Instructional Overview Launch Question Summary Performance Task With so many ways to represent a linear relationship, where do you start? Use what you know to move between equations, graphs, tables, and contexts. There is a by matrix, and each cell asks the student to fill in different information about the same equation. Each problem will provide the information for a different cell, so the students will have a different starting place. Teacher Notes Model the problem, starting with y 2x 5. Have the students work in groups or guide them as they work through each cell. Situation: Sample answer: Your friend owes her mom $5, and she earns $2 for every day she makes her bed. Supplies Mathematical Discourse Writing/Discussion Prompts Table: Sample answer: 1,, 2, 1,, 1 Slope-intercept form: given Graph: Standard form: 2x y 5 Sample answer: f 1, f 2 1, f 1 Point-slope form: y 1 2 x Sample answer: Sample answer: y 2x 1 Sample answer: y 1 x 2 Handouts, copies of the matrix ( per student), graph paper If you are given the slope of a line, and a point on that line, where would you start to fill in the table? Where would you go next? 1. Why does each different representation provide enough information to arrive at the other forms? 2. If you are given a choice on which cell to start with, which one would you select and why? 59
Name Date Curriculum Content TEKS Content Standards Mathematical Thinking A.2.B, A.2.C, A..A 1. E. Create and use representations to organize, record, and communicate mathematical ideas. Students learn that a linear relationship is the same regardless of the format used to represent it. Rubric 1. Situation: Sample answer: An international call requires $ to connect and $0.25 for each additional minute. Table: given Slope-intercept form: y 1 x Graph: All cells correct Most cells correct, with minor Standard form: x y 12 Sample answer: f f 8 5, 2 f, Point-slope form: Sample answer: y 1 x Sample answer: y 1 x Sample answer: y x 1 60 Algebra 1 Copyright Big Ideas Learning, LLC
Rubric (continued) 2. Situation: Sample answer: The temperature is 1 Fahrenheit and dropping 2 Fahrenheit each hour. Table: Sample answer: 0, 1,,, 6, 5 Slope-intercept form: y 2 x 1 Graph: Standard form: 2x y Sample answer: f 0 1, f, f 6 5 Point-slope form: Sample answer: 2 x y Sample answer: y 2 x 2 Sample answer: y x 1 2. Situation: given Table: Sample answer: 1, 0, 2, 5,, 50 Slope-intercept form: y 5x 5 Graph: Standard form: 5x y 5 Sample answer: f 1 0, f 2 5, f 50 Point-slope form: y 0 5 x 1 Sample answer: Sample answer: y 5x 0 Sample answer: y 1 x 10 5 All cells correct Most cells correct, with minor All cells correct Most cells correct, with minor 61
Name Date Rubric (continued). Situation: Fencing for each rose bush is feet and the contractor includes feet for trimming errors. Table: Sample answer: 1, 7, 2, 11,, 15 Slope-intercept form: y x Graph: Mathematical Thinking: Standard form: given Sample answer: f 1 7, f 2 11, f 15 Point-slope form: Sample answer: y 7 x 1 Sample answer: y x 2 Sample answer: y 1 x 2 Create and use representations to organize, record, and communicate mathematical ideas. The students create and move between different representations to communicate the mathematical idea of a linear relationship. Total All cells correct Most cells correct, with minor The student demonstrates the ability to use the different representation starting in any cell. The student explains the path. Award partial credit as needed. 20 62 Algebra 1 Copyright Big Ideas Learning, LLC
With so many ways to represent a linear relationship, where do you start? Use what you know to move between equations, graphs, tables, and contexts. Each cell of the matrix contains a different format for the same problem. Make four copies of the matrix. For each problem, start with the given information and fill in the rest of the chart. Each time, you will start in a different place. 1. Table:,, 8, 5,, 2 2. Slope and intercept: m 2 and b 1. Situation: The photography studio charges an initial fee of $5 and $5 for each picture.. Standard Form: x y Situation Table Slope-intercept form x y Graph Standard form in functional notation Point-slope form Equation of a parallel line Equation of a perpendicular line For each of the four problems, describe the order in which you filled in the matrix and why you chose that order. 6