Understand that the probability of a chance event is a number between 0 and 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 1/2 indicates an event that is neither unlikely nor likely, and a probability near 1 indicates a likely event.
Use proportional relationships to solve multistep ratio and percent problems.
Develop a probability model (which may not be uniform) by observing frequencies in data generated from a chance process.
Add, subtract, factor, and expand linear expressions with rational coefficients by applying the properties of operations.
Represent sample spaces for compound events using methods such as organized lists, sample space tables, and tree diagrams.
For an event described in everyday language, identify the outcomes in the sample space which compose the event.
Represent a proportional relationship using an equation.
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 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.
Understand addition of rational numbers; p + q is the number located a distance |q| from p, in the positive or negative direction depending on whether q is positive or negative. 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.
Solve real-world and mathematical problems involving the four operations with rational numbers.
Compute unit rates associated with ratios of fractions.
Identify the constant of proportionality (unit rate) in tables, graphs, equations, diagrams, and verbal descriptions of proportional relationships.
Solve problems involving scale drawings of geometric figures, including computing actual lengths and areas from a scale drawing and reproducing a scale drawing at a different scale.
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.
Use measures of center and measures of variability for quantitative data from random samples or populations to draw informal comparative inferences about the populations.
Track each student's skills and progress in your Mastery dashboards
