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 write 3 x 4 x 5. 60, let’s now see how this applies to a rational equation. Let’s 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
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