I want to transcribe a bit my thought-process for how I planned the questions for this lesson. I also want to remind you that there is no such thing as a perfect lesson plan of questions. The process is mostly intended to get us thinking about the questions we would like to ask--the process I call premeditation--and the answers/responses students are likely to give. This leads us to more questions to ask, thus creating a more complete scaffold of questions overall. Our goal throughout is to scaffold the mental acts of the students from lower to higher order thinking through the questions we ask. So, we’re really running them through certain mental hoops, if you will, and the content is the vehicle by which to do so.
Content & Assessment
The very first thing I notice about this lesson is that there is no ‘assessment’ component. If you remember, Steps 1-5 apply to ‘content’ and Steps Q and A apply to ‘assessment’. Here, there are no sample problems for the students to solve independently. Examples 1-3 and then 4-6, good examples no doubt, are already used or solved in the content of the lesson. So I would probably just create another example of two equations for them to solve and you’ll see that in the explanation of Steps Q/A below. Step 1 Questions
Step 1 questions ask students to notice the important or key facts on the page. I definitely want the students to notice the title to the content/lesson. I also want them to notice that each of the examples has two linear questions; the two equations form a “system.” I notice that the word system is not defined, so I may have to get them to infer that later. There are also two variables-- two “unknowns”--per equation that are set equal to some number and I will ask them about, too. It occurs to me that the idea or concept of “adding equations” so that one variable gets “eliminated” is not explicit from the instructions. I’m guessing that they have been taught what it means to do this in the direct instruction that should have come previous to our questioning. But just in case, I’ll have the students label and identify what those concepts mean and there is a line in the instructions in which those phrases appear. So, I’ll direct them to that line and ask them about each one. Step 2 Questions
Step 2 questions ask students to make connections, inferences, or more generally to explain why stuff is happening or how it is happening. It’s not a bright line between some Step 1 questions and Step 2 questions all the time. For instance, I ask the students to identify or read the title directly, which gives me the words to the title, but then to hopefully infer what the title is saying, that we have to eliminate one variable. If the student simply reads but does not infer, then I’ll have to explicitly ask about the inference, so I write down that question to ask. I also want a student to connect that we have to get the x’s or instead y’s to cancel out, and that you can’t add the x’s and y’s together. Where I ask, “Should we add the X and Y variables together?” I’m basically hoping the students will see the obvious ‘disconnection’ and say something like, “No, you can’t do that.” I also want to get students to order or re-order the equations so that the variables align properly for easy addition. x + 2y = 7 5x + 3y = 6 rather than x + 2y = 7 3y + 5x = 6
I notice that some of these Step 2 questions are already embedded formally in the content, which is good. For instance, I ask, “What’s the difference between the equations used in Examples 1, 2, and 3 and then in Examples 4, 5, and 6?” That question mostly parallels what’s in the content where it asks, “Does the same
thing happen when you add the following equations together?” (referring to Examples 4, 5, and 6). Lastly, I want to make sure that students see the connection between multiplying on both sides of the equals sign. Step 3 Questions
Step 3 questions, as this content really just describes a particular process, looks to have students describe that process in order. So, my questions are pretty much “what are the steps here?” Step 4 Questions
Step 4 questions tend to be less about straight-forward application than the idea of making changes in the content--in this case a process--and asking students about that. Like, why does this process only work for situations when we are given two linear equations and not a third? Step 5 Questions
Step 5 questions just ask the students to tell me what they have learned, again. Simple enough. Steps Q and A
Steps Q and A require us to form some sample problems for the students to work through to give us an assessment component. I’ve done so as below. Example A 1/2x + 1/4y = 2 x + 3y = 4
Step Q for Example A: What is the problem asking us to do? Step A for Example A: What is your answer and why?
Example B The air-mail rate for letters to Mexico is 45 cents per ounce and to Brazil as 65 cents per ounce. If Shirley paid $18.55 to send 35 half-ounce letters abroad, how many did she send to Brazil? Step Q for Example A: What is the problem presenting?