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A1-A-4-1

Page history last edited by Brenda Butz 6 years, 3 months ago

A1.A.4.1 Calculate and interpret slope and the x and y intercepts of a line using a graph, an equation, two points, or a set of data points to solve real-world and mathematical problems.

In a Nutshell

Students will use their understanding of linear relationships to find the slope, x- and y-intercepts. They will also explain the meanings of these in the context of the problem, both mathematical and real-world.

	Teacher Actions
Students will develop accurate and appropriate procedural fluency when calculating the slope and intercepts of a line using known formulas. Students will develop mathematical reasoning by comparing multiple models of linear equations including graphs, equations, sketches and verbal models to identify slopes and intercepts, and interpreting those correctly in context of the problem. Students will develop the ability to communicate mathematically as they justify their processes to teachers and peers and demonstrate their understanding of the meanings of slope and intercepts in the context of both mathematical problems and real-world situations.	Implement tasks that promote reasoning and problem solving by asking students to examine and interpret data sets, equations and graphs which represent real-world problems. Use and connect mathematical representations, presenting both mathematical and real-world problems as graphs, tables, data sets and equations and asking students to look for patterns in and among them. Pose purposeful questions, asking students to not only find the slopes and intercepts of linear relationships but also to interpret their findings accurately. Build procedural fluency from conceptual understanding as students work to find slopes and intercepts given different types of information, building on their understanding of working with formulas and the concepts of what slope and intercepts represent. Elicit and use evidence of student thinking as students justify their processes and explain their interpretations of solutions in context.
Key Understandings	Misconceptions
Students will be able to identify the slope and y-intercept of an equation given the equation in slope-intercept form. Example: y=2x+4, slope = 2 and y-intercept = 4 Students will be able to calculate the x- and y-intercepts of a line algebraically given the equation of the line. Example: 2x+3y=18 2(0)+3y=18 y=6 2x+3(0)=18 x=6 Students will be able to identify the slope and intercepts of an equation given a graph. Students will apply the slope formula to calculate the slope of a line given two points or a large set of data. Students will interpret the slope and intercepts of a linear relationship in the context of the problem. Example: Bobby has $1100 in his savings account. Each month, he spends $75. This can be represented with the equation S=1100-75m the slope, x-intercept and y-intercept. Tell what each of those mean. slope= -75, decrease in savings each month x-intercept= 14.67, the number of months until the account reaches $0 y-intercept= 1100, the beginning amount in the savings account.	Students will often confuse x and y values with the x and y intercepts. Students will often confuse the x and y intercepts when computing them algebraically. Students will often flip the slope formula, putting x above y. They will sometimes also use the x and y values out of order in the formula. Some students will miscalculate positive or negative slope.