Course Guide - USAID Teacher Education Project

d) As in the cartoon below, youngsters may assume that once they have found thevalue for what x "is" in a given equation, that x has that same specific numerical valuefor x in other equations. For example, suppose there are three problems on aworksheet, the first being x + 3 = 7. The teacher expects a youngster will correctlysolve for x and discover that its value is 4. If the next problem is x + 5 = 9, the valuefor x is still 4. However, if the third problem is x + 3 = 9, youngsters may be lookingfor a pattern and determine that x must once again be 4.3. What is essential to know or do in class?a) Review the Algebra Tiles homework assignment using prompts from the TeacherNotes section.b) Introduce a new definition for x: x, the unknown. Note common misconceptionsthat youngsters may have about this.c) Review the "balance model" of equivalence and how it works in algebrad) Review the commutative, associative, distributive, and identity properties and notehow they work in algebra.e) Introduce the idea of "like terms" and how they can be combined to solve for x.f) Note the strategy of isolating x by using the arithmetic properties and the conceptof equivalence.g) To end this Algebra unit, allow time for a discussion about students' reflections onwhat they think about algebraic thinking and the teaching of algebra—which may bequite different from how they learned this subject when they were in school.4. Class Activitiesa) Begin by reviewing the homework assignment, A Geometry GraphingConnection. How did the questions about the Algebra Tiles as a visual model relateto the past assignment, Graphing Equations? What did students notice about theequations of "incomplete rectangles" using the Algebra Tiles? What does that imply?Use the discussion prompts in the section Parabolas. (Since you have given theTeacher Notes page to students they should be prepared to discuss these questions.)b) Shift the focus to x as the unknown in a given equation. If possible, use thiscartoon to illustrate the way youngsters may think about this: