Course Guide - USAID Teacher Education Project

Unit 2 AlgebraWeek 3, Session 3: Order of Operations1. What are the important concepts?a) There are conventions when multiple operations are required to evaluate anexpression.b) These conventions are made easier in algebra by using parentheses to clarifywhich operations need to be done before others.c) The context of a given problem can provide clues for using the order of operationsto model the problem.2. How do children think about these concepts?a) The order of operations can be strange and confusing to children. They assumethat they should calculate all numbers from left to right.In fact, since a basic calculator adds numbers in sequential order, the resulting answeris often incorrect for a given problem. This only strengthens children's belief that thismethod must be correct because "the calculator says so."b) When told the correct order of operations, children either do not remember it orthey rely on a mnemonic. Remembering the mnemonic, however, is purelyprocedural and does not help youngsters understand why the conventional order ofoperations is crucial not just in basic calculations but also in real world situations.c) Once parentheses are introduced into an expression, it makes calculation using theorder of operations much easier for children to understand and use.3. What is essential to know or do in class?a) Review the homework assignment that helped students use "slope triangles" tovisualize slope, especially negative slope and negative y-intercepts. Have studentsdevelop an equation in y = mx + b form for several of the graphs.b) Have students work in pairs to solve an arithmetic equation designed to assesstheir understanding of the conventional order of operations without parentheses.c) Introduce the conventional order of operations. Then add how parentheses canclarify how to evaluate expressions that appear confusing.d) Have students work on a problem that involves order of operations involving a reallife situation, then generalize this by using variables.4. Class Activitiesa) Begin class by having students share what they learned by working the homeworkassignment. Since the assignment focused only on the graph, extend the conversation