6.2D: order a set of rational numbers arising from mathematical and real-world contexts

6.4G: generate equivalent forms of fractions, decimals, and percents using real-world problems, including problems that involve money

6.2A: classify whole numbers, integers, and rational numbers using a visual representation such as a Venn diagram to describe relationships between sets of numbers

6.2B: identify a number, its opposite, and its absolute value

6.2C: locate, compare, and order integers and rational numbers using a number line

6.4E: represent ratios and percents with concrete models, fractions, and decimals

6.4F: represent benchmark fractions and percents such as 1%, 10%, 25%, 33 1/3%, and multiples of these values using 10 by 10 grids, strip diagrams, number lines, and numbers

6.5C: use equivalent fractions, decimals, and percents to show equal parts of the same whole

6.3D: add, subtract, multiply, and divide integers fluently

6.3E: multiply and divide positive rational numbers fluently

6.2E: extend representations for division to include fraction notation such as a/b represents the same number as a ÷ b where b ≠ 0

6.3A: recognize that dividing by a rational number and multiplying by its reciprocal result in equivalent values

6.3B: determine, with and without computation, whether a quantity is increased or decreased when multiplied by a fraction, including values greater than or less than one

6.3C: represent integer operations with concrete models and connect the actions with the models to standardized algorithms

6.4B: apply qualitative and quantitative reasoning to solve prediction and comparison of real-world problems involving ratios and rates

6.4H: convert units within a measurement system, including the use of proportions and unit rates

6.5B: solve real-world problems to find the whole given a part and the percent, to find the part given the whole and the percent, and to find the percent given the part and the whole, including the use of concrete and pictorial models

6.4C: give examples of ratios as multiplicative comparisons of two quantities describing the same attribute

6.4D: give examples of rates as the comparison by division of two quantities having different attributes, including rates as quotients

6.4E: represent ratios and percents with concrete models, fractions, and decimals

6.5A: represent mathematical and real-world problems involving ratios and rates using scale factors, tables, graphs, and proportions

6.12C: summarize numeric data with numerical summaries, including the mean and median (measures of center) and the range and interquartile range (IQR) (measures of spread), and use these summaries to describe the center, spread, and shape of the data distribution

6.12D: summarize categorical data with numerical and graphical summaries, including the mode, the percent of values in each category (relative frequency table), and the percent bar graph, and use these summaries to describe the data distribution

6.13A: interpret numeric data summarized in dot plots, stem-and-leaf plots, histograms, and box plots

6.12A: represent numeric data graphically, including dot plots, stem-and-leaf plots, histograms, and box plots

6.12B: use the graphical representation of numeric data to describe the center, spread, and shape of the data distribution

6.13B: distinguish between situations that yield data with and without variability

6.7A: generate equivalent numerical expressions using order of operations, including whole number exponents and prime factorization

6.7D: generate equivalent expressions using the properties of operations: inverse, identity, commutative, associative, and distributive properties