6.RP.3 Use tables of equivalent ratios, tape diagrams, double number line diagrams, and equations to reason about ratios and rates in real world and mathematical problems.
6.RP.3.a Make tables of equivalent ratios relating quantities with whole-number measurements, find missing values in the tables, and plot the pairs of values on the coordinate plane. Use tables to compare ratios.
6.NS.4.ii Use the distributive property to express a sum of two whole numbers 1 to 100 with a common factor as a multiple of a sum of two whole numbers with no common factor.
Apply and extend previous understandings of numbers to the system of rational numbers.
6.NS.5.i Understand that rational numbers are used together to describe quantities having opposite directions or values (may include temperature above/below zero, elevation above/below sea level, debits/credits, positive/negative electric charge, etc.).
6.NS.6.ii Extend number line diagrams and coordinate axes from previous grades to represent points on the line and in the plane with negative number coordinates.
6.NS.6.ii.a Recognize opposite signs of numbers as indicating locations on opposite sides of 0 on the number line. Recognize that the opposite of the opposite of a number is the number itself, for example: –(–3) = 3, and that 0 is its own opposite.
6.NS.6.ii.b Understand signs of numbers in ordered pairs as indicating locations in quadrants of the coordinate plane. Recognize that when two ordered pairs differ only by signs, the locations of the points are related by reflections across one or both axes.
6.NS.7.c Understand the absolute value of a rational number as its distance from 0 on the number line. Interpret absolute value as magnitude for a positive or negative quantity in a real world situation.
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.
6.EE.2.b Identify parts of an expression using mathematical terms (sum, term, product, factor, quotient, coefficient, difference, quantity, etc.); view one or more parts of an expression as a single entity.
6.EE.2.c Evaluate expressions at specific values of their variables. Include expressions that arise from formulas used in real world problems. Perform arithmetic operations, including those involving whole-number exponents, in the conventional order when there are no parentheses to specify a particular order (Order of Operations).
6.G.1.iii Apply these techniques in the context of solving real world mathematical problems.
6.G.2.i Using cubes of an appropriate size, pack a right rectangular prism having fractional edge lengths to find its volume. Then show that the volume is the same as would be found by multiplying the edge lengths of the prism.
6.G.2.ii Apply the formulas V = lwh and V= Bh to find volumes of right rectangular prisms with fractional edge lengths in the context of solving real world and mathematical problems.
6.SP.3 Recognize that a measure of center for a numerical data set summarizes all of its values using a single number, while a measure of spread (variation) describes how its values vary with a single number.
6.SP.5.c Calculating quantitative measures of center (median and/or mean) and variability (interquartile range and/or mean absolute deviation), as well as describing any overall pattern and any striking deviations from the overall pattern with reference to the context in which the data was gathered.