# MAFS.6.NS.3.8

Solve real-world and mathematical problems by graphing points in all four quadrants of the coordinate plane. Include use of coordinates and absolute value to find distances between points with the same first coordinate or the same second coordinate.

### Clarifications

Examples of Opportunities for In-Depth Focus

When students work with rational numbers in the coordinate plane to solve problems, they combine and consolidate elements from the other standards in this cluster.
General Information
Subject Area: Mathematics
Domain-Subdomain: The Number System
Cluster: Level 2: Basic Application of Skills & Concepts
Cluster: Apply and extend previous understandings of numbers to the system of rational numbers. (Major Cluster) -

Clusters should not be sorted from Major to Supporting and then taught in that order. To do so would strip the coherence of the mathematical ideas and miss the opportunity to enhance the major work of the grade with the supporting clusters.

Date Adopted or Revised: 02/14
Date of Last Rating: 02/14
Status: State Board Approved
Assessed: Yes
Test Item Specifications
Assessed with: MAFS.6.NS.3.6
Sample Test Items (1)
• Test Item #: Sample Item 1
• Question: The points (4, –6) and (9, –6) represent the location of two towns on a coordinate grid, where one unit is equal to one mile.

What is the distance, in miles, between the two towns?

• Difficulty: N/A
• Type: EE: Equation Editor

## Related Courses

This benchmark is part of these courses.
1205010: M/J Grade 6 Mathematics (Specifically in versions: 2014 - 2015, 2015 - 2022 (current), 2022 and beyond)
1205020: M/J Grade 6 Accelerated Mathematics (Specifically in versions: 2014 - 2015, 2015 - 2020, 2020 - 2022 (current), 2022 and beyond)
1204000: M/J Foundational Skills in Mathematics 6-8 (Specifically in versions: 2014 - 2015, 2015 - 2022, 2022 and beyond)
7812015: Access M/J Grade 6 Mathematics (Specifically in versions: 2014 - 2015, 2015 - 2018, 2018 and beyond)
7912110: Fundamental Explorations in Mathematics 1 (Specifically in versions: 2013 - 2015, 2015 - 2017 (course terminated))

## Related Access Points

Alternate version of this benchmark for students with significant cognitive disabilities.
MAFS.6.NS.3.AP.8a: Graph or identify points in all four quadrants of the coordinate plane, given a coordinate plane on graph paper.
MAFS.6.NS.3.AP.8b: Given two points plotted on a coordinate plane, find the distance between two points on a coordinate plane.

## Related Resources

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

## Assessments

Sample 4 - Sixth Grade Math State Interim Assessment:

This is a State Interim Assessment for sixth grade.

Type: Assessment

Sample 3 - Sixth Grade Math State Interim Assessment:

This is a State Interim Assessment for sixth grade.

Type: Assessment

## 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

## Educational Software / Tool

Free Graph Paper:

A variety of graph paper types for printing, including Cartesian, polar, engineering, isometric, logarithmic, hexagonal, probability, and Smith chart.

Type: Educational Software / Tool

## Formative Assessments

Garden Area:

Students are given coordinates of three vertices of a rectangle and asked to determine the fourth vertex and the area of the rectangle.

Type: Formative Assessment

Determine the Distance:

Students are given the coordinates of three points (with the same x- or y-coordinate) and asked to determine the distance between pairs of points without graphing.

Type: Formative Assessment

Garden Coordinates:

Students are given the coordinates of the vertices of a rectangle and are asked to graph the rectangle and find its perimeter.

Type: Formative Assessment

Bike Lot Coordinates:

Students are asked to graph two points given their coordinates and to find the coordinates of two other points so that the four points represent the vertices of a square.

Type: Formative Assessment

## Lesson Plans

Coding Geometry Challenge # 16, 18 & 19:

This set of geometry challenges focuses on creating a variety of polygons using the coordinate plane as students problem solve and think as they learn to code using block coding software.  Student will need to use their knowledge of the attributes of polygons and mathematical principals of geometry to accomplish the given challenges. The challenges start out fairly simple and move to more complex situations in which students can explore at their own pace or work as a team. Computer Science standards are seamlessly intertwined with the math standards while providing “Step it up!” and “Jump it up!” opportunities to increase rigor.

Type: Lesson Plan

Raja Rangoli:

Rangoli is a traditional Indian art that is used in decorating the entrance of the house to welcome guests. In this activity students will explore and practice the concepts of positive numbers, negative numbers, absolute value, origin, coordinates etc. and will create their own Rangoli design at the end.

Type: Lesson Plan

Let's Ride!:

Let's Ride! is a model-eliciting activity that asks students to use pluses and minuses to indicate if eight models of 4-door sedans meet specific standards based on gas mileage, seating capacity, warranty, and type of engine. The students then have to rank the cars and indicate their top four choices.

Type: Lesson Plan

Profit Plaza:

This lesson requires students to use mathematical data and logic/reasoning to place vendors into retail spaces in a shopping plaza. Students will first rank five vendor types on their profitability (based on average sales and average overhead/upkeep costs), then place the vendor types into the 11-13 retail spaces. They are also required to find the area of each space and calculate the total leasing charges. The plans for the plaza are given on a coordinate plane, so students will need to find the lengths of horizontal and vertical line segments (using the coordinates of the endpoints) to calculate the areas of the rectangular and composite spaces.

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

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 and distances 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

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 previous knowledge of graphing in a 4 quadrant coordinate grid and individually solve a real world problem involving finding distance on a coordinate grid. Students must utilize their knowledge of absolute value as well as subtracting integers to determine distances between points.

Type: Lesson Plan

Dig It! (A Thematic Integrated Geology Unit):

This lesson (2 parts) is an engaging way to strengthen student understanding of the Law of Superposition and evidence of Earth's changes over time. Students will excavate "fossils" from plastic tubs in class and then have the option of a larger outside excavation. The lesson not only supports science benchmarks but Math and Language Arts Standards as well and has an optional Social Studies extension. Materials are required but can be easily obtained and are reusable year after year. The more imagination you put into setting the context, the more powerful the lesson's outcome.

Type: Lesson Plan

## Perspectives Video: Professional/Enthusiast

Art and Prototyping with Laser-cut Materials:

Blaze a trail when you utilize laser technology to make art.

Type: Perspectives Video: Professional/Enthusiast

## Student Center Activity

Edcite: Mathematics Grade 6:

Students can practice answering mathematics questions on a variety of topics. With an account, students can save their work and send it to their teacher when complete.

Type: Student Center Activity

## Tutorials

Coordinate Plane: Word Problem Exercises:

This video demonstrates solving word problems involving the coordinate plane.

Type: Tutorial

The Coordinate Plane, plotting an ordered pair:

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

Type: Tutorial

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

Type: Tutorial

## STEM Lessons - Model Eliciting Activity

Let's Ride!:

Let's Ride! is a model-eliciting activity that asks students to use pluses and minuses to indicate if eight models of 4-door sedans meet specific standards based on gas mileage, seating capacity, warranty, and type of engine. The students then have to rank the cars and indicate their top four choices.

Profit Plaza:

This lesson requires students to use mathematical data and logic/reasoning to place vendors into retail spaces in a shopping plaza. Students will first rank five vendor types on their profitability (based on average sales and average overhead/upkeep costs), then place the vendor types into the 11-13 retail spaces. They are also required to find the area of each space and calculate the total leasing charges. The plans for the plaza are given on a coordinate plane, so students will need to find the lengths of horizontal and vertical line segments (using the coordinates of the endpoints) to calculate the areas of the rectangular and composite spaces.

Raja Rangoli:

Rangoli is a traditional Indian art that is used in decorating the entrance of the house to welcome guests. In this activity students will explore and practice the concepts of positive numbers, negative numbers, absolute value, origin, coordinates etc. and will create their own Rangoli design at the end.

## MFAS Formative Assessments

Bike Lot Coordinates:

Students are asked to graph two points given their coordinates and to find the coordinates of two other points so that the four points represent the vertices of a square.

Determine the Distance:

Students are given the coordinates of three points (with the same x- or y-coordinate) and asked to determine the distance between pairs of points without graphing.

Garden Area:

Students are given coordinates of three vertices of a rectangle and asked to determine the fourth vertex and the area of the rectangle.

Garden Coordinates:

Students are given the coordinates of the vertices of a rectangle and are asked to graph the rectangle and find its perimeter.

## Student Resources

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

## 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

## Student Center Activity

Edcite: Mathematics Grade 6:

Students can practice answering mathematics questions on a variety of topics. With an account, students can save their work and send it to their teacher when complete.

Type: Student Center Activity

## Tutorials

Coordinate Plane: Word Problem Exercises:

This video demonstrates solving word problems involving the coordinate plane.

Type: Tutorial

The Coordinate Plane, plotting an ordered pair:

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

Type: Tutorial