ALEX Resources

   View Standards     Standard(s): [MA2019] (6) 11 :

11. Find the position of pairs of integers and other rational numbers on the coordinate plane.

a. Identify quadrant locations of ordered pairs on the coordinate plane based on the signs of the x and y coordinates.

b. Identify (a,b) and (a,-b) as reflections across the x-axis.

c. Identify (a,b) and (-a,b) as reflections across the y-axis.

d. Solve real-world and mathematical problems by graphing points in all four quadrants of the coordinate plane, including finding distances between points with the same first or second coordinate.

[MA2019] (6) 22 :

22. Write examples and non-examples of statistical questions, explaining that a statistical question anticipates variability in the data related to the question.

This lesson is created to have students compare themselves to Michael Phelps and the features that make him such a good swimmer. Students will measure their height and arm span and graph them on a coordinate graph. Students will then compare their height and arm span to their classmates' to see who might be the best swimmer in the class!

This is a College- and Career-Ready Standards showcase lesson plan.

   View Standards     Standard(s): [MA2019] (6) 11 :

11. Find the position of pairs of integers and other rational numbers on the coordinate plane.

a. Identify quadrant locations of ordered pairs on the coordinate plane based on the signs of the x and y coordinates.

b. Identify (a,b) and (a,-b) as reflections across the x-axis.

c. Identify (a,b) and (-a,b) as reflections across the y-axis.

d. Solve real-world and mathematical problems by graphing points in all four quadrants of the coordinate plane, including finding distances between points with the same first or second coordinate.

In this learning activity from GeoGebra, students will plot the points on the coordinate plane to successfully sink the submarine in this interactive Coordinates Boat Game. 

   View Standards     Standard(s): [MA2019] (6) 11 :

11. Find the position of pairs of integers and other rational numbers on the coordinate plane.

a. Identify quadrant locations of ordered pairs on the coordinate plane based on the signs of the x and y coordinates.

b. Identify (a,b) and (a,-b) as reflections across the x-axis.

c. Identify (a,b) and (-a,b) as reflections across the y-axis.

d. Solve real-world and mathematical problems by graphing points in all four quadrants of the coordinate plane, including finding distances between points with the same first or second coordinate.

In this learning activity from Geogebra, students will practice graphing ordered pairs. Students will complete three separate tasks: Task 1: Practicing plotting ordered pairs, Task 2: Plotting ordered pairs, and Task 3: Creating ordered pairs. Each task will have instructions to help the students to complete the lesson. 

   View Standards     Standard(s): [MA2019] (6) 11 :

11. Find the position of pairs of integers and other rational numbers on the coordinate plane.

a. Identify quadrant locations of ordered pairs on the coordinate plane based on the signs of the x and y coordinates.

b. Identify (a,b) and (a,-b) as reflections across the x-axis.

c. Identify (a,b) and (-a,b) as reflections across the y-axis.

d. Solve real-world and mathematical problems by graphing points in all four quadrants of the coordinate plane, including finding distances between points with the same first or second coordinate.

In this learning activity, students will watch a video Graphing on the Coordinate Plane from Simplify the Middle. Students will learn how to graph points as well as how to identify a point that has already been graphed. After watching the video, students will complete an exit ticket to demonstrate their understanding.

   View Standards     Standard(s): [MA2019] (6) 11 :

11. Find the position of pairs of integers and other rational numbers on the coordinate plane.

a. Identify quadrant locations of ordered pairs on the coordinate plane based on the signs of the x and y coordinates.

b. Identify (a,b) and (a,-b) as reflections across the x-axis.

c. Identify (a,b) and (-a,b) as reflections across the y-axis.

d. Solve real-world and mathematical problems by graphing points in all four quadrants of the coordinate plane, including finding distances between points with the same first or second coordinate.

In this learning activity, students will watch a video to introduce them to the 4 quadrants of the coordinate plane. Students will then complete a 3-2-1 Exit Ticket listing 3 new ideas they learned about coordinate planes, 2 questions they have from the activity, and 1 statement that summarizes the learning goal.

   View Standards     Standard(s): [MA2019] (6) 11 :

11. Find the position of pairs of integers and other rational numbers on the coordinate plane.

a. Identify quadrant locations of ordered pairs on the coordinate plane based on the signs of the x and y coordinates.

b. Identify (a,b) and (a,-b) as reflections across the x-axis.

c. Identify (a,b) and (-a,b) as reflections across the y-axis.

d. Solve real-world and mathematical problems by graphing points in all four quadrants of the coordinate plane, including finding distances between points with the same first or second coordinate.

In this learning activity from Geogebra, students will learn how to identify the parts of the Cartesian plane and how to determine the signs of the coordinates of points on it. Then the students will use an applet to test their understanding of the rules governing the signs of the coordinates of points on the Cartesian plane. 

   View Standards     Standard(s): [MA2019] (6) 11 :

11. Find the position of pairs of integers and other rational numbers on the coordinate plane.

a. Identify quadrant locations of ordered pairs on the coordinate plane based on the signs of the x and y coordinates.

b. Identify (a,b) and (a,-b) as reflections across the x-axis.

c. Identify (a,b) and (-a,b) as reflections across the y-axis.

d. Solve real-world and mathematical problems by graphing points in all four quadrants of the coordinate plane, including finding distances between points with the same first or second coordinate.

In this learning activity from MathsLinks, students will complete a treasure-hunt activity centered on locating points on the number plane and identifying which quadrant they are in or points on the axes.

   View Standards     Standard(s): [MA2019] REG-8 (8) 9 :

9. Interpret y = mx + b as defining a linear equation whose graph is a line with m as the slope and b as the y-intercept.

a. Use similar triangles to explain why the slope m is the same between any two distinct points on a non-vertical line in a coordinate plane.

b. Given two distinct points in a coordinate plane, find the slope of the line containing the two points and explain why it will be the same for any two distinct points on the line.

c. Graph linear relationships, interpreting the slope as the rate of change of the graph and the y-intercept as the initial value.

d. Given that the slopes for two different sets of points are equal, demonstrate that the linear equations that include those two sets of points may have different y-intercepts.

[MA2019] REG-8 (8) 12 :

12. Solve systems of two linear equations in two variables by graphing and substitution.

a. Explain that the solution(s) of systems of two linear equations in two variables corresponds to points of intersection on their graphs because points of intersection satisfy both equations simultaneously.

b. Interpret and justify the results of systems of two linear equations in two variables (one solution, no solution, or infinitely many solutions) when applied to real-world and mathematical problems.

[MA2015] (8) 13 :

13 ) Interpret the equation y = mx + b as defining a linear function whose graph is a straight line; give examples of functions that are not linear. [8-F3]

Example: The function A = s² giving the area of a square as a function of its side length is not linear because its graph contains the points (1,1), (2,4), and (3,9), which are not on a straight line.

[MA2019] REG-8 (8) 27 :

27. Apply the Pythagorean Theorem to find the distance between two points in a coordinate plane.

[MA2019] (6) 11 :

11. Find the position of pairs of integers and other rational numbers on the coordinate plane.

a. Identify quadrant locations of ordered pairs on the coordinate plane based on the signs of the x and y coordinates.

b. Identify (a,b) and (a,-b) as reflections across the x-axis.

c. Identify (a,b) and (-a,b) as reflections across the y-axis.

d. Solve real-world and mathematical problems by graphing points in all four quadrants of the coordinate plane, including finding distances between points with the same first or second coordinate.

[MA2019] ACC-7 (7) 6 :

6. Interpret y = mx + b as defining a linear equation whose graph is a line with m as the slope and b as the y-intercept.

a. Use similar triangles to explain why the slope m is the same between any two distinct points on a non-vertical line in a coordinate plane.

b. Given two distinct points in a coordinate plane, find the slope of the line containing the two points and explain why it will be the same for any two distinct points on the line.

c. Graph linear relationships, interpreting the slope as the rate of change of the graph and the y-intercept as the initial value.

d. Given that the slopes for two different sets of points are equal, demonstrate that the linear equations that include those two sets of points may have different y-intercepts. [Grade 8, 9]

Students will create a map of a shopping excursion by solving systems of linear equations through graphing, substitution, or elimination. Students will then be able to determine the distance traveled through the mall using Pythagorean Theorem. Students will utilize previous grade level standards as a spiral review such as plotting coordinate pairs and using those pairs to find the distance between two points.

This activity is a result of the ALEX Resource Development Summit.

   View Standards     Standard(s): [MA2019] (5) 20 :

20. Graph points in the first quadrant of the coordinate plane, and interpret coordinate values of points to represent real-world and mathematical problems.

[MA2019] (6) 11 :

11. Find the position of pairs of integers and other rational numbers on the coordinate plane.

a. Identify quadrant locations of ordered pairs on the coordinate plane based on the signs of the x and y coordinates.

b. Identify (a,b) and (a,-b) as reflections across the x-axis.

c. Identify (a,b) and (-a,b) as reflections across the y-axis.

d. Solve real-world and mathematical problems by graphing points in all four quadrants of the coordinate plane, including finding distances between points with the same first or second coordinate.

Students lead a quest for buried treasure in this geometry game. Students must follow clues to identify x- and y-coordinates on a treasure map, to lead them around the island before landing on the pirate booty. Students will also graph points on the coordinate plane.  

This activity results from the ALEX Resource Gap Project.

   View Standards     Standard(s): [MA2019] (6) 11 :

11. Find the position of pairs of integers and other rational numbers on the coordinate plane.

a. Identify quadrant locations of ordered pairs on the coordinate plane based on the signs of the x and y coordinates.

b. Identify (a,b) and (a,-b) as reflections across the x-axis.

c. Identify (a,b) and (-a,b) as reflections across the y-axis.

d. Solve real-world and mathematical problems by graphing points in all four quadrants of the coordinate plane, including finding distances between points with the same first or second coordinate.

In this video lesson, students explore ways to find vertical and horizontal distances in the coordinate plane. In the first activity, students use repeated reasoning to explore the relationship between points with opposite coordinates. In the second activity, students develop strategies for finding the distance between two points where the coordinates might not be integers. Students can use previous strategies, such as considering the distance of a point from zero or counting squares.

   View Standards     Standard(s): [MA2015] (6) 9 :

9 ) Understand a rational number as a point on the number line. Extend number line diagrams and coordinate axes familiar from previous grades to represent points on the line and in the plane with negative number coordinates. [6-NS6]

a. Recognize opposite signs of numbers as indicating locations on opposite sides of 0 on the number line; recognize that the opposite of the opposite of a number is the number itself, e.g., - (-3) = 3, and that 0 is its own opposite. [6-NS6a]

b. Understand signs of numbers in ordered pairs as indicating locations in quadrants of the coordinate plane; recognize that when two ordered pairs differ only by signs, the locations of the points are related by reflections across one or both axes. [6-NS6b]

c. Find and position integers and other rational numbers on a horizontal or vertical number line diagram; find and position pairs of integers and other rational numbers on a coordinate plane. [6-NS6c]

[MA2019] (6) 11 :

11. Find the position of pairs of integers and other rational numbers on the coordinate plane.

a. Identify quadrant locations of ordered pairs on the coordinate plane based on the signs of the x and y coordinates.

b. Identify (a,b) and (a,-b) as reflections across the x-axis.

c. Identify (a,b) and (-a,b) as reflections across the y-axis.

d. Solve real-world and mathematical problems by graphing points in all four quadrants of the coordinate plane, including finding distances between points with the same first or second coordinate.

In Module 3, Topic C, students extend their understanding of the ordering of rational numbers in one dimension (on a number line) to the two-dimensional space of the coordinate plane. They construct the plane’s vertical and horizontal axes, discovering the relationship between the four quadrants and the signs of the coordinates of points that lie in each quadrant (6.NS.C.6b, 6.NS.C.6c). Students build upon their foundational understanding from 5th Grade (5.G.1, 5.G.2) of plotting points in the first quadrant and transition to locating points in all four quadrants. Students apply the concept of absolute value to find the distance between points located on vertical or horizontal lines and solve real-world problems related to distance, segments, and shapes (6.NS.C.8).