Students will understand… Rational expressions and equations may have restrictions. *AN.4, AN.5, AN.6 Students will know … there may undefined values when there is a variable in the denominator restrictions are found on original expressions a solution may not be a restriction 8888 *AN = Algebra and Number Skills: Enduring Understanding Specific Outcomes List the reference # from the Alberta Program of Studies Description of Skills Students will understand… The operations on rational expressions are similar to fractional operations. *AN.4, AN.5, AN.6 Students will be able to… +, -, x, ÷ rational expressions write equivalent forms of rational expressions solve a rational equation, limited to numerators involving monomials, binomials and trinomials model a situation using a rational equation Students will understand… *AN.4, AN.5, AN.6 Students will be able to…
basic operations in mathematics are addition, subtraction, multiplication, division and exponentiation. rational equation – An equation formed by setting a rational expression equal to 0 rational expression – An algebraic fraction with a numerator and denominator that are polynomials [Math 20-1 (McGraw-Hill Ryerson: page 590)]
Assessment Mathematics 20-1 Rational Reno’s Rubric Level Criteria Excellent 4 Proficient 3 Adequate 2 Limited 1 Insufficient or Blank Performing calculations for Question 1 Checking solution(s) against NPV’S and domain Correctly solving the rational equation Setting up a logical rational equation Setting up fractions to represent data No score is awarded because there is no evidence of student performance. No data is presented. No explanation is provided. Performing calculations for question 2 Checking solution(s) against NPV’S and domain Correctly solving the rational equation Setting up a logical rational equation Setting up fractions to represent data No score is awarded because there is no evidence of student performance. No data is presented. No explanation is provided. When work is judged to be limited or insufficient, the teacher makes decisions about appropriate intervention to help the student improve.
Students will learn to construct a rational equation to model a real-life situation (generally involving rates). Students will learn to solve rational equations and verify their answer(s) in case of against non-permissible values (NPVs). Activate Prior Knowledge Students should be reminded of NPVs (and how to identify them) and factoring. Lesson Begin with an equation involving fractions and discuss the steps necessary to solve. ex. One possible strategy would be to identify the least common multiple of the denominator and multiply both sides of the equation through by this LCM. This will allow us to transform a rational equation into a polynomial one. Though the LCM of the above example is 60, let’s write 3 x 4 x 5. Let’s now see how this applies to a rational equation. Continue with more examples, as needed. It would likely help to show an example where the LCM of the denominators is less obvious. Once students understand how to solve a rational equation, move on to word problems (such as distance-rate-time problems) and discuss strategies for constructing a table and, from it, a rational equation. Going Beyond Give students an example with an irrational solution that will require the use of the quadratic formula. Resources Math 20-1 (McGraw-Hill Ryerson: sec 6.4, pages 341-351) Supporting Assessment