Lesson 4.1.5 – Teacher Notes Standard: 8.F.A.2 Compare properties of two functions each represented in a different way (algebraically, graphically, numerically in tables, or by verbal descriptions). For example, given a linear function represented by a table of values and a linear function represented by an algebraic expression, determine which function has the greater rate of change. 8.F.A.4 Construct a function to model a linear relationship between two quantities. Determine the rate of change and initial value of the function from a description of a relationship or from two (x, y) values, including reading these from a table or from a graph. Interpret the rate of change and initial value of a linear function in terms of the situation it models, and in terms of its graph or a table of values. Chapter 7 –More practice comparing representations. Lesson Focus: The focus of the lesson is to bring attention back to the many ways functions can be modeled. It is a good idea to complete 4-42 part b as a whole group to model the expectations for the class. Then, assign every student to complete 4-42 parts a, c, and d. (4-42) I can represent functions in multiple ways. Calculator: Yes Literacy/Teaching Strategy: Teammates Consult (4-42); I Spy or Huddle (When students struggle)
Bell work
In the last several lessons, you have been finding connections and relationships between different representations of patterns. You have worked backward and forward. You have also used information about Figure 0 (or the starting point) and the pattern of growth to write rules. In today’s activity, you will use pieces of information from various parts of the web to generate a complete pattern.
4-42. CHECKING THE CONNECTIONS: TEAM CHALLENGE Today you are going to apply what you know about the starting point (Figure 0), the pattern of growth, and the connections between representations to answer some challenging questions. The information in each question, parts (a) through (d), describes a different pattern. The graph of each pattern is a line. From this information, generate the rule, x → y table, graph, and tile pattern (Figures 0 through 3) that follow the pattern.
4-42 Continued You may answer these questions in any order, but make sure you answer each one completely before starting another problem. Work together as a team. The more you listen to how other people see the connections and the more you share your own ideas, the more you will know at the end of the lesson. Stick together and be sure to talk through every idea.
4-42 Continued Each person will turn in his or her own paper at the end of this activity, showing four complete representations for each pattern. Your work does not need to be identical to your teammates’ work, but you should have talked and agreed that all explanations are correct.
Participation Quiz
a. b.
c. d.
Practice