find their decimal equivalents. They also use factors and multiples to solve real-world problems.

Unit 2a: Rational Explorations Students extend their understandings of number to the full system of rational numbers, which includes negative integers. They understand the meaning of negative numbers in real-world applications. They compare, order, and find the absolute value of rational numbers as well as graph points on number lines and in all four quadrants of the coordinate plane.

Unit 2b: Rational Operations
Students extend their knowledge of addition, subtraction, multiplication, and division to compute with rational numbers, particularly with negatives. They apply properties of operations to explain and interpret strategies to add, subtract, multiply, and divide negative integers. Students solve real-world and math problems involving the four operations.

Unit 3: Expressions Students understand the use of variables in algebraic expressions. They write expressions that correspond to given situations, identify parts of expressions, and both evaluate and simplify expressions. They include exponents in solving problems with order of operations. Students understand that expressions can be rewritten in different, equivalent forms using properties of numbers. Rewriting expressions in equivalent forms can clarify a real-world problem, leading to new insight.

Unit 4: One-Step Equations and Inequalities Students identify that solving an equation or inequality means finding the value(s) that make that equation or inequality true. They know a variable can represent an unknown value or any value from a set of numbers. They solve one-step equations and inequalities with rational numbers. They also graph the solution set of inequalities on a number line.

Unit 5a: Rate, Ratio, and Proportional Reasoning (Models to Equations) Students understand the concepts of ratio, rate, and unit rate. They use ratios to solve real-world and math problems using strategies such as equivalent ratio tables and model drawings. Students solve unit rate problems, percentage problems, and measurement conversions.

SECOND SEMESTER

Unit 5b: Applying Proportional Relationships
Students graph proportional relationships and interpret the unit rate. They distinguish proportional relationships from other relationships. In addition, students identify the independent and dependent variable on the graph. They write equations for proportional relationships, identifying the constant of proportionality (unit rate) and interpreting the points on the graph in context of the problem.

Unit 6: Area and Volume Students determine area, surface area, and volume of geometric figures. They develop and justify formulas for areas of triangles. Using this information, they find areas of special quadrilaterals and polygons by composing them into rectangles or decomposing them into triangles. Students find surface areas of prisms and pyramids by using their nets. They apply the formula for the volume of a right rectangular prism to find the volume of prisms with fractional edge lengths filled with fractional unit cubes.

Unit 7: Statistics Building on and reinforcing their understanding of number, students begin to develop their ability to think statistically. They recognize statistical questions. Students analyze numerical data distributions, which include dot plots, histograms, and box plots. They summarize these data distributions based on their center, spread, and shape. Because shape often affects the measures of center and measures of variability, students will decide which summary measures are most accurate based on the shape of a graph and the context in which the data was gathered.

Unit 8: Equations and Proportional Relationships Students solve multi-step problems with rational numbers, including solving more complex equations and inequalities. For equations, students solve and identify the operations required to solve. For inequalities, students solve and graph the solution set on a number line. Finally, students use proportional reasoning to solve problems about percentages and scale drawings. They are able to work with percentages in taxes, tips, interest, and commissions. They relate an object to its scale drawing using a scale factor, which allows them to compute lengths and areas of the object.