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 understanding of rational functions. It is suggested to be taught in close proximity to the students’ unit because of the connection of rational expressions to the division of polynomials. This unit should begin with reviewing both polynomials 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 A. Recognize rational expressions A1. I can rewrite and simplify a rational expression by factoring, long NC.M3.A-APR.6 as the division of two polynomials division, or synthetic division. NC.M3.A-APR.7 and use properties of simple A2. I can explain how operations on rational expressions are the same as NC.M3.A-CED.1 fractions to analyze, perform simple fractions. NC.M3.A-CED.2 arithmetic operations, create and A3. I can multiply and divide rational expressions. NC.M3.A-REI.2 solve equations that model real A4. I can find LCD in order to add and subtract rational expressions. world phenomena. 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 B. Understand and interpret the B1. I can determine the domain and discontinuities of a rational function NC.M3.F-IF.7 key features, uses and limitations by finding vertical asymptotes and holes of the function.
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.