Allow students about three minutes to discuss homework answers (Football Helmets activity questions five – 10 and 14 - 16) with members of their cooperative group. After discussions hold a mini wrap-up of all the work from the previous day and homework. Asking students to script answers to each question on a group marker board would be a good and efficient formative assessment of what each group has learned so far. Asking student to present their thinking at the board for the rest of the class would also be wonderful if you have some articulate students who can explain their thinking well, maybe even with your prompting.
At this point in the year, I am still modeling how to set up a graph. When my students struggle to graph they typically struggle in two main areas - labeling x and y axis or numbering x and y axis with a consistent interval. I really focus on setting up the graph completely before trying to graph any points. I have a graphing bell ringer I use with students who continue to leave the x and y axis blank after weeks of practice. This bell ringer is located in my functions unit if you would like to use it. Walking students through graphing is time consuming and not much fun. I tell students we are about to have the most boring lesson in the world but if they focus and learn from today I will never put them through this lesson again. If they choose to ignore my instructions on graphing and from this day forward continue to create ugly or naked graphs, then we will repeat the most boring lesson in the world.
After this riveting introduction, lead students (using your projector and document camera) through the thinking process of creating a graph. Where do the independent and dependent quantities label? What is a reasonable interval and what do I do if I want to skip lines when numbering (not a good idea and nearly always messes them up because they forget to skip the very first line after 0). Once you have walked about the room to provide feedback and ensure all your students were following along and creating correct graphs, then allow about five minutes for students to discuss questions 12 and 13 in cooperative groups.
Hold a deep mini wrap-up session over questions 12 and 13 plus some other good graphing questions you can ask verbally. Other possible graphing questions could include: Which company is cheaper before the break even point and how do you know by looking at the graph? Who is cheaper after the break even point and how do you know by looking at the graph? Why does one company start out cheaper but then become more expensive later? Why does one company start out more expensive but become cheaper later? What is unique about each company's pricing strategy that directly affects the graph?
Assign practice problems 3 – 8, 15, 16, 19, and 20 for homework tonight so students continue their understanding of solving equations with equivalent expressions and variables on both sides. The homework is simply algebraic however, asking students to decontextualize the math and manipulate the numbers and symbols from a purely algebraic sense. Moving students into the purely algebraic process is a definite goal at this grade level and is the ultimate goal of these two lessons combined (Break Even and Football Helmets). By using both lessons together you are asking students to apply math practice standards four and two. Students use mathematical practice four to model real world math algebraically and graphically to understand the context. Then, students are asked to decontextualize the math using math practice two and manipulate these complex equations as purely algebraic representations.
Lesson Preperation Reminders for the Formative Assessment Lesson tomorrow:
1. Finish sorting pre-lesson assessments into cooperative pairs or groups to begin the activity.
2. finish your guiding quesitons based on student misconcpetions and decide how you will present these to your students.
3. Copy and cut if possible a set of cards (page S-3) for each cooperative group.
4. Gather poster paper (sometimes I tape several white 81/2 X 11 sheets together), markers, small envelops for storing cards, and glue sticks for each cooperative group to use during the activity.
Read all the pages of the Lesson Guide (Website under Resources at the bottom of the webpage) so you are familiar with framing the lesson and the activity.