Grade 6 Mathematics

Required Materials:

You will need the following items to complete this course:

• Printer

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

Module 01: Rational Numbers

• Rational Numbers Introduction
• Rational Numbers Pretest
• Operations with Decimal Numbers
• Operations with Fractions
• Manipulating Positive Rational Numbers
• Opposites and Absolute Value
• Exponents
• Factoring

Module 02: Integers and Algebraic Expressions

• Integers and Algebraic Expressions Introduction
• Adding Integers
• Subtracting Integers
• Multiplying and Dividing Integers
• Operations with Absolute Value
• Translating Algebraic Expressions
• Evaluating Algebraic Expressions
• Properties of Operations

Module 03: Equations and Inequalities

• Equations and Inequalities Introduction
• Equations and Inequalities Pretest
• Evaluating Equations
• Solving One-Step Equations with Integers
• Writing One-Step Equations with Integers
• Solving One-Step Equations with Rational Numbers
• Translating Algebraic Inequalities
• Evaluating Inequalities

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

Module: Ratios and Rates

• Ratios and Rates Introduction
• Ratios and Rates Pretest
• Ratios
• Rates
• Two-Column Tables
• Three-Column Tables
• Percentages
• Multi-Step Percent Problems
• Proportions

Module 06: Statistics

• Statistics Introduction
• Statistics Pretest
• Statistical Measurements
• Box Plots
• Histograms and Line Plots
• Effects of Changes in Data
• Appropriate Measures
• Comparing Data
• Making Predictions

Module 07: Geometry

• Geometry Introduction
• Geometry Pretest
• Plotting Ordered Pairs
• Distance on the Coordinate Plane
• Perimeter and Area on the Coordinate Plane
• Finding Area Using Triangles and Rectangles
• Area of Polygons and Composite Figures
• Surface Area of Rectangular Prisms and Pyramids
• Volume of Rectangular Prisms