Course Guide - USAID Teacher Education Project

y asking students to consider how they might use the slope they discovered and they-intercept to create an equation in the form of y = mx + b.Do a few of these together, then have them see how quickly they can write equationsfor the rest of the graphs on the page.b) Move to this session's focus topic, Order of Operations, by writing the followingexpression on the board: 5 x 8 + 6 ÷ 6 - 12 x 2. Have students work in pairs toevaluate it. (The correct answer is 17.)As they work on the problem, notice how they engage with their partner. Whatrationales do they have for the way they think the expression should be evaluated?Are students negotiating with each other as to how to proceed? For students whomove from left to right their answer will be 0.66666... (This is the answer thatentering the numbers sequentially into a basic calculator would give--which is not theright answer!)Notice how long students are working to solve the problem. Students operating fromthis sequential left-to-right assumption will likely take more time since they will bedealing with fractions or decimals as opposed to students who are working withintegers.c) Ask students to share their answers and how they determined them. This shouldgive rise to several alternative ways of thinking about the problem. Ask why thisoccurred.Honour the fact that all students were clever and resourceful when thinking about howto deal with such a confusing calculation but that some of their procedures did notfollow the conventional way for dealing with these types of equations.At this point, tell students that there is a conventional way to deal with these types ofequations: order of operations.d) Introduce the idea that order of operations insists on doing multiplication anddivision first. Only then can we add and subtract. Have students use this informationto re-evaluate the expression so that it results in 40 + 1 - 24.e) Proceed to say that algebra uses a particular notation, parentheses, to make all ofthis easier. Parentheses group certain numbers and operations together so it is clearwhat operation to perform first. By using parentheses, the above expression becomes(5 x 8) + (6 ÷ 6) - (12 x 2). Make clear to students that when looking at anexpression, they need to perform the operation in the parentheses before doinganything else. Then they would do any remaining multiplication/division, and finallyany addition/subtraction.(At this point do not mention how the order of operations deals with exponents. Thiswill be included in next week's focus on quadratic [square] equations.)f) Present the following equation where C is cost: C = 100 + 15 x 20. How wouldstudents calculate the cost given what they now know about order of operations?