MAJOR CONCEPTS

Segment One

• Multiply and divide positive multi-digit numbers with decimals to the thousandths
• Solve multi-step, real-world problems involving any of the four operations with positive multi-digit decimals or positive fractions, including mixed numbers
• Compute products and quotients of positive fractions by positive fractions, including mixed numbers
• Rewrite positive rational numbers in different but equivalent forms, including fractions, terminating decimals, and percentages
• Define, plot, order, and compare rational numbers
• Represent and compare rational numbers that have opposite direction on a number line and explain the meaning of zero within a real-world context
• Find, interpret, and compare the absolute values of rational numbers as the distance from zero on a number line, given a mathematical or real-world context
• Define, plot, order, and compare rational numbers
• Evaluate positive rational numbers and integers with natural number exponents
• Rewrite the sum of two composite whole numbers having a common factor, as a common factor multiplied by the sum of two whole numbers
• Express composite whole numbers as a product of prime factors with natural number exponents
• Find the greatest common factor and least common multiple of two whole numbers given a mathematical or real-world context
• Add, subtract, multiply, and divide integers
• Translate written descriptions into algebraic expressions and translate algebraic expressions into written descriptions given a mathematical or real-world context
• Evaluate algebraic expressions using substitution and order of operations
• Apply the properties of operations to generate equivalent algebraic expressions with integer coefficients
• Determine which values make the equation or inequality true or false given an equation or inequality and a specified set of integer values
• Write and solve one-step equations in one variable using addition, subtraction, multiplication, and division within a mathematical or real-world context
• Translate a real-world written description into an algebraic inequality and represent the solution on a number line
• Add, subtract, multiply, and divide rational numbers (accelerated)
• Solve real-world problems involving any of the four operations with rational numbers (accelerated)
• Solve mathematical problems using multi-step order of operations with rational numbers including grouping symbols, whole-number exponents, and absolute value (accelerated)
• Apply properties of operations to add and subtract linear expressions with rational coefficients (accelerated)
• Determine whether two linear expressions are equivalent (accelerated)
• Write and solve one-step inequalities in one variable within a mathematical context and represent solutions algebraically or graphically (accelerated)

Segment Two

• Write and interpret ratios to show the relative sizes of two quantities given a real-world context
• Solve mathematical and real-world problems involving ratios, rates, and unit rates, including comparisons, mixtures, ratios of lengths and conversions within the same measurement system
• Determine a rate for a ratio of quantities with different units, and calculate and interpret the corresponding unit rate given a real-world context
• Generate or complete a two- or three-column table to display equivalent part-to-part ratios and part-to-part-to-whole ratios
• Apply ratio relationships to solve mathematical and real-world problems involving percentages using the relationship between two quantities
• Solve multi-step, real-world percent problems (accelerated)
• Apply ratios to solve real-world problems involving proportions (accelerated)
• Recognize and formulate a statistical question that would generate numerical data
• Find and interpret mean, median, mode, and range given a numerical data set within a real-world context
• Determine the minimum, the lower quartile, the median, the upper quartile, and the maximum given a box plot within a real-world context and use a summary of the data to describe the spread and distribution of the data
• Create box plots and histograms to represent sets of numerical data within real-world contexts
• Describe and interpret the spread and distribution of the data, including any symmetry, skewness, gaps, clusters, outliers, and the range given a histogram or line plot within a real-world context
• Determine and describe how changes in data values impact measures of center and variation given a real-world scenario
• Determine an appropriate measure of center or measure of variation to summarize numerical data, represented numerically or graphically, taking into consideration the context and any outliers (accelerated)
• Use the measure(s) of center and measure(s) of variability to make comparisons, interpret results, and draw conclusions about two populations given two numerical or graphical representations of data (accelerated)
• Use proportional relationships to make predictions about a population, given categorical data from a random sample (accelerated)
• Plot rational number ordered pairs in all four quadrants and on both axes and identify the x- or y-axis as the line of reflection when two ordered pairs have an opposite x- or y-coordinate
• Find distances between ordered pairs, limited to the same x-coordinate or the same y-coordinate, represented on the coordinate plane
• Solve mathematical and real-world problems by plotting points on a coordinate plane, including finding the perimeter or area of a rectangle
• Derive a formula for the area of a right triangle using a rectangle and apply the formula to find the area of a triangle
• Solve mathematical and real-world problems involving the area of quadrilaterals and composite figures by decomposing them into triangles or rectangles
• Apply formulas to find the areas of trapezoids, parallelograms, and rhombi (accelerated)
• Solve mathematical or real-world problems involving the area of polygons or composite figures by decomposing them into triangles or quadrilaterals (accelerated)
• Find the surface area of right rectangular prisms and right rectangular pyramids using the figure’s net given a mathematical or real-world context
• Solve mathematical and real-world problems involving the volume of right rectangular prisms with positive rational number edge lengths
• Determine the sample space for a simple experiment (accelerated)
• Find the theoretical probability of an event related to a simple experiment (accelerated)
• Interpret the likelihood of a chance event occurring and compare the probabilities of chance events (accelerated)
• Find experimental probabilities and compare them to theoretical probabilities (accelerated)