Identify the constant of proportionality (unit rate) in tables, graphs, equations, diagrams, and verbal descriptions of proportional relationships.
Solve word problems leading to equations of the form px + q = r and p(x + q) = r, where p, q, and r are rational numbers. Solve equations of these forms fluently. Compare an algebraic solution to an arithmetic solution, identifying the sequence of the operations used in each approach.
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.
Solve word problems leading to inequalities of the form px+q>r, px+q≥r, px+q≤r,or px + q < r, where p, q, and r are rational numbers. Graph the solution set of the inequality on the number line and interpret it in the context of the problem.
Understand that rewriting an expression in different forms in a problem context can shed light on the problem and how the quantities in it are related.
Add, subtract, factor, and expand linear expressions with rational coefficients by applying the properties of operations.
Construct and interpret box-plots, find the interquartile range, and determine if a data point is an outlier.
Apply properties of operations as strategies to add and subtract rational numbers.
Solve multi-step real-life and mathematical problems posed with positive and negative rational numbers in any form (whole numbers, fractions, and decimals), using tools strategically. Apply properties of operations to calculate with numbers in any form; convert between forms as appropriate. Assess the reasonableness of answers using mental computation and estimation strategies.
Represent a proportional relationship using an equation.
Compute unit rates associated with ratios of fractions.
Use proportional relationships to solve multistep ratio and percent problems.
Solve real-world and mathematical problems involving the four operations with rational numbers.
Describe situations in which opposite quantities combine to make 0.
Informally assess the degree of visual overlap of two quantitative data distributions.
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