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see if other students can guess what they observed. If technology is not available, have students construct the table and graph by hand on a posterboard.Activity 4: Patterns and Slope (GLEs: 13, 15, 25)Materials List: math learning log, paper, pencil, square algebra tiles, Patterns and Slope BLM, graph paperHave students use the Patterns and Slope BLM to complete this activity. Divide students into groups and provide them with square algebra tiles. Have the studentsarrange 3 tiles in a rectangle and record the width (x) and the perimeter (y) on the BLM. Have the students fit 3 more tiles under the previous tiles and continue adding tiles, putting the values in a table. Students should continue working with their groups to Algebra IUnit 3Linear Functions and Their Graphs28
Louisiana Comprehensive Curriculum, Revised 2008complete the BLM through the completion of the table. Guide students as they complete the remainder of the BLM. Have students notice that the change in the y-values is the same. Have them graph the data and decide if it is linear. Ask students what changed in the pattern (the widths that keep increasing)and what remained constant (the length of the sides added together (3+3)). Have them write a formula to describe the pattern (y = 6 +2x). Guide students toconclude that what remained constant in the pattern will be the constant in the formula and the rate of change in the pattern will be the slope. Guide students to make a connection between the tabular, graphical and algebraic representation of the slope.In their mathlearning logs(view literacy strategy descriptions) have students respond to the following prompt: A child’s height is an example of a variable showing a positive rate of change over time. Give two examples of a variable showing a negative rate of change over time. Explain your answer. Have students share their answers with the class and combine a class list of all studentanswers. Discuss the answers and have students determine whether the examples areindeed negative rates of change.Activity 5: Recognizing Linear Relationships (GLEs: 9, 39, 40)Materials List: paper, pencilProvide students with several input-output tables (linear) paired with a graph of that samedata. Include examples of real-life linear relationships. (Examples of linear data sets can be found in any algebra textbook.) Introduce slope as the concept ofriserun. Have students determine the slope of the line and then investigate the change in the x-coordinates and the accompanying change in the y-coordinates. Ask if a common difference was found. How does this common difference in the y-coordinates compare to the slope (rate of change) found for the line? Using this information, have students conjecture how to determine if an input-output table defines a linear relationship. (There is a common difference in the change in y over the change in x.)Have students write a linear equation for each of the graphs. Have students compare the input-output tables, the graphs, and theequations to see how the slope and y-intercepts affect each.