Today's opener is another that we'll start today and before revisiting later, when this problem will serve to illustrate the use of Guess & Check versus graphing, and to introduce the elegance of substitution.
For today, I give students the first five minutes of class to see what they can figure out. The only note I provide is to confirm that perimeter is the distance around the outside of a two-dimensional figure, and that a rectangle's perimeter is the sum of the lengths of its sides. Other than that, I circulate and get an idea for who knows what. In my mind, I keep track of how confidently each student attempts to solve the problem, and I note which of my students already know about algebraic substitution in some form.
This opener and today's quiz are as much about starting to motivate kids toward substitution as they're about assessing what kids already know. Of course, I don't say that - I want to let students get there on their own.
This quiz serves as evidence toward two learning targets:
Students will choose which of the two SLT's they'd like to be graded on. I like to have another chance to assess student skills at graphing lines in slope-intercept form. We've done this before, but it's always important to continuously loop back to the most important skills and ideas. Some of my students never quite demonstrated mastery of this skill earlier in the year, so this and tomorrow's lesson will provide opportunities for that.
I give students the last 15 minutes of today's class to work on the quiz. I provide this Graphing Quiz Template, which has enough room to count by 1's from -15 to 15 on each axis. On this particular quiz, all solutions are within a domain and range of -10 to 10, so there's plenty of room. If kids ask, I'll tell them it's fine to count by 1's on each axis.
After I distribute the quiz template, I review learning targets 1.7 and 5.2. Then I tell students to choose which one they'd like to be assessed on, and to write the number of that target at the top-right corner of the page. When I grade these, four perfect graphs will earn a "4" on SLT 1.7, while four perfect graphs and appropriately labeled intersection points will earn a "3" on SLT 5.2. To earn higher than on SLT 5.2, students will have to show that they can use graphing to solve and interpret the solution to a problem in context.
The four equations comprising today's quiz are on the second of today's lesson slides, and this structure is easily adapted and reused as necessary. By printing a big pile of the quiz templates, I'm ready to adjust the level of difficulty for a particular class, and to make new versions of this quiz in subsequent lessons.
This quiz also serves to preview the idea that not all intersection points are so "nice" - and it's important to get this idea out there sooner rather than later. Seeing that lines can intersect in-between the integer points is an important part of developing a need for algebraic methods for solving systems, like substitution and elimination. That's really what the standard REI.6 is getting at with the idea of "approximate" solutions. Different solution strategy yield different levels precise results, and it's important to be able to distinguish between the two.