NC.6.NS.8 Solve real-world and mathematical problems by graphing points in all four quadrants of the coordinate plane. Include use of coordinates and absolute value to find distances between points with the same first coordinate or the same second coordinate.
NC.6.NS.9 Apply and extend previous understandings of addition and subtraction.
NC.6.NS.9.a Understand additive inverses when adding and subtracting integers.
NC.6.NS.9.a.1 Describe situations in which opposite quantities combine to make 0.
NC.6.NS.9.a.2 Understand p + q as the number located a distance q from p, in the positive or negative direction depending on the sign of q. Show that a number and its additive inverse create a zero pair.
NC.6.NS.9.a.3 Understand subtraction of integers as adding the additive inverse, p – q = p + (– q). Show that the distance between two integers on the number line is the absolute value of their difference.
NC.6.NS.9.a.4 Use models to add and subtract integers from -20 to 20 and describe real-world contexts using sums and differences.
NC.6.EE Expressions and Equations
Apply and extend previous understandings of arithmetic to algebraic expressions.
NC.6.EE.1 Write and evaluate numerical expressions, with and without grouping symbols, involving whole-number exponents.
NC.6.EE.2 Write, read, and evaluate algebraic expressions.
NC.6.EE.2.a Write expressions that record operations with numbers and with letters standing for numbers.
NC.6.EE.5 Use substitution to determine whether a given number in a specified set makes an equation true.
NC.6.EE.6 Use variables to represent numbers and write expressions when solving a real-world or mathematical problem.
NC.6.EE.7 Solve real-world and mathematical problems by writing and solving equations of the form:
NC.6.EE.7.a x + p = q in which p, q and x are all nonnegative rational numbers; and,
NC.6.EE.7.b p ? x = q for cases in which p, q and x are all nonnegative rational numbers.
Reason about one variable inequalities.
NC.6.EE.8 Reason about inequalities by:
NC.6.EE.8.a Using substitution to determine whether a given number in a specified set makes an inequality true.
NC.6.EE.8.b Writing an inequality of the form x > c or x < c to represent a constraint or condition in a real-world or mathematical problem.
NC.6.EE.8.c Recognizing that inequalities of the form x > c or x < c have infinitely many solutions.
NC.6.EE.8.d Representing solutions of inequalities on number line diagrams.
Represent and analyze quantitative relationships between dependent and independent variables.
NC.6.EE.9 Represent and analyze quantitative relationships by:
NC.6.EE.9.a Using variables to represent two quantities in a real-world or mathematical context that change in relationship to one another.
NC.6.EE.9.b Analyze the relationship between quantities in different representations (context, equations, tables, and graphs).
Solve real-world and mathematical problems involving area, surface area, and volume.
NC.6.G.1 Create geometric models to solve real-world and mathematical problems to:
NC.6.G.1.a Find the area of triangles by composing into rectangles and decomposing into right triangles.
NC.6.G.1.b Find the area of special quadrilaterals and polygons by decomposing into triangles or rectangles.
NC.6.G.2 Apply and extend previous understandings of the volume of a right rectangular prism to find the volume of right rectangular prisms with fractional edge lengths. Apply this understanding to the context of solving real-world and mathematical problems.
NC.6.G.3 Use the coordinate plane to solve real-world and mathematical problems by:
NC.6.G.3.a Drawing polygons in the coordinate plane given coordinates for the vertices.
NC.6.G.3.b Using coordinates to find the length of a side joining points with the same first coordinate or the same second coordinate.
NC.6.G.4 Represent right prisms and right pyramids using nets made up of rectangles and triangles, and use the nets to find the surface area of these figures. Apply these techniques in the context of solving real-world and mathematical problems.
NC.6.SP Statistics and Probability
Develop understanding of statistical variability.
NC.6.SP.1 Recognize a statistical question as one that anticipates variability in the data related to the question and accounts for it in the answers.
NC.6.SP.3 Understand that both a measure of center and a description of variability should be considered when describing a numerical data set.
NC.6.SP.3.a Determine the measure of center of a data set and understand that it is a single number that summarizes all the values of that data set.
NC.6.SP.3.a.1 Understand that a mean is a measure of center that represents a balance point or fair share of a data set and can be influenced by the presence of extreme values within the data set.
NC.6.SP.3.a.2 Understand the median as a measure of center that is the numerical middle of an ordered data set.
NC.6.SP.3.b Understand that describing the variability of a data set is needed to distinguish between data sets in the same scale, by comparing graphical representations of different data sets in the same scale that have similar measures of center, but different spreads.
Summarize and describe distributions.
NC.6.SP.4 Display numerical data in plots on a number line.
NC.6.SP.4.a Use dot plots, histograms, and box plots to represent data.
NC.6.SP.4.b Compare the attributes of different representations of the same data.
NC.6.SP.5 Summarize numerical data sets in relation to their context.
NC.6.SP.5.a Describe the collected data by:
NC.6.SP.5.a.1 Reporting the number of observations in dot plots and histograms.
NC.6.SP.5.a.2 Communicating the nature of the attribute under investigation, how it was measured, and the units of measurement.
NC.6.SP.5.b Analyze center and variability by:
NC.6.SP.5.b.1 Giving quantitative measures of center, describing variability, and any overall pattern, and noting any striking deviations.
NC.6.SP.5.b.2 Justifying the appropriate choice of measures of center using the shape of the data distribution.