"Graphing Calculator Template - DOC"
Technology Integration Unit Template Title: Investigating Slope with a Graphing Calculator Overview of the Technology Integration Unit (Brief Description): This lesson is an introductory activity on the effects of slope on the graphs of equations. It uses graphing calculators to help students make the connection between changes in equations and corresponding changes in graphs. Grade Level: High School (General) Time allotment: 1 Hour Curriculum Area: Mathematics Learning Objectives: - Students will understand the effect of changing the x-coefficient of a linear equation on its graph. - Students will gain initial familiarity with the slope-intersect form of an equation. - Students will become more skilled in calculator use. Curriculum Standards Delaware Mathematics Standard #1 Students will develop their ability to SOLVE PROBLEMS by engaging in developmentally appropriate problem-solving opportunities in which there is a need to use various approaches to investigate and understand mathematical concepts; to formulate their own problems; to find solutions to problems from everyday situations; to develop and apply strategies to solve a wide variety of problems; and to integrate mathematical reasoning, communication and connections. Delaware Mathematics Standard #3 Students will develop their ability to REASON MATHEMATICALLY by solving problems in which there is a need to investigate significant mathematical ideas in all content areas; to justify their thinking; to reinforce and extend their logical reasoning abilities; to reflect on and clarify their own thinking; to ask questions to extend their thinking; and to construct their own learning. Delaware Mathematics Standard #7 Students will develop an understanding of ALGEBRA by solving problems in which there is a need to progress from the concrete to the abstract using physical models, equations and graphs; to generalize number patterns; and to describe, represent and analyze relationships among variable quantities. Specifically, this lesson corresponds with subgoals: 7.90 model relationships among quantities using symbols and expressions; 7.91 develop appropriate symbol sense to use algebraic technology; 7.92 use tables and graphs to interpret expressions, equations and inequalities; 7.93 describe relationships between variable quantities verbally, symbolically and graphically (including slope as a rate of change); 7.94 translate and make connections from narrative to table, graph and function; 7.98 explore algebraic relationships using technology Technology Standards 1 Basic operations and concepts • Students demonstrate a sound understanding of the nature and operation of technology systems. • Students are proficient in the use of technology. Performance indicators: 1. Demonstrate an understanding of concepts underlying hardware, software, and connectivity, and of practical applications to learning and problem solving 2 Technology productivity tools • Students use technology tools to enhance learning, increase productivity, and promote creativity. • Students use productivity tools to collaborate in constructing technology- enhanced models, prepare publications, and produce other creative works. Performance indicators: 1. Research and evaluate the accuracy, relevance, appropriateness, comprehensiveness, and bias of electronic information sources concerning real-world problems. Resources Hardware One graphing calulator (any type, TI-82 through TI-86 or equivalent) for each student. If less, have students work in pairs. One overhead graphing calculator projector. OR, 1 computer for each student (use web-based GC) and one computer with projector diplay. Software None Relevant Material Handout for student responses Bookmarked Sites http://www.coolmath.com/graphit/index.html (if using computer instead of graphing calculator) Activities To begin the lesson, use existing warm-up, review of previous lesson, or start immediately with instruction. To begin (this section can be removed if students are very familiar with using graphing calculators), the teacher should graph the equation y=2x on the overhead calculator display. Students should graph the same equation on their calculators along with her. This will give a chance for students to go through the sequence of graphing. Next, the teacher should ask the students to describe the graph, asking questions like "Would you describe this line as steep?" "Where does it cross the x-axis? The y-axis?" Now, the teacher should either use the table function on the calculator to display a table of values for the equation, or construct one by hand. The teacher can then draw comparisons between the equation, table, and graph (such as the fact that there is a 2 in the equation and the y-values in the table go up by 2 each time, as well as x- and y- intercepts). The students should draw the graph and table and write their observations in their notes. At this point, the students will engage in guided practice using the worksheet. The teacher should circulate around the room looking for misconceptions, technology issues, exemplary student responses to share, etc. The students can complete the worksheets individually or in pairs. For homework, the students could be asked to predict what the graph of each of the following equations would look like. They should draw their prediction and then make a table for each euqation to check their prediction. If the table and graph do not match, they should sketch a new graph based on their table. Equations: y = 5x y = (1/2)x y = 0.7x 2y = x Assessment Students can be assessed by collecting their handouts at the beginning of the next class period with their homework (they may need the handouts to complete the homework). Responses could be graded based on depth of mathematical conversation, use of good mathematics language, and the completeness of graphs and tables. Interdisciplinary Connections This lesson could be connected to a science lesson on graphs or fundamental equations. For example, if students were studying physics, a connection could be made to graphs of the equation F=MA, by asking what effect the changing the mass would have on the force needed for acceleration. Helpful Notes This lesson could easily be modified to explore the effect of y-intercepts on graphs of linear equation (by simply changing the prompts on the worksheet) or even to explore the effects of different parameters on quadratic and cubic graphs. This lesson could also be adapted for use in a "Families of Functions" unit in trig/precalc by varying the type of equation as well as the parameters. Theory to Practice Connection This lesson reflects a constructivist learning theory because it asks students to interact with an environment (the graphing calculator) to construct their own understanding about the effects of these parameters. If students work on the handout in groups, the social aspect of learning could be highlighted. In addition, this lesson could be considered to reflect the situative perspective because it is authentic in two ways. First, it mirrors the kinds of activities that mathematicians do to figure out problems, and second, it encourages the use of thinking skills which are authentic to everyday life.