7.RP.2 Recognize and represent proportional relationships between quantities.
7.RP.2.a Decide whether two quantities are in a proportional relationship by testing for equivalent ratios in a table or graphing on a coordinate plane and observing whether the graph is a straight line through the origin.
7.NS.1.b Understand p + q as the number located a distance |q| from p on a number line, in the direction indicated by the sign of q. Show that a number and its opposite have a sum of 0 (are additive inverses). Interpret sums of rational numbers by describing real world contexts.
7.NS.1.c Understand subtraction of rational numbers as adding the additive inverse, p – q = p + (–q). Show that the distance between two rational numbers on the number line is the absolute value of their difference, and apply this principle in real world contexts.
7.NS.2 Apply and extend previous understandings of multiplication, division, and fractions to multiply and divide rational numbers.
7.NS.2.a Understand that multiplication is extended from fractions to rational numbers by requiring that operations continue to satisfy the properties of operations, particularly the distributive property, leading to products such as (–1)(–1) = 1 and the rules for multiplying rational numbers. Interpret products of rational numbers by describing real world contexts.
7.NS.2.b Understand that integers can be divided, provided that the divisor is not zero, and every quotient of integers (with non-zero divisor) is a rational number. If p and q are integers, then –(p/q) = –p/q = p/(–q). Interpret products of rational numbers by describing real world contexts.
7.EE.4 Use variables to represent quantities in a real world or mathematical problem, and construct simple equations and inequalities to solve problems by reasoning about the quantities.
7.EE.4.a Solve word problems leading to equations of the form px + q = r and p(x + q) = r, where p, q, and r are specific rational numbers. Solve equations of these forms fluently. Compare the algebraic solution to an arithmetic solution, identifying the sequence of the operations used in each approach.
7.EE.4.b Solve word problems leading to inequalities of the form px + q > r or px + q < r, where p, q, and r are specific rational numbers. Graph the solution set of the inequality and interpret it in the context of the problem.
7.G.2 Draw geometric shapes from given conditions. Focus on constructing triangles from three measures of angles or sides, noticing when the conditions determine a unique triangle, more than one triangle, or no triangle. Use a variety of methods such as freehand, with ruler and protractor, and with technology.
7.G.3 Describe the cross-sections (two-dimensional figures that result from slicing three-dimensional figures, as in plane sections) of right rectangular prisms and right rectangular pyramids.
7.SP.2.ii Generate multiple samples (or simulated samples) of the same size to gauge the variation in estimates or predictions.
Draw informal comparative inferences about two populations.
7.SP.3 Informally assess the degree of visual overlap of two numerical data distributions with similar variabilities, measuring the difference between the centers by expressing it as a multiple of a measure of variability.
7.SP.4 Use measures of center and measures of variability for numerical data from random samples to draw informal comparative inferences about two populations.
Investigate chance processes and develop, use, and evaluate probability models.
7.SP.5 Understand that the probability of a chance event is a number from 0 through 1 that expresses the likelihood of the event occurring. Larger numbers indicate greater likelihood. A probability near 0 indicates an unlikely event, a probability around ½ indicates an event that is neither unlikely nor likely, and a probability near 1 indicates a likely event.
7.SP.8.b Represent sample spaces for compound events using methods such as organized lists, tables and tree diagrams. For an event described in everyday language (such as "rolling double sixes"), identify the outcomes in the sample space which compose the event.