Standards - Mathematics

Represent constraints by equations and/or inequalities, and interpret solutions as viable or nonviable options in a modeling context. Limit to contexts arising from linear. [Algebra I with Probability, 13 partial]

Solve multi-step linear equations in one variable, including rational number coefficients, and equations that require using the distributive property and combining like terms.

Determine whether linear equations in one variable have one solution, no solution, or infinitely many solutions of the form x = a, a = a, or a = b (where a and b are different numbers).

Represent and solve real-world and mathematical problems with equations and interpret each solution in the context of the problem. [Grade 8, 11]

Identify the effect on the graph of replacing $f(x)$ by $f(x) + k,$ $k \cdot f(x), f (kx),$ and $f(x + k)$ for specific values of $k$ (both positive and negative); find the value of $k$ given the graphs. Experiment with cases and explain the effects on the graph using technology, where appropriate. Limit to linear functions. [Algebra I with Probability, 23]

Construct a function to model the linear relationship between two variables.

Interpret the rate of change (slope) and initial value of the linear function from a description of a relationship from two points in a table or graph. [Grade 8, 16]

Explain why the x-coordinates of the points where the graphs of the equations $y = f(x)$ and $y = g(x)$ intersect are the solutions of the equation $f(x) = g(x)$. Limit to linear equations. [Algebra I with Probability, 19]

Find approximate solutions by graphing the functions, making tables of values, or finding successive approximations, using technology where appropriate.

Note: Include cases where $f(x)$ is linear and $g(x)$ is constant or linear. [Algebra I with Probability, 19 edited]

Examine a sample of a population to generalize information about the population.

Differentiate between a sample and a population.

Compare sampling techniques to determine whether a sample is random and thus representative of a population, explaining that random sampling tends to produce representative samples and support valid inferences.

Determine whether conclusions and generalizations can be made about a population based on a sample.

Use data from a random sample to draw inferences about a population with an unknown characteristic of interest, generating multiple samples to gauge variation and make predictions or conclusions about the population.

Informally explain situations in which statistical bias may exist. [Grade 7, 10]

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. [Grade 7, 11]

Make informal comparative inferences about two populations using measures of center and variability and/or mean absolute deviation in context. [Grade 7, 12]

Use a number between 0 and 1 to represent the probability of a chance event occurring, explaining that larger numbers indicate greater likelihood of the event occurring, while a number near zero indicates an unlikely event. [Grade 7, 13]

Define and develop a probability model, including models that may or may not be uniform, where uniform models assign equal probability to all outcomes and non-uniform models involve events that are not equally likely.

Collect and use data to predict probabilities of events.

Compare probabilities from a model to observe frequencies, explaining possible sources of discrepancy. [Grade 7, 14]

Approximate the probability of an event by using data generated by a simulation (experimental probability) and compare it to theoretical probability.

Observe the relative frequency of an event over the long run, using simulation or technology, and use those results to predict approximate relative frequency. [Grade 7, 15]

Find probabilities of simple and compound events through experimentation or simulation and by analyzing the sample space, representing the probabilities as percents, decimals, or fractions.

Represent sample spaces for compound events using methods such as organized lists, tables, and tree diagrams, and determine the probability of an event by finding the fraction of outcomes in the sample space for which the compound event occurred.

Design and use a simulation to generate frequencies for compound events.

Represent events described in everyday language in terms of outcomes in the sample space which composed the event. [Grade 7, 16]

Solve problems involving scale drawings of geometric figures including computation of actual lengths and areas from a scale drawing and reproduction of a scale drawing at a different scale. [Grade 7, 17]

Construct geometric shapes (freehand, using a ruler and a protractor, and using technology) given measurement constraints with an emphasis 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. [Grade 7, 18]

Describe the two-dimensional figures created by slicing three-dimensional figures into plane sections. [Grade 7, 19]

Explain the relationships among circumference, diameter, area, and radius of a circle to demonstrate understanding of formulas for the area and circumference of a circle.

Informally derive the formula for area of a circle.

Solve area and circumference problems in real-world and mathematical situations involving circles. [Grade 7, 20]

Use facts about supplementary, complementary, vertical, and adjacent angles in multi-step problems to write and solve simple equations for an unknown angle in a figure. [Grade 7, 21]

Analyze and apply properties of parallel lines cut by a transversal to determine missing angle measures.