Spend 10 minutes or so discussing how the proportional graph of the ratio 3/7 could be useful in solving the proportion given for homework. If you reviewed the posts in Edmodo prior to the lesson then put a badge on all the great, thought provoking posts and use these as catalysts for further discussion at the start of class today.
Your goal today is to finish the activity by making some essential connections to slope today in Big Idea #3. Tell students that the main question addressed in the activity today is really all three of the questions at once:
Write these questions on the board again and begin to answer them out to the side. Ask what does it mean to be linear? Which question is answered by linear graph (question 3)? Ask what is unique about the ratio each student walked? They were all proportional. Which question does this answer - question 1. Now, let's begin big idea #3.
Allow about 10-12 minutes for students to work in cooperative groups to complete questions one through three as you move about the room assessing progress, providing feedback that moves learning forward, and selecting groups to present during the wrap-up session. Questions one through three really ask students to draw triangles and compare these triangles for similarity. By finding similar triangles, they can see the proportional relationship again. Hold a mini wrap-up over these questions before you begin to discuss the word "slope" in question 4. During the mini wrap-up session of question 3 is a great time to show the enhanced video and/or still shots of the activity that trace the triangluar path of students as they walked the graph. It might be hard for students to "see" the relationship of similarity between the colored triangles drawn on the page. You could discuss the proporitonal side lengths and then ask them to check the hypoentuse for the same ratio to prove a dilation. You coud also give them tracing paper and allow them to compare corresponding angles for congruence. Either way, let them apply math practice standard one (MP1) and persevere in answering the questions but with the resources to explore properties.
After the wrap-up, allow students about 5-8 minutes to discuss and answer questions four and five. Again move about the room as students work and question student groups to consider deeper ideas such as parallel lines and what it means to be parallel. How to find the slope of a line? Hold a good mini wrap-up session over these questions and script the discussion on the board for notes and consolidation of the ideas.
Students should have a good understanding of applying similar triangles to find the slope of a line. Pass out the homework sheet and allow student groups one minute to work on finding the slope of the first graph. After one minute, ask for ideas from students to get started and script these ideas on the board. Allow students about two to three more minutes to work before asking for further ideas from students to keep moving forward on finding slope. As students are working and talking move about the room providing feedback to move their learning forward. Post all scripted notes to your website or Edmodo to help students as they complete the homework page tonight - finding slope of each line.
Homework: Only copy the first page - questions 1 through 8 all finding slope from a graph and assign as homework.