United States · Common Core State Standards
6th Grade Mathematics
This course transitions students from elementary arithmetic to algebraic reasoning. Students explore proportional relationships, the system of rational numbers, and the foundational language of expressions and equations.
01Ratios and Proportional Reasoning
Students develop a formal understanding of ratios and rates to solve real world problems involving multiplicative comparisons.
Students will define ratios and use ratio language to describe relationships between two quantities.
Students will explore various ways to represent ratios, including using fractions, colons, and words, and understand their equivalence.
Students will define unit rates and apply ratio reasoning to calculate them in various real-world contexts.
Students will solve problems involving unit rates, including those with unit pricing and constant speed.
Students will connect the concept of percent to a rate per 100 and represent percentages as ratios and fractions.
Students will solve problems involving finding the whole, finding a part, or finding the percentage of a quantity.
Students will use ratio tables and graphs to represent equivalent ratios and solve problems.
Students will use ratio reasoning to convert measurement units within and between systems.
Students will use visual models and equations to interpret and compute quotients of fractions.
Students will solve real-world problems involving division of fractions by fractions.
Students will fluently divide multi-digit numbers using the standard algorithm.
Students will fluently add and subtract multi-digit decimals using the standard algorithm.
Students will fluently multiply and divide multi-digit decimals using the standard algorithm.
02The Number System, Rational Numbers, and Expressions
Develops number sense across three CCSS domains: fraction division and decimal computational fluency (6.NS.A–B); integers, absolute value, rational numbers, and the coordinate plane (6.NS.C); and writing, evaluating, and solving algebraic expressions, equations, and inequalities (6.EE).
Students will find the greatest common factor (GCF) and least common multiple (LCM) of two whole numbers.
Students will apply GCF and LCM to solve real-world problems, including distributing items evenly or finding when events will recur.
Students will understand positive and negative numbers in real-world contexts and represent them on a number line.
Students will understand the concept of opposites and interpret absolute value as magnitude.
Students will compare and order integers using number lines and inequality symbols.
Students will extend their understanding of the number line to include all rational numbers, including fractions and decimals.
Students will locate and plot points using ordered pairs across all four quadrants.
Students will draw polygons in the coordinate plane and calculate side lengths and perimeter.
Students will use variables to represent numbers and write expressions for real-world problems.
Students will evaluate expressions at specific values of their variables, including those with exponents.
Students will apply properties of operations to generate and identify equivalent expressions.
Students will understand that solutions to equations and inequalities are values that make them true.
Students will use inverse operations to isolate variables and solve one-step equations.
03Geometry and Statistics
Develops geometric reasoning and statistical thinking across two CCSS domains: area of triangles and quadrilaterals, volume of rectangular prisms, and surface area using nets (6.G); and statistical questions, measures of center, measures of variability, and data summaries (6.SP). Also introduces dependent and independent variable relationships (6.EE.C).
Students will solve one-step inequalities and represent their solutions on a number line.
Students will use variables to represent two quantities that change in relationship to one another.
Students will write an equation to express one quantity as a dependent variable of the other, and graph the relationship.
Students will find the area of triangles by decomposing them into simpler shapes or using formulas.
Students will find the area of various quadrilaterals (parallelograms, trapezoids, rhombuses) by decomposing them.
Students will find the area of complex polygons by decomposing them into rectangles and triangles.
Students will calculate the volume of rectangular prisms with fractional edge lengths using unit cubes and formulas.
Students will use two-dimensional nets to represent three-dimensional figures.
Students will calculate the surface area of three-dimensional figures using nets.
Students will recognize statistical questions that anticipate variability in data.
Students will calculate and interpret the mean and median of a data set.
Students will calculate and interpret the range and interquartile range (IQR) of a data set.
Students will summarize numerical data sets in relation to their context, including measures of center and variability.
04Data Displays and Cumulative Review
Extends statistical reasoning through histograms, box plots, interpretation of data distributions, and selection of appropriate measures of center and variability (6.SP). Concludes with a structured cumulative review of all Grade 6 CCSS domains: ratios and proportional reasoning (6.RP), the number system (6.NS), expressions and equations (6.EE), and geometry (6.G).
Students will create and interpret dot plots and histograms to display data distributions.
Students will create and interpret box plots to summarize and compare data distributions.
Students will interpret various data displays, including dot plots, histograms, and box plots, to answer statistical questions.
Students will understand methods for collecting data and organizing it for analysis.
Students will describe the overall shape, center, and spread of data distributions.
Students will choose appropriate measures of center and variability based on the shape of the data distribution.
Students will review and apply concepts of ratios, rates, and proportional reasoning to solve complex problems.
Students will review and apply operations with fractions, decimals, and integers, including GCF and LCM.
Students will review and apply concepts of rational numbers, absolute value, and graphing on the coordinate plane.
Students will review and apply writing, evaluating, and solving expressions and one-step equations/inequalities.
Students will review and apply concepts of area, surface area, volume, and statistical data analysis.