### PR: Proportional Reasoning

#### 1.1: Analyze proportional relationships and use them to solve real-world and mathematical problems.

PR.1: Students will… Calculate unit rates of length, area, and other quantities measured in like or different units that include ratios or fractions.

PR.2: Students will… Represent a relationship between two quantities and determine whether the two quantities are related proportionally.

PR.2.a: Use equivalent ratios displayed in a table or in a graph of the relationship in the coordinate plane to determine whether a relationship between two quantities is proportional.

PR.2.b: Identify the constant of proportionality (unit rate) and express the proportional relationship using multiple representations including tables, graphs, equations, diagrams, and verbal descriptions.

PR.2.c: Explain in context the meaning of a point (x, y) on the graph of a proportional relationship, with special attention to the points (0, 0) and (1, r) where r is the unit rate.

PR.3: Students will… Solve multi-step percent problems in context using proportional reasoning, including simple interest, tax, gratuities, commissions, fees, markups and markdowns, percent increase, and percent decrease.

### NO: Number Systems and Operations

#### 2.1: Apply and extend prior knowledge of addition, subtraction, multiplication, and division to operations with rational numbers.

NO.4: Students will… Apply and extend knowledge of operations of whole numbers, fractions, and decimals to add, subtract, multiply, and divide rational numbers including integers, signed fractions, and decimals.

NO.4.a: Identify and explain situations where the sum of opposite quantities is 0 and opposite quantities are defined as additive inverses.

NO.4.b: Interpret the sum of two or more rational numbers, by using a number line and in real-world contexts.

NO.4.d: Use a number line to demonstrate 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.

NO.4.e: Extend strategies of multiplication to rational numbers to develop rules for multiplying signed numbers, showing that the properties of the operations are preserved.

NO.4.g: Convert a rational number to a decimal using long division, explaining that the decimal form of a rational number terminates or eventually repeats.

NO.5: Students will… Solve real-world and mathematical problems involving the four operations of rational numbers, including complex fractions. Apply properties of operations as strategies where applicable.

### AF: Algebra and Functions

#### 3.1: Create equivalent expressions using the properties of operations.

AF.6: Students will… Apply properties of operations as strategies to add, subtract, factor, and expand linear expressions with rational coefficients.

AF.7: Students will… Generate expressions in equivalent forms based on context and explain how the quantities are related.

#### 3.2: Solve real-world and mathematical problems using numerical and algebraic expressions, equations, and inequalities.

AF.8: Students will… Solve multi-step real-world and mathematical problems involving rational numbers (integers, signed fractions and decimals), converting between forms as needed. Assess the reasonableness of answers using mental computation and estimation strategies.

AF.9: Students will… Use variables to represent quantities in real-world or mathematical problems and construct algebraic expressions, equations, and inequalities to solve problems by reasoning about the quantities.

AF.9.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 an algebraic solution to an arithmetic solution, identifying the sequence of the operations used in each approach.

AF.9.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.

### DSP: Data Analysis, Statistics, and Probability

#### 4.1: Make inferences about a population using random sampling.

DSP.10: Students will… Examine a sample of a population to generalize information about the population.

DSP.10.a: Differentiate between a sample and a population.

DSP.10.b: 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.

DSP.10.c: Determine whether conclusions and generalizations can be made about a population based on a sample.

DSP.10.d: 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 making predictions or conclusions about the population.

DSP.10.e: Informally explain situations in which statistical bias may exist.

#### 4.2: Make inferences from an informal comparison of two populations.

DSP.11: Students will… 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.

DSP.12: Students will… Make informal comparative inferences about two populations using measures of center and variability and/or mean absolute deviation in context.

#### 4.3: Investigate probability models.

DSP.13: Students will… Use a number from 0 to 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.

DSP.14: Students will… 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.

DSP.14.a: Collect and use data to predict probabilities of events.

DSP.14.b: Compare probabilities from a model to observed frequencies, explaining possible sources of discrepancy.

DSP.15: Students will… Approximate the probability of an event using data generated by a simulation (experimental probability) and compare it to the theoretical probability.

DSP.15.a: Observe the relative frequency of an event over the long run, using simulation or technology, and use those results to predict approximate relative frequency.

DSP.16: Students will… 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.

DSP.16.a: 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.

DSP.16.b: Design and use a simulation to generate frequencies for compound events.

DSP.16.c: Represent events described in everyday language in terms of outcomes in the sample space which composed the event.

### GM: Geometry and Measurement

#### 5.1: Construct and describe geometric figures, analyzing relationships among them.

GM.17: Students will… 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.

GM.18: Students will… Construct geometric shapes (freehand, using a ruler and a protractor, and using technology), given a written description or 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.

GM.19: Students will… Describe the two-dimensional figures created by slicing three-dimensional figures into plane sections.

#### 5.2: Solve real-world and mathematical problems involving angle measure, circumference, area, surface area, and volume.

GM.20: Students will… 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.

GM.20.a: Informally derive the formula for area of a circle.

GM.20.b: Solve area and circumference problems in real-world and mathematical situations involving circles.

GM.21: Students will… 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.

GM.22: Students will… Solve real-world and mathematical problems involving area, volume, and surface area of two- and three-dimensional objects composed of triangles, quadrilaterals, polygons, cubes, and right rectangular prisms.

Correlation last revised: 3/2/2020

This correlation lists the recommended Gizmos for this state's curriculum standards. Click any Gizmo title below for more information.