Unit: RATIONAL FUNCTIONS Suggested Order: 5 of 8 Suggested Time: 10 days on semester schedule (90-minute classes) Rationale: This unit is intended to develop students’ understanding of rational functions. It is suggested to be taught in close proximity to the polynomials unit because of the connection of rational expressions to the division of polynomials. This unit should begin with reviewing both simplification of fractions and all arithmetic operations to help students understand the similarities and differences between rational numbers and expressions. Overarching Standards - NC.M3.A-SSE.1b, NC.M3.A-SSE.2, NC.M3.A-REI.1, NC.M3.F-BF.1b Major Work Standards Learning Intentions Success Criteria NC.M3.A-SSE.1 NC.M3.A-APR.6 NC.M3.A-APR.7 NC.M3.A-CED.1 NC.M3.A-CED.2 NC.M3.A-REI.2 A. Recognize rational expressions as the division of two polynomials and use properties of simple fractions to analyze, perform arithmetic operations, create and solve equations that model real world phenomena. A1. I can rewrite and simplify a rational expression by factoring, long division, or synthetic division. A2. I can explain how operations on rational expressions are the same as simple fractions. A3. I can multiply and divide rational expressions. A4. I can find LCD in order to add and subtract rational expressions. A5. I can recognize the difference between adding rational expressions and solving rational expressions. A6. I can solve a one variable rational equation algebraically or using a graph. A7. I can give examples showing how extraneous solutions may arise when solving rational equation. A8. I can create and solve a rational equation to solve an application. A9. I can interpret the terms, factors, and coefficients of rational expressions. NC.M3.F-IF.4 NC.M3.F-IF.7 B. Understand and interpret the key features, uses and limitations B1. I can determine the domain and discontinuities of a rational function by finding vertical asymptotes and holes of the function.
Unit: TRIGONOMETRIC FUNCTIONS Suggested Order: 7 of 8 Suggested Time: 10 days on semester schedule (90-minute classes) Rationale: This unit should immediately follow the Reasoning with Geometry unit. Students’ understanding of radians and the idea of circular motion are connections that can help students better understand trigonometric functions. Overarching Standards - NC.M3.A-SSE.1b, NC.M3.A-SSE.2, NC.M3.A-REI.1, NC.M3.F-BF.1b Major Work Standards Learning Intentions Success Criteria NC.M3.F-IF.1 NC.M3.F-IF.4 NC.M3.F-IF.7 NC.M3.F-IF.9 A. Understand that triangular trigonometric functions are related to circular trigonometric functions in the coordinate plane. A1. I can define a radian measure of an angle as the length of the arc on the unit circle subtended by the angle. A2. I can explain how a ratio represents a value of a trig function for an angle. A3. I can use key features to construct the graph of sine and cosine functions and interpret in context. A4. I can state the amplitude, period, and midline of sine and cosine functions. A5. I can use technology, graphs, and tables to compare sine graphs. NC.M3.F-BF.3 NC.M3.F-TF.1 NC.M3.F-TF.2 NC.M3.F-TF.5 B. Understand and interpret the key features, uses and limitations of multiple representations of trigonometric functions that model real world periodic behavior. B1. I can describe the effect of a transformation on the graph of a sine function. B2. I can explain that the radius of a circle is the ratio of the length of a subtended arc and its corresponding central angle. B3. I can use technology to interpret the key features of sine graphs in a real world situation. B4. I can work with angles in standard position to find coterminal and reference angles. Vocabulary: Initial side of an angle, terminal side of an angle, ray, coterminal angles, sine, cosine, tangent, radian (angle measure), unit circle, domain, range, period, midline, amplitude, frequency, cycle, phase shift.
Unit: STATISTICS Suggested Order: 8 of 8 Suggested Time: 5 days on semester schedule (90-minute classes) Rationale: This unit, Statistics, is more flexible in the pacing, than the other suggested units. Statistics can be taught as a stand-alone unit, since there is less integration and connection between standards. However, it is suggested that you do not break up the coherency of units that have intentionally been suggested to be taught in a certain order. (i.e - do not teach this unit between Reasoning with Geometry and Trigonometric Functions) Major Work Standards Learning Intentions Success Criteria NC.M3.S-IC.1 NC.M3.S-IC.3 A. Understand statistics as a process of making inferences about a population (parameter) based on results from a random sample (statistic). Acknowledge the role of randomization in using sample surveys, experiments, and observational studies to collect data and understand the limitations of generalizing results to populations (related to randomization). A1. I can distinguish between a sample (statistic) and a population (parameter). A2. I can describe how to select a random sample from a given population. A3. I can explain the purposes and the differences of sample surveys, observational studies, and experiments, including how randomization applies to each. A4. I can distinguish between sample surveys, observational studies, and experiments. A5. I can determine how results of a statistical study can be generalized to make conclusions about a population based on the sample. NC.M3.S-IC.4 NC.M3.S-IC.5 B. Understand simulation is useful for using data to make decisions. B1. I can use data from a sample survey to estimate a population mean or proportion with a margin of error.