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Algebra I Lesson Plans – Donna Minniear – November 4-8CSCOPE UNIT 4: INVESTIGATING LINEAR FUNCTIONSTEKSA.1C Describe functional relationships for given problem situations and write equations or inequalities to answer questions arising from the situations. Supporting StandardA.1D Represent relationships among quantities using concrete models, tables, graphs, diagrams, verbal descriptions, equations, and inequalities. Readiness StandardA.1E Interpret and make decisions, predictions, and critical judgments from functional relationships. Readiness StandardA.2A Identify and sketch the general forms of linear (y = x) and quadratic (y = x2) parent functions. Supporting StandardA.2B Identify mathematical domains and ranges and determine reasonable domain and range values for given situations, both continuous and discrete. Readiness StandardA.2C Interpret situations in terms of given graphs or creates situations that fit given graphs. Supporting StandardA.2D Collect and organize data, make and interpret scatterplots (including recognizing positive, negative, or no correlation for data approximating linear situations), and model, predict, and make decisions and critical judgments in problem situations. Readiness StandardA.5A Determine whether or not given situations can be represented by linear functions. Supporting StandardA.5B Determine the domain and range for linear functions in given situations. Supporting StandardA.5C Use, translate, and make connections among algebraic, tabular, graphical, or verbal descriptions of linear functions. Readiness StandardA.6A Develop the concept of slope as rate of change and determine slopes from graphs, tables, and algebraic representations. Supporting StandardA.6B Interpret the meaning of slope and intercepts in situations using data, symbolic representations, or graphs. Readiness StandardA.6C Investigate, describe, and predict the effects of changes in m and b on the graph of y = mx + b. Readiness StandardA.6E Determine the intercepts of the graphs of linear functions and zeros of linear functions from graphs, tables, and algebraic representations. Supporting StandardA.6F Interpret and predict the effects of changing slope and y-intercept in applied situations. Readiness StandardA.6G Relate direct variation to linear functions and solve problems involving proportional change. Supporting StandardPerformance indicatorAnalyze two related problem situations where one can be represented by y = mx and the other can be represented by y = mx + b, b ? 0 such as the following:Builders, Inc. has been contracted to build a high rise in downtown El Paso from ground level. The company averages a rate of two stories per week. After 16 weeks, how many stories of the high rise would Builders, Inc. have completed? How many weeks would it take Builders, Inc. to complete 24 stories of the high rise?Construction Corp. has been contracted to increase the number of stories on a six-story high rise in downtown Amarillo. The company averages a rate of of a story each week. After 16 weeks, how many stories of the high rise would Construction Corp. have completed? How many weeks would it take Construction Corp. to complete 24 stories of the high rise?Create a graphic organizer for each situation that includes a representative function, table, graph, and specific characteristics (domain/range, slope, y-intercept, x-intercept, and their meaning in the problem situation). Write a summary of the effects of changing the slope and y-intercept on the graph of the function and in the problem situation. Compare and contrast the characteristics of the two functions with a Venn diagram. Use the representations to make predictions and critical judgments in the problem situation.Key UnderstandingsVocabularyThe linear parent function is y = x. Linear functions can be proportional (direct variation, y = kx) where y = mx or non-proportional where y = mx + b, b ? 0.Linear functions can be represented using tables, graphs, and algebraic generalizations, and connections can be used to translate between representations.Slope (constant rate of change), x-intercepts, and y-intercepts can be found from a table, graph, or algebraic generalization and have specific meanings in mathematical and real world situations.Changes in the slope and y-intercept have specific effects on the graph of the representative function and in the problem situation.Problem situations can be modeled using two-variable inequalities, and the solution can be represented graphically on a coordinate plane.decreasingdependentdirect variationdomainfunction notationhorizontal changeincreasingindependentlinear functionlinear inequalityparameter changeparent functionrangerate of changeslopevertical changex-intercepty-interceptzero of a functionMondayLEADERSHIP MEETING:Leaders and Co-Leaders preview the activities that will be completed during rotations this week. They do examples and ask questions so that they will be able to effectively lead their teams through the rotations.LINEAR PARENT FUNCTION – Students investigate the linear parent function y = x by creating a table and graph of the function. They also explore the characteristics of other linear functions in the form of y = mx + b and learn that m is the slope and b is the y-intercept. WRITING: In an equation such as y = 2x + 5, how can you determine the slope and the y-intercept?SGPT: In a problem situation how can you determine the slope and the y-intercept?We Will & I Will StatementsLINEAR PARENT FUNCTIONWe will investigate the characteristics of the linear parent functionI will create a table and graph that represent the linear parent function.CHANGES IN MWe will observe how changes in m affect the shape of a graph.I will use a calculator to graph functions with different slopes and record my observations about the steepness of the line in comparison to the parent function.CHANGES IN BWe will observe how changes in b affect the shape of a graph.I will use a calculator to graph functions with different y-intercepts and record my observations about where the line intersects the y-axis in comparison to the parent function.SLOPE OF A LINEWe will find the slope of a given linear graph.I will identify two points on a line and find the ratio of the change in y to the change in x in order to determine the slope.FINDING SLOPE FROM TWO POINTSWe will find the slope from two given coordinates.I will subtract the y values and the x values in order to find the ratio of the change in y to the change in x and determine the slope.Tuesday-Friday – Team Rotations1. CHANGES IN M – Students use the calculator to observe how changes in m affect a graph. They discover that m (slope) determines the steepness of a line.SGPT – How does a negative number affect the slope? What do you notice about slope values that are less than one whole? When the slope changes, does the line intersect the y-axis in a different location?WRITING – Through your observations, what changes to the parent function did you observe as m (the slope) changed?2. CHANGES IN B – Students use the calculator to observe how changes in b affect a graph. They discover that b (y-intercept) determines where the line intersects the y-axis.SGPT – When you add a negative number to x, what changes do you see in the line? When you add a positive number to x what changes do you see in the line? Do changes in b affect the steepness of the line?WRITING – Through your observations, what changes to the parent function did you observe as b (the y-intercept) changed?3. SLOPE OF A LINE – Students watch a Khan Academy video that demonstrates how to find the slope of a line. Students practice finding the slope of four different graphs following the video.SGPT – When finding the slope of a line, how can you use the shape of the line to tell if your answer is reasonable?WRITING – Describe in words how you would determine the slope of a line?4. FINDING SLOPE FROM TWO POINTS – Teacher led group learns how to find the slope when given two coordinates.SGPT – When determining the slope from two points, you will get the same result regardless of which point you start with…why?WRITING – Describe in writing how you can use two coordinates to find the slope of a line? ................
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