ALEX | Alabama Learning Exchange

Distances on a Coordinate Plane

Classroom Resource Information

Title:

Distances on a Coordinate Plane

URL:

https://aptv.pbslearningmedia.org/resource/our20-math-6714/distances-on-a-coordinate-plane/

Content Source:

PBS

Type:

Audio/Video

Overview:

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.

Content Standard(s):

Mathematics
MA2019 (2019)
Grade: 6

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.

Unpacked Content

Evidence Of Student Attainment:

Students:

Create and interpret coordinate axes with positive and negative coordinates.
Given ordered pairs made up of rational numbers, locate and explain the placement of the ordered pair on a coordinate plane.
Given two ordered pairs that differ only by signs, locate the points on a coordinate plane and explain the relationship of the locations of the points as reflections across one or both axes.
Given real-world and mathematical problems where a coordinate graph will aid in the solution and given a graph of a real-world or mathematical situation, interpret the coordinate values of the points in the context of the situation including finding vertical and horizontal distances.

Teacher Vocabulary:

Coordinate plane
Quadrants
Coordinate values
ordered pairs
x axis
y axis
Reflection

Knowledge:

Students know:

Strategies for creating coordinate graphs.
Strategies for finding vertical and horizontal distance on coordinate graphs.

Skills:

Students are able to:

Graph points corresponding to ordered pairs,
Represent real-world and mathematical problems on a coordinate plane.
Interpret coordinate values of points in the context of real-world/mathematical situations.
Determine lengths of line segments on a coordinate plane when the line segment joins points with the same first coordinate (vertical distance) or the same second coordinate (horizontal distance).

Understanding:

Students understand that:

A graph can be used to illustrate mathematical situations and relationships. These representations help in conceptualizing ideas and in solving problems,
Distances on lines parallel to the axes on a coordinate plane are the same as the related distance on the axis (number line).

Diverse Learning Needs:

Essential Skills:

Learning Objectives:
M.6.11.1: Define quadrant, coordinate plane, coordinate axes (x-axis and y-axis), horizontal, vertical, and reflection.
M.6.11.2: Demonstrate an understanding of an extended coordinate plane.
M.6.11.3: Draw a four-quadrant coordinate plane.
M.6.11.4: Draw and extend vertical and horizontal number lines.
M.6.11.5: Interpret graphing points in all four quadrants of the coordinate plane in real-world situations.
M.6.11.6: Recall how to graph points in all four quadrants of the coordinate plane.
M.6.11.7: Define ordered pairs.
M.6.11.8: Name the pairs of integers and/or rational numbers of a point on a coordinate plane.
M.6.11.9: Demonstrate when two ordered pairs differ only by signs, the locations of the points are related by reflections across one or both axes.
M.6.11.10: Identify which signs indicate the location of a point in a coordinate plane.
M.6.11.11: Recall how to plot ordered pairs on a coordinate plane.
M.6.11.12: Define reflections.
M.6.11.13: Calculate the distances between points having the same first or second coordinate using absolute value.

Prior Knowledge Skills:

Model writing ordered pairs.
Identify the x- and y- values in ordered pairs.
Label the vertical axis (y).
Label the horizontal axis (x).
Define ordered pair of numbers, quadrant one, coordinate plane, and plot points.
Locate positive numbers on a vertical number line.
Examples: thermometer, map.
Locate positive numbers on a horizontal number line.
Locate negative numbers on a horizontal number line.
Label x- and y-axis and zero on a coordinate.
Illustrate vertical and horizontal number lines.
Specify locations on the coordinate system.
Define x-axis, y-axis, and zero on a coordinate.
Define ordered pair of numbers.
Locate positive numbers on a horizontal number line.
Locate negative numbers on a horizontal number line.
Define symmetry.
Identify lines of symmetry on one-dimensional figures.