# MA.5.GR.4.2

Represent mathematical and real-world problems by plotting points in the first quadrant of the coordinate plane and interpret coordinate values of points in the context of the situation.

### Examples

For Kevin’s science fair project, he is growing plants with different soils. He plotted the point (5,7) for one of his plants to indicate that the plant grew 7 inches by the end of week 5.

### Clarifications

Clarification 1: Coordinate planes include axes scaled by whole numbers. Ordered pairs contain only whole numbers.
General Information
Subject Area: Mathematics (B.E.S.T.)
Strand: Geometric Reasoning
Status: State Board Approved

## Benchmark Instructional Guide

• Origin
• x-axis
• y-axis

### Vertical Alignment

Previous Benchmarks

Next Benchmarks

### Purpose and Instructional Strategies

The purpose of this benchmark is for students to interpret coordinate values plotted in mathematical and real-world contexts. Students have been plotting and interpreting numbers on a number line since Kindergarten. Students’ first experience with interpreting points plotted on a coordinate plane is in grade 5, which leads to the foundational understanding needed throughout middle school.
• An example of interpreting coordinate values of points in a mathematical context could be identifying points of a rectangle plotted on the coordinate plane.
• An example of interpreting coordinate values of points in a real-world context could look like the example in the benchmark description. In this real-world example, students would interpret that each axis represents a variable describing a situation. The x-axis represents number of weeks and the y-axis represents plants’ heights in inches.
• During instruction, teachers should provide plenty of opportunities for students to both plot and interpret ordered pairs on a coordinate plane. Teachers should connect the expectations of this benchmark with MA.5.GR.4.1 by having students represent the points plotted on two-column tables as well (MTR.4.1, MTR.7.1).
• In real-world contexts teachers should allow students the flexibility to decide which variable is represented by x and which is represented by y. Students may be encouraged to explain their preference.
• During instruction, students should be given the flexibility to decide how to scale their graphs for a given real-world context. Students may be encouraged to explain their preference.

### Common Misconceptions or Errors

• Students can confuse the x- and y-values in an ordered pair and move vertically along the y-axis before moving horizontally along the x-axis.
• For example, they may mean to plot and label the ordered pair (2, 4), but plot and label (4, 2) instead.
• Some students may not understand what an x- or y-coordinate value of 0 represents. During instruction, students should justify why ordered pairs with a 0 will plot on the x- axis or y-axis.

### Strategies to Support Tiered Instruction

• Instruction includes the teacher providing coordinate points to graph in quadrant 1 of the coordinate plane along with two small objects. The students explain how they move the object along the x-axis and then up the y-axis to the location provided. The teacher then provides the points reversed to graph and has students explain the difference in how they move the second object compared to the first.
• For example, the teacher may provide students with a coordinate plane like the one shown below. The teacher provides a set of coordinate points such as (8,2). Students take turns moving an object, such as a two-colored counter, and explain the location of the point using the x- and y-axis in their explanation. The teacher will then provide the points in reverse, (2,8). Students will move a second object and explain the location of the point as well as the difference between the two locations.
• Instruction includes the teacher providing a set of cards that have coordinates points on them, some with 0 as the location on the x-axis, some with 0 as the location on the y- axis, others with no 0 in the coordinates. Students sort the cards into three categories: points located on the x-axis, points located on the y-axis and neither. Students justify their reasoning by explaining how the 0, or lack of a 0, in each set of points helped them.
• For example, the teacher provides cards with the following points on them: (2,5), (0,8), (3,0), (2,0), (1,9), (0,4), (6,0), (7,2), (9,0), (0,5)
• Students sort the points into three categories as shown below.

• Instruction includes the teacher creating a giant coordinate plane on the floor with painters' tape or outside with sidewalk chalk. The teacher or a student will then create directions for their peers to follow. The teacher or student provides a set of coordinate points, including those with 0 as the x- or y-coordinate. Another student physically moves to the location, describing as they move, which axis they are moving on and counting the spaces until they reach their final location.
• For example, the teacher or a student tells another student to move to the location of (4,6) on the coordinate plane. The student says, “I begin at the origin which is (0,0) and move 1, 2, 3, 4 spaces to the right on the x-axis. I then move 1, 2, 3, 4, 5, 6 spaces up on the y-axis to my final location of (4,6).”
• For example, the teacher provides a student with the location (5,0). The student moves along the x-axis 5 spaces and stop. The teacher provides another student with the location (0,5). That student moves up the y-axis 5 spaces and stop. The teacher then has students explain how their location ended up on the x- or y-axis as well as the relationship between those located on the y-axis and those located on the y-axis.

Lukas can make four bracelets per hour and he will work for five hours. Make a two-column table where the first column contains the numbers 1, 2, 3, 4, 5 indicating the number of hours worked, and the second column shows how many total bracelets he has made in that many hours.
Plot points on the coordinate plane to represent your table, where the x-coordinate represents the number of hours worked and the y-coordinate represents the number of bracelets made.

### Instructional Items

Instructional Item 1

The map below shows the location of several places in a town.

The fire department is 2 blocks north of the library. What ordered pair represents the location of the fire department?
• a. (4, 2)
• b. (2, 4)
• c. (4, 8)
• d. (8. 4)

Instructional Item 2

Deanna is plotting a square on the coordinate plane below.

What ordered pair would represent the fourth vertex?
• a. (6, 2)
• b. (2, 6)
• c. (2, 0)
• d. (0, 2)

*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.
5012070: Grade Five Mathematics (Specifically in versions: 2014 - 2015, 2015 - 2022, 2022 and beyond (current))
7712060: Access Mathematics Grade 5 (Specifically in versions: 2014 - 2015, 2015 - 2018, 2018 - 2022, 2022 and beyond (current))
5012065: Grade 4 Accelerated Mathematics (Specifically in versions: 2019 - 2022, 2022 and beyond (current))
5012015: Foundational Skills in Mathematics 3-5 (Specifically in versions: 2019 - 2022, 2022 and beyond (current))

## Related Access Points

Alternate version of this benchmark for students with significant cognitive disabilities.
MA.5.GR.4.AP.2: Plot and label ordered pairs in the first quadrant of the coordinate plane.

## Related Resources

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

## Formative Assessments

Name the Ordered Pair:

Students determine the coordinates of the fourth vertex of a rectangle on the coordinate plane.

Type: Formative Assessment

Making Bracelets:

Students determine and graph the relationship between two variables set in a real world context, and interpret coordinate values of points in the context of the situation.

Type: Formative Assessment

Mowing the Lawn:

Students are asked to determine and graph the relationship between two variables within a real world context.

Type: Formative Assessment

Comic Books:

Students are asked to complete one of two number patterns, write ordered pairs composed of corresponding terms, graph the ordered pairs, and identify a relationship between corresponding terms of the patterns.

Type: Formative Assessment

## Lesson Plans

Voter Turnout and the 19th Amendment:

Students will graph and analyze voting data to explain how the 19th Amendment expanded civic participation in this lesson plan.

Type: Lesson Plan

How Does Force Affect Motion?:

Students will explore how force affects an object's motion. Students will discuss how the greater the mass of an object, the greater the force required to move an object.  Students will use data gathered through experimentation to justify their reasoning and understanding of forces and motion.

Type: Lesson Plan

Graphy Graphy:

In this lesson, students will learn how to create a situational story problem using two coordinate points on a grid. The students will then be able to plot and describe the path traveled from the starting point to the destination based on the information presented in the situation.

Type: Lesson Plan

On this MEA activity, students will create a procedure to rank five lunch bags as to which one is the best in keeping food and drinks at a safe temperature and appealing to the taste, while keeping design and price on target.

Type: Lesson Plan

Cool School:

In this lesson, students will take an imaginary trip to my lake house. They will solve a variety of real life word problems. Once at the lake they will experience many activities where they will need number sense. For the assessment, students will record and analyze data in order to determine who the best angler was at "Cool School."

Type: Lesson Plan

Dig That Grid!:

In this lesson, students will use their knowledge of coordinates and coordinate pairs in a real life situation as they become archaeologists excavating a dig site. They will measure their site, label the grids with correct coordinates and use coordinate pairs to record the location of the artifacts they discover.

Type: Lesson Plan

In this game, a student challenges a partner to recreate his or her quadrilateral or other shape on a geoboard by calling out the ordered pairs of the quadrilateral's vertices.

Type: Lesson Plan

Cartesian Classroom:

The classroom is turned into a human Cartesian coordinate plane, thereby introducing students to the characteristics of the Cartesian coordinate system.  The example given is for all 4 quadrants but the 5th grade standard may be addressed by designing the classroom as only the first quadrant.  In this case, questions regarding negative numbers would not be asked.

Type: Lesson Plan

Map It Out!!:

In this lesson, students will use real life maps and apply their knowledge of coordinates (ordered pairs) in order to identify and name specific locations on a map and explain the relevance to their life.

Type: Lesson Plan

## Original Student Tutorial

Just Get to the Point!:

Practice plotting coordinates, in Quadrant I, using ordered pairs in this interactive tutorial for students.

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

## Tutorial

Coordinate Plane: Graphing Points Word Problem:

This Khan Academy tutorial video presentation represents a word problem's solution on a coordinate plane to determine the number of blocks walked from a home to a school.

Type: Tutorial

## Worksheet

Graphing Growth-SeaWorld Classroom Activity:

Given the known weights of a killer whale at various ages, students will graph these weights, then use this information to estimate a killer whale's weight at other ages.

Type: Worksheet

## STEM Lessons - Model Eliciting Activity

On this MEA activity, students will create a procedure to rank five lunch bags as to which one is the best in keeping food and drinks at a safe temperature and appealing to the taste, while keeping design and price on target.

## MFAS Formative Assessments

Comic Books:

Students are asked to complete one of two number patterns, write ordered pairs composed of corresponding terms, graph the ordered pairs, and identify a relationship between corresponding terms of the patterns.

Making Bracelets:

Students determine and graph the relationship between two variables set in a real world context, and interpret coordinate values of points in the context of the situation.

Mowing the Lawn:

Students are asked to determine and graph the relationship between two variables within a real world context.

Name the Ordered Pair:

Students determine the coordinates of the fourth vertex of a rectangle on the coordinate plane.

## Original Student Tutorials Mathematics - Grades K-5

Just Get to the Point!:

Practice plotting coordinates, in Quadrant I, using ordered pairs in this interactive tutorial for students.

## Student Resources

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

## Original Student Tutorial

Just Get to the Point!:

Practice plotting coordinates, in Quadrant I, using ordered pairs in this interactive tutorial for students.

Type: Original Student Tutorial

## Tutorial

Coordinate Plane: Graphing Points Word Problem:

This Khan Academy tutorial video presentation represents a word problem's solution on a coordinate plane to determine the number of blocks walked from a home to a school.

Type: Tutorial

## Parent Resources

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