6-18.104.22.168 Understand and explain procedures for multiplying and dividing fractions by using the meanings of fractions, multiplication and division, and the inverse relationship between multiplication and division.
6-22.214.171.124 Understand and explain procedures for multiplying and dividing decimals by using the relationship between decimals and fractions, as well as the relationship between finite decimals and whole numbers (i.e., a finite decimal multiplied by an appropriate power of 10 is a whole number).
6-8.1.2 Understand, apply, and be computationally fluent with rational numbers, including negative numbers.
6-126.96.36.199 Understand negative numbers in terms of their position on the number line, their role in the system of all rational numbers, and in everyday situations (e.g., situations of owing money or measuring elevations above and below sea level).
6-188.8.131.52 By applying properties of arithmetic and considering negative numbers in everyday contexts, explain why the rules for adding, subtracting, multiplying, and dividing with negative numbers make sense.
6-184.108.40.206 Use scientific notation and rational and irrational numbers to model and solve problems.
6-8.1.4 Understand and apply ratio and rate, including percents, and connect ratio and rate to fractions and decimals.
6-220.127.116.11 Build on understanding of fractions and part-whole relationships to understand ratios (by, for example, analyzing the relative quantities of boys and girls in the classroom or triangles and squares in a drawing).
6-18.104.22.168 Understand proportional relationships (y = kx or y/x = k), and distinguish proportional relationships from other relationships, including inverse proportionality (xy = k or y = k/x).
6-22.214.171.124 Understand that in a proportional relationship of two variables, if one variable doubles or triples, for example, then the other variable also doubles or triples, and if one variable changes additively by a specific amount, a, then the other variable changes additively by the amount ka.
6-126.96.36.199 Graph proportional relationships and identify the constant of proportionality as the slope of the related line.
6-188.8.131.52 Use ratios and proportionality to solve a wide variety of percent problems, including problems involving discounts, interest, taxes, tips, and percent increase or decrease.
6-184.108.40.206 Understand that expressions in different forms can be equivalent, and rewrite an expression to represent a quantity in a different way (e.g., to make it more compact or to feature different information).
6-220.127.116.11 Formulate linear equations and inequalities in one variable and use them to solve problems, including in applied settings, and justify the solution using multiple representations.
6-8.2.4 Understand and apply linear functions.
6-18.104.22.168 Understand linear functions and slope of lines in terms of constant rate of change.
6-22.214.171.124 Understand that the slope of a line is constant, for example by using similar triangles (e.g., as shown in the rise and run of "slope triangles"), and compute the slope of a line using any two points on the line.
6-126.96.36.199 Build on the concept of proportion, recognizing a proportional relationship (y/x = k, or y = kx) as a special case of a linear function. In this special case, understand that if one variable doubles or triples, for example, then the other variable also doubles or triples; and understand that if the input, or x-coordinate in this case, changes additively by a specific amount, a, then the output, or y-coordinate in this case, changes additively by the amount ka.
6-188.8.131.52 Understand that the graph of the equation y = mx + b is a line with y-intercept b and slope m.
6-184.108.40.206 Translate among verbal, tabular, graphical, and algebraic representations of functions, including recursive representations such as NEXT = NOW +3 (recognizing that tabular and graphical representations often only yield approximate solutions), and describe how such aspects of a linear function as slope, constant rate of change, and intercepts appear in different representations.
6-220.127.116.11 Select appropriate two-and three-dimensional shapes to model real-world situations and solve a variety of problems (including multi-step problems) involving surface area, area and circumference of circles, and volume of prisms and cylinders.
6-8.3.4 Analyze two-dimensional space and figures by using distance, angle, coordinates, and transformations.
6-18.104.22.168 Explore and explain the relationships among angles when a transversal cuts parallel lines.
6-22.214.171.124 Use facts about the angles that are created when a transversal cuts parallel lines to explain why the sum of the measures of the angles in a triangle is 180 degrees, and apply this fact about triangles to find unknown measures of angles.
6-126.96.36.199 Understand and explain how particular configurations of lines give rise to similar triangles because of the congruent angles created when a transversal cuts parallel lines (e.g., "slope triangles").
6-188.8.131.52 Use reasoning about similar triangles to solve a variety of problems, including those that involve determining heights and distances.
6-184.108.40.206 Explain why the Pythagorean Theorem is valid by using a variety of methods - for example, by decomposing a square in different ways.
6-220.127.116.11 Apply the Pythagorean theorem to find distances between points in the Cartesian coordinate plane and to measure lengths and analyze polygons.
6-18.104.22.168 Understand and apply transformations - reflection, translation, rotation, and dilation, and understand similarity, congruence, and symmetry in terms of transformations.
6-22.214.171.124 Extend prior work with bar graphs, line graphs, line plots, histograms, circle graphs, and stem and leaf plots as graphical representations of data to include box-and-whisker plots and scatterplots.
6-126.96.36.199 Create and interpret box-and-whisker plots and scatterplots.
6-8.4.2 Analyze and summarize data sets, including initial analysis of variability.
6-188.8.131.52 Select, determine, explain, and interpret appropriate measures of center for given data sets (mean, median, mode).
6-184.108.40.206 Select, create, explain, and interpret appropriate graphical representations for given data sets (bar graphs, circle graphs, line graphs, histograms, line plots, stem and leaf plots, box-and-whisker plots, scatterplots).
6-220.127.116.11 Understand that a measure of center alone does not thoroughly describe a data set because very different data sets can share the same measure of center, and thus consider and describe the variability of the data (e.g., range and interquartile range).
6-18.104.22.168 Informally determine a line of best fit for a scatterplot to make predictions and estimates.
6-22.214.171.124 Formulate questions, gather data relevant to the questions, organize and analyze the data to help answer the questions, including informal analysis of randomness and bias.
6-8.4.3 Use proportions and percentages to analyze data and chance.
6-126.96.36.199 Use proportions to make estimates relating to a population on the basis of a sample.
6-188.8.131.52 Apply percentages to make and interpret histograms and circle graphs.
6-184.108.40.206 Explore situations in which all outcomes of an experiment are equally likely, and thus the theoretical probability of an event is the number of outcomes corresponding to the event divided by total number of possible outcomes.