If you are citizen of an European Union member nation, you may not use this service unless you are at least 16 years old.
You already know Dokkio is an AI-powered assistant to organize & manage your digital files & messages. Very soon, Dokkio will support Outlook as well as One Drive. Check it out today!

A1-A-4-2

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

A1.A.4.2 Solve mathematical and real-world problems involving lines that are parallel, perpendicular, horizontal, or vertical.

In a Nutshell

Students will apply their knowledge of lines to focus on identifying parallel and perpendicular lines by comparing the slopes of each line and use that knowledge to recognize horizontal and vertical lines by their slopes.

Student Actions	Teacher Actions
Develop Mathematical Reasoning when identifying parallel and perpendicular lines by comparing the slopes of each line. Develop a Deep and Flexible Conceptual Understanding by graphing lines to determine whether they are parallel or perpendicular. Develop the Ability to Make Conjectures, Model, and Generalize using an equation and a point not on the line to write an equation that may be parallel, perpendicular, vertical or horizontal to the given equation through the given point. Develop the Ability to Communicate Mathematically by analyzing a real-world graph where a part is a vertical or horizontal line and where there are groups of line which may be parallel or perpendicular.	Give students opportunities to use and connect mathematical representations to compare a variety of lines on a graph and the equation. Pose purposeful questions to students about what they notice for all the lines that are parallel, perpendicular, horizontal and vertical. Facilitate meaningful mathematical discourse to expect and encourage students to prove their observations of parallel or perpendicular by finding the slopes of the lines. Build procedural fluency from conceptual understanding about discussing lines that are vertical and horizontal. Discuss with students what it means to have a slope of 0 and a slope that is undefined. Encourage students to plot the points and draw the line so they make a connection between the line and the result of plugging coordinate pairs into the slope formula.
Key Understandings	Misconceptions
Parallel lines are lines with the same slopes. Example: Write an equation of a line that is parallel to 2x-4y=10 through the point (3, 5). Slope = ½ y-5=12x-3 2y-10=x-3 x-2y= -7 Perpendicular lines are lines with negative (opposite) reciprocal slopes. Example: Which lines are perpendicular to y = 1/2x + 3? y = 2x +3 2x + y = -1 y = -½x + 4 y = -½ x - ⅓ y = -2x - 5 2x - y = 6 The correct solution is: 2x + y = -1 y = -2x – 5 Horizontal lines have a slope of zero and show no change in the dependent variable. Example: Discuss what the horizontal parts of this graph represent for the speed of the racing car. Possible Answer: The moments in time when the car is at a constant speed. Vertical lines have no slope or an undefined slope and show no change in the independent variable.	Students will confuse the slopes of parallel and perpendicular lines. Students may sometimes look at two lines and assume they are either parallel or perpendicular without checking slopes. When asked to find an equation that is parallel to a given equation, sometimes students will give an equation that has the same slope, but also the same y-intercept. This is the same line, NOT parallel. Students think that a slope of zero and no slope or undefined slope are the same. Students will mistake a horizontal line of y=a, where a is a real number with a vertical line of x=b, where b is a real number.