6: Grade 6

Grade 6

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Ratios, rates, and proportional reasoning extend into unit rate problems and percent applications. The number system expands to include negative numbers and rational number arithmetic; numerical and algebraic expressions, one-variable equations and inequalities, and dependent/independent variables introduce formal algebra. Area, surface area, and volume of 2D and 3D figures, along with statistical distributions and data displays, complete the grade.

6.1Use appropriate notations [a/b, a to b, a:b] to represent a proportional relationship between quantities and use ratio language to describe the relationship between quantities.6.10Locate integers and other rational numbers on a horizontal or vertical line diagram.6.11Find the position of pairs of integers and other rational numbers on the coordinate plane.6.12Explain the meaning of absolute value and determine the absolute value of rational numbers in real-world contexts.6.13Compare and order rational numbers and absolute value of rational numbers with and without a number line in order to solve real-world and mathematical problems.6.14Write, evaluate, and compare expressions involving whole number exponents.6.15Write, read, and evaluate expressions in which letters represent numbers in real-world contexts.6.16Generate equivalent algebraic expressions using the properties of operations, including inverse, identity, commutative, associative, and distributive.6.17Determine whether two expressions are equivalent and justify the reasoning.6.18Determine whether a value is a solution to an equation or inequality by using substitution to conclude whether a given value makes the equation or inequality true.6.19Write and solve an equation in the form of x+p=q or px=q for cases in which p, q, and x are all non-negative rational numbers to solve real-world and mathematical problems.6.2Use unit rates to represent and describe ratio relationships.6.20Write and solve inequalities in the form of x>c, x<c, x≥ c, or x ≤ c to represent a constraint or condition in a real-world or mathematical problem.6.21Identify, represent, and analyze two quantities that change in relationship to one another in real-world or mathematical situations.6.22Write examples and non-examples of statistical questions, explaining that a statistical question anticipates variability in the data related to the question.6.23Calculate, interpret, and compare measures of center (mean, median, mode) and variability (range and interquartile range) in real-world data sets.6.24Represent numerical data graphically, using dot plots, line plots, histograms, stem and leaf plots, and box plots.6.25Graph polygons in the coordinate plane given coordinates of the vertices to solve real-world and mathematical problems.6.26Calculate the area of triangles, special quadilaterals, and other polygons by composing and decomposing them into known shapes.6.27Determine the surface area of three-dimensional figures by representing them with nets composed of rectangles and triangles to solve real-world and mathematical problems.6.28Apply previous understanding of volume of right rectangular prisms to those with fractional edge lengths to solve real-world and mathematical problems.6.3Use ratio and rate reasoning to solve mathematical and real-world problems (including but not limited to percent, measurement conversion, and equivalent ratios) using a variety of models, including tables of equivalent ratios, tape diagrams, double number lines, and equations.6.4Interpret and compute quotients of fractions using visual models and equations to represent problems.6.5Fluently divide multi-digit whole numbers using a standard algorithm to solve real-world and mathematical problems.6.6Add, subtract, multiply, and divide decimals using a standard algorithm.6.7Use the distributive property to express the sum of two whole numbers with a common factor as a multiple of a sum of two whole numbers with no common factor.6.8Find the greatest common factor (GCF) and least common multiple (LCM) of two or more whole numbers.6.9Use signed numbers to describe quantities that have opposite directions or values and to represent quantities in real-world contexts.
Example Problems
Solve for x:
What is ?
What is the distance between the following points?
 and
Round your answer to the nearest hundredth, if necessary.
What is ?
What is ?
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