# MA.6.GR.1.1

Extend previous understanding of the coordinate plane to plot rational number ordered pairs in all four quadrants and on both axes. Identify the x- or y-axis as the line of reflection when two ordered pairs have an opposite x- or y-coordinate.
General Information
Subject Area: Mathematics (B.E.S.T.)
Strand: Geometric Reasoning
Status: State Board Approved

## Benchmark Instructional Guide

### Terms from the K-12 Glossary

• Axes (of a graph)
• Coordinate Plane
• Coordinate
• Origin

### Vertical Alignment

Previous Benchmarks

Next Benchmarks

### Purpose and Instructional Strategies

In grade 5, students plotted and labeled ordered pairs of whole numbers in the first quadrant. Students in grade 6 plot ordered pairs of rational numbers in all four quadrants. In grade 7, students will apply their knowledge of the plotting of ordered pairs to the graphing of proportional relationships.
• Instruction includes making connections to opposites on a number line and absolute value, as well as to reflections across the $x$-and $y$-axes.
• Instruction includes using academic terminology including calling ordered pairs as coordinates and as a coordinate pair.
• Instruction includes students’ plotting ordered pairs on graphs with different scales.
• For example, students can plot the ordered pair ($\frac{\text{1}}{\text{2}}$ , 3), where the $x$-and $y$-axis have a scale of 2 or a scale of 0.5.

### Common Misconceptions or Errors

• Students may switch the location of the $x$-coordinate and the $y$-coordinate in the ordered pair.
• Students may misunderstand that a point on an axis has at least one coordinate of zero.
• For example, the point on the graph identified as (3,0) may have a student incorrectly identify the location as (3,3) or just 3.
• Students may misunderstand the numbering of the four quadrants (upper right in a counter-clockwise rotation) as well as which coordinate is positive and which coordinate is negative.

### Strategies to Support Tiered Instruction

• Teacher creates an anchor chart while students create their own graphic organizer to include key features of a coordinate plane. Features include the $x$-axis, $y$-axis, origin, quadrants, and an ordered pair.
• Instruction includes building connections to plotting points on number lines. On one sheet of tracing paper, label a horizontal number line as the ??-axis and plot the $x$-value. On another sheet of tracing paper, label a vertical number line as the $y$-axis and plot the $y$-value. Overlap the two number lines with a point of intersection at the origin (0,0). Place a third sheet of tracing paper on top of the two number lines, trace and label the $x$- and $y$-axis to produce a coordinate plane. The location of a new point should then be plotted in the appropriate quadrant to represent the horizontal and vertical locations of the two previously plotted points. This same strategy helps to draw connections to a point laying on an axis if one of the coordinates is zero.
• Teachers may provide instruction on using reasonable estimations when plotting rational coordinates on the coordinate plane.
• For example, if a student is plotting −4$\frac{\text{3}}{\text{5}}$ for an $x$-value and 3 for $y$-value, they need to know that $\frac{\text{3}}{\text{5}}$ is more than half, so to graph the $x$-value, they should plot a point between −4 and −5, with the point closer to the −5. Then the student can more precisely adjust the point if necessary (if any other value is between −4 and −5 they can adjust, but if not, they will see that their estimation will be a valid way to order.)
• When plotting rational coordinates, teacher provides a coordinate plane with an appropriate scaling to match the fractional or decimal units so the points graphed will fall on the intersection of two minor grid lines.
• For example, if a student is graphing the ordered pair (−0.5, 2.25) the $x$-and $x$-axis could have a scale of 0.25.

Part A. On a graph paper, draw a coordinate grid. Label the axis and plot the ordered pairs below.
• $A$ (2 , $\frac{\text{5}}{\text{2}}$)
• $B$ (−4, 5)
• $C$ (−4, −7)
• $D$ ($\frac{\text{3}}{\text{2}}$,−5)
• $E$ (0, 0)
• $F$ (2, −8)
• $G$ (0, 0.6)
• $H$ (−4, −5)
Part B. Which ordered pair(s) are located on an axis?
Part C. Which points are in quadrant III?
Part D. Which points are a reflection of each other and over which axis are they reflected?

Part A. Create a picture with fewer than 20 coordinates in the four quadrants. Write your coordinates on a separate piece of paper.
Part B. Trade your list of ordered pairs with a partner. Recreate your partner’s picture on a new sheet of graph paper.
Part C. Discuss differences and discuss possible errors you or your partner may have made when recreating each other’s pictures.

If given $x$ > 0 and $y$ > 0, in which quadrant or axis will each ordered pair described below lie? Explain your answer.
a. (−$x$, $y$)

b. (−$x$, 0)

c.($x$, −$y$

d. (0, $y$)

### Instructional Items

Instructional Item 1
What is the value of the $x$-coordinate of the ordered pair that reflects (5$\frac{\text{1}}{\text{2}}$,−8) over the $y$-axis?

Instructional Item 2
Using the graph below, state the ordered pair that describes the point plotted in Quadrant II?

*The strategies, tasks and items included in the B1G-M are examples and should not be considered comprehensive.

## Related Courses

This benchmark is part of these courses.
1205010: M/J Grade 6 Mathematics (Specifically in versions: 2014 - 2015, 2015 - 2022, 2022 and beyond (current))
1205020: M/J Accelerated Mathematics Grade 6 (Specifically in versions: 2014 - 2015, 2015 - 2020, 2020 - 2022, 2022 and beyond (current))
1204000: M/J Foundational Skills in Mathematics 6-8 (Specifically in versions: 2014 - 2015, 2015 - 2022, 2022 and beyond (current))
7812015: Access M/J Grade 6 Mathematics (Specifically in versions: 2014 - 2015, 2015 - 2018, 2018 - 2022, 2022 and beyond (current))

## Related Access Points

Alternate version of this benchmark for students with significant cognitive disabilities.
MA.6.GR.1.AP.1: Plot integer ordered pairs in all four quadrants and on both axes.

## Related Resources

Vetted resources educators can use to teach the concepts and skills in this benchmark.

## Educational Games

BattleGraph:

A game that is an off-shoot of the classic game Battleship, for practice with coordinate graphing, complete with reproducible templates and animated PowerPoint introduction.

Type: Educational Game

Maze Game:

In this activity, students enter coordinates to make a path to get to a target destination while avoiding mines. This activity allows students to explore Cartesian coordinates and the Cartesian coordinate plane. This activity includes supplemental materials, including background information about the topics covered, a description of how to use the application, and exploration questions for use with the java applet.

Type: Educational Game

## Formative Assessments

Graphing Points in the Plane:

Students are asked to graph points given their coordinates and describe the coordinates of graphed points.

Type: Formative Assessment

Graphing on Cartesian Planes:

Students are asked to graph points given their coordinates and describe the coordinates of graphed points when the axes have different scales.

Type: Formative Assessment

Point Locations:

Students are asked to compare the graphs of coordinates that are opposite in sign on a number line and in the coordinate plane.

Type: Formative Assessment

Students are asked to determine in what quadrant or on which axis, points described algebraically, are located.

Type: Formative Assessment

## Lesson Plans

Where Will I Land?:

This is a beginning level lesson on predicting the effect of a series of reflections or a quick review of reflections for high school students.

Type: Lesson Plan

Newscast Weather Report:

This activity engages the students in using data on weather conditions for a set of hurricanes to understand relationships between wind speed, air pressure, and water temperature as well as the impact of global wind and water patterns on hurricane paths. The integrated lesson involves the knowledge of a coordinate plane and its application in ocean mapping.

Type: Lesson Plan

Mapping the School:

This project is used to help students enhance their ability to use and understand the coordinate plane by creating a map of their school.

Type: Lesson Plan

Modern Math Target Practice:

The lesson uses the classroom as a coordinate plane then moves into plotting points on a graph. It culminates with a target-practice game.

Type: Lesson Plan

Game Room Copy Cat:

In this lesson, students will learn to plot points in all four quadrants of the coordinate grid, create a game room using only polygons, and describe the points in hopes of having their partner draw the exact room which will be kept a secret until the end. It's all about giving and following instructions while applying an understanding of positive and negative numbers on the coordinate grid.

Type: Lesson Plan

Capture the Boat - Sink the Teacher's Fleet!:

In this lesson, students learn about the four quadrants of a coordinate plane and how to plot points in those quadrants. Students also learn how to use linear equations to predict future input and output pairs. Students work together to try to sink the teacher's fleet in a Battleship-type game while the teacher tries to sink theirs first.

Type: Lesson Plan

Plotting Polygons with GeoGebra:

This introductory lesson guides students through the process of graphing polygons on the coordinate plane and finding vertical and horizontal side lengths. Explicit instructions are given for teachers who are new to GeoGebra. A detailed summative assessment includes extensions and an answer key is provided.

Type: Lesson Plan

Dogpound Graphing:

Students will graph ordered pairs within all four quadrants of a coordinate plane in order to complete the picture of a bulldog.

Type: Lesson Plan

Exploring Rotations with GeoGebra:

This lesson will help students understand the concept of geometric rotations. The teacher/students will use a GeoGebra applet to derive the rules for rotating a point on the coordinate plane about the origin for a 90-degree, 180-degree, and a 270-degree counterclockwise rotation.

Type: Lesson Plan

Coordinate Grids: The Key to the City (solving real-world problems using the coordinate grid):

This lesson contains a small group activity in which students use knowledge of graphing in a 4-quadrant coordinate grid. Students will individually solve a real-world problem to find the distance between two points on a coordinate grid. Students must utilize their knowledge of absolute value and subtracting integers to determine distances between points.

Type: Lesson Plan

The Mystery of Crop Circles...on a coordinate plane:

In this lesson, students will use their knowledge of plotting points on quadrant I of the coordinate plane to figure out other coordinate pairs within quadrants II, III, and IV. Students are challenged to match description cards to the matching "map" (four-coordinate grid).

Type: Lesson Plan

## Original Student Tutorial

Capturing Flags on the Coordinate Plane Part 1:

Get ready for an epic Capture the Flag Tournament as you explore the coordinate plane in this interactive tutorial.

Type: Original Student Tutorial

## Perspectives Video: Teaching Idea

Supporting English Language Learners in the Math Classroom:

Unlock an effective teaching strategy for using cognates to help English Language Learners in the Mathematics classroom in this Teacher Perspectives video for educators.

Type: Perspectives Video: Teaching Idea

## Tutorials

The Coordinate Plane:

Students will plot an ordered pair on the x (horizontal) axis and y (vertical) axis of the coordinate plane.

Type: Tutorial

Coordinate Plane:

Students will become familiar with the coordinate plane.

Type: Tutorial

This video contains examples of plotting coordinate pairs and identifying their quadrant.

Type: Tutorial

Students will learn how to identify the four quadrants in the coordinate plane.

Type: Tutorial

The Cartesian Coordinate System:

The Cartesian Coordinate system, formed from the Cartesian product of the real number line with itself, allows algebraic equations to be visualized as geometric shapes in two or three dimensions.  While this tutorial includes the basis of Coordinate system, it also includes ideas beyond fifth grade standards.  Most likely only advanced fifth graders would find the video engaging.

Type: Tutorial

## MFAS Formative Assessments

Graphing on Cartesian Planes:

Students are asked to graph points given their coordinates and describe the coordinates of graphed points when the axes have different scales.

Graphing Points in the Plane:

Students are asked to graph points given their coordinates and describe the coordinates of graphed points.

Students are asked to determine in what quadrant or on which axis, points described algebraically, are located.

Point Locations:

Students are asked to compare the graphs of coordinates that are opposite in sign on a number line and in the coordinate plane.

## Original Student Tutorials Mathematics - Grades 6-8

Capturing Flags on the Coordinate Plane Part 1:

Get ready for an epic Capture the Flag Tournament as you explore the coordinate plane in this interactive tutorial.

## Student Resources

Vetted resources students can use to learn the concepts and skills in this benchmark.

## Original Student Tutorial

Capturing Flags on the Coordinate Plane Part 1:

Get ready for an epic Capture the Flag Tournament as you explore the coordinate plane in this interactive tutorial.

Type: Original Student Tutorial

## Educational Game

Maze Game:

In this activity, students enter coordinates to make a path to get to a target destination while avoiding mines. This activity allows students to explore Cartesian coordinates and the Cartesian coordinate plane. This activity includes supplemental materials, including background information about the topics covered, a description of how to use the application, and exploration questions for use with the java applet.

Type: Educational Game

## Tutorials

The Coordinate Plane:

Students will plot an ordered pair on the x (horizontal) axis and y (vertical) axis of the coordinate plane.

Type: Tutorial

Coordinate Plane:

Students will become familiar with the coordinate plane.

Type: Tutorial

This video contains examples of plotting coordinate pairs and identifying their quadrant.

Type: Tutorial

Students will learn how to identify the four quadrants in the coordinate plane.

Type: Tutorial

The Cartesian Coordinate System:

The Cartesian Coordinate system, formed from the Cartesian product of the real number line with itself, allows algebraic equations to be visualized as geometric shapes in two or three dimensions.  While this tutorial includes the basis of Coordinate system, it also includes ideas beyond fifth grade standards.  Most likely only advanced fifth graders would find the video engaging.

Type: Tutorial

## Parent Resources

Vetted resources caregivers can use to help students learn the concepts and skills in this benchmark.

## Educational Game

BattleGraph:

A game that is an off-shoot of the classic game Battleship, for practice with coordinate graphing, complete with reproducible templates and animated PowerPoint introduction.

Type: Educational Game