Understand that the probability of a chance event is a number between 0 and 1 that expresses the likelihood of the event occurring.
Collect data to calculate the experimental probability of a chance event, observing its long-run relative frequency. Use this experimental probability to predict the approximate relative frequency.
Develop a probability model and use it to find probabilities of simple events.
Develop a uniform probability model by assigning equal probability to all outcomes and use the model to determine probabilities of events.
Develop a probability model (which may not be uniform) by repeatedly performing a chance process and observing frequencies in the data generated.
Compare theoretical and experimental probabilities from a model to observed frequencies; if the agreement is not good, explain possible sources of the discrepancy.
Determine probabilities of compound events using organized lists, tables, tree diagrams, and simulation.
Understand that, just as with simple events, the probability of a compound event is the fraction of outcomes in the sample space for which the compound event occurs.
For an event described in everyday language, identify the outcomes in the sample space which compose the event, when the sample space is represented using organized lists, tables, and tree diagrams.
Design and use a simulation to generate frequencies for compound events.
Apply properties of operations as strategies to:
• Add, subtract, and expand linear expressions with rational coefficients.
• Factor linear expression with an integer GCF.
Understand that equivalent expressions can reveal real-world and mathematical relationships. Interpret the meaning of the parts of each expression.
Recognize and represent proportional relationships between quantities.
Understand that a proportion is a relationship of equality between ratios.
Represent proportional relationships using tables and graphs.
Recognize whether ratios are in a proportional relationship using tables and graphs. o Compare two different proportional relationships using tables, graphs, equations, and verbal descriptions.
Identify the unit rate (constant of proportionality) within two quantities in a proportional relationship using tables, graphs, equations, and verbal descriptions.
Create equations and graphs to represent proportional relationships.
Use a graphical representation of a proportional relationship in context to:
Explain the meaning of any point (x, y).
Explain the meaning of (0, 0) and why it is included.
Understand that the y-coordinate of the ordered pair (1, r) corresponds to the unit rate and explain its meaning