Cluster 3: Apply and extend previous understandings of numbers to the system of rational numbers. (Major Cluster)Archived

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

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

Type: Educational Software / Tool

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

Type: Formative Assessment

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

Students are asked about numbers and their opposites.

Type: Formative Assessment

Students are asked to graph -4, 0, and 4 on a number line and to explain the relationship between a number and its opposite in terms of the number line.

Type: Formative Assessment

Students are asked to interpret an inequality relating two temperatures.

Type: Formative Assessment

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

Students are asked to identify a number’s possible locations on a number line when given the number’s absolute value.

Type: Formative Assessment

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

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 write integers to represent quantities given in context and to relate the integers with an inequality.

Type: Formative Assessment

Students are asked to describe the positions of numbers relative to each other on a number line.

Type: Formative Assessment

Students are asked to compare two elevations and their absolute values and then interpret these comparisons within a given real-world context.

Type: Formative Assessment

Students are given positive and negative fractions and asked to explain their meanings within the context of a problem.

Type: Formative Assessment

Students are asked to use numbers to represent gains/losses and to interpret the meaning of zero in the context of football.

Type: Formative Assessment

Students are asked to explain the meaning of positive and negative decimals within the context of a problem.

Type: Formative Assessment

Students are asked to interpret values given in a chart that represent positive and negative deviations from average rainfall.

Type: Formative Assessment

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

Type: Formative Assessment

Students are asked to find the coordinates of graphed points and graph points with rational coordinates on a number line.

Type: Formative Assessment

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

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

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

A two day STEM lesson where students get a hands-on experience understanding positive and negative integers. Students will understand how temperature demonstrations and their own created models are used to visualize positive and negative integers in relation to 0 in real-world settings. Students will summarize their understanding of the relationship between positive and negative integers in relation to 0 for the evaluation of this lesson in a journal format.

Type: Lesson Plan

This lesson aligns to the Mathematics Formative Assessment System (MFAS) Task Submarines (CPALMS Resource ID# ). In this lesson, students with similar instructional needs are grouped according to MFAS rubric levels: Getting Started, Moving Forward, Almost There, and Got It. Students in each group complete an exercise designed to move them toward a better understanding of the ordering of rational numbers.

Type: Lesson Plan

Students will learn the functions and characteristics of the four main layers of Earth's atmosphere. They will also determine the thickness of each layer and display them to scale. Students will plot the layers' temperatures, noting the change in temperature from the bottom to the top on a number line.

Type: Lesson Plan

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.

Model Eliciting Activities, MEAs, are open-ended, interdisciplinary problem-solving activities that are meant to reveal students’ thinking about the concepts embedded in realistic situations. Click here to learn more about MEAs and how they can transform your classroom.

Type: Lesson Plan

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.

Model Eliciting Activities, MEAs, are open-ended, interdisciplinary problem-solving activities that are meant to reveal students’ thinking about the concepts embedded in realistic situations. Click here to learn more about MEAs and how they can transform your classroom.

Type: Lesson Plan

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.

Model Eliciting Activities, MEAs, are open-ended, interdisciplinary problem-solving activities that are meant to reveal students’ thinking about the concepts embedded in realistic situations. Click here to learn more about MEAs and how they can transform your classroom.

Type: Lesson Plan

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

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

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

This lesson is an introduction to integers. Students will compare, order, and describe real-life situations using positive and negative whole numbers. The concepts of opposites and vertical as well as horizontal number lines are addressed.

Type: Lesson Plan

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

This lesson introduces students to the concept of negative and positive integers as opposites and as indicators of movement, beginning with elevation and ending with real-world application to money.

Type: Lesson Plan

This lesson involves students using positive and negative numbers to represent quantities in real-world contexts, explaining the meaning of zero in each situation. Students will understand the positive and negative numbers are used together to describe quantities having opposite values.

Type: Lesson Plan

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

Students will review how to graph positive numbers and then negative numbers on a number line. The students will review absolute value and apply this to different integers. They will then play a fun game to check their understanding.

Type: Lesson Plan

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

Follow Matteo as he explores opposite numbers, positive and negative rational numbers, and zero in real-world contexts while planning and going on a cruise in Alaska in this interactive tutorial. 

Type: Original Student Tutorial

Learn how to create and use number lines with positive and negative numbers, graph positive and negative numbers, find their distance from zero, find a number’s opposite using a number line and signs, and recognize that zero is its own opposite with this interactive, golf-themed tutorial.

Type: Original Student Tutorial

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

Type: Perspectives Video: Professional/Enthusiast

What's the shortest path between point A and B on the ocean? It depends on wind and currents, but coordinates can help you track your position.

Related Resources:
KROS Pacific Ocean Kayak Journey: GPS Data Set[.XLSX]
KROS Pacific Ocean Kayak Journey: Path Visualization for Google Earth[.KML]

Download the CPALMS Perspectives video student note taking guide.

Type: Perspectives Video: Professional/Enthusiast

The purpose of this task is to help students interpret signed numbers in a context as a magnitude and a direction and to make sense of the absolute value of a signed number as its magnitude. The questions about the elevation of New Orleans are fairly natural: it is a standard convention to use positive numbers to represent elevations above sea level and negative numbers below sea level. However, it is possible to represent them the other way around.

Type: Problem-Solving Task

Students are asked to reason about and explain the position of two locations relative to sea level.

Type: Problem-Solving Task

The purpose of this task is meant to reinforce students' understanding of rational numbers as points on the number line and to provide them with a visual way of understanding that the sum of a number and its additive inverse (usually called its "opposite") is zero.

Type: Problem-Solving Task

The purpose of the task is for students to compare signed numbers in a real-world context.

Type: Problem-Solving Task

The purpose of this task is to help students get a better understanding of fractions on a number line.

Type: Problem-Solving Task

The purpose of this task is for students to get a better understanding of the relative positions and values of positive and negative numbers.

Type: Problem-Solving Task

The purpose of this task is for students to apply their knowledge of integers in a real-world context.

Type: Problem-Solving Task

This purpose of this task is to help students understand the absolute value of a number as its distance from 0 on the number line. The context is not realistic, nor is meant to be; it is a thought experiment to help students focus on the relative position of numbers on the number line.

Type: Problem-Solving Task

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

In this tutorial, you will compare rational numbers using a number line.

Type: Tutorial

This video demonstrates solving word problems involving the coordinate plane.

Type: Tutorial

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

Type: Tutorial

Students will become familiar with the coordinate plane.

Type: Tutorial

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

Type: Tutorial

This video discusses the negative sign as meaning "opposite."

Type: Tutorial

Locate fractions and decimals on the same number line in this tutorial.

Type: Tutorial

Let's order negative numbers from least to greatest in this video.

Type: Tutorial

In this tutorial, you will learn how to order rational numbers using a number line.

Type: Tutorial

In this tutorial you will compare the absolute value of numbers using the concepts of greater than (>), less than (<), and equal to (=).

Type: Tutorial

This video guides you through comparisons of values, including opposites.

Type: Tutorial

This video demonstrates sorting values including absolute value from least to greatest using a number line.

Type: Tutorial

This video demonstrates evaluating inequality statements, some involving absolute value, using a number line.

Type: Tutorial

This video demonstrates solving absolute value inequality statements.

Type: Tutorial

This video is about interpreting absolute value in a real-life situation.

Type: Tutorial

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

Type: Tutorial

This video uses a number line to describe the opposite of a number.

Type: Tutorial

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

The first fractions used by ancient civilizations were "unit fractions." Later, numerators other than one were added, creating "vulgar fractions" which became our modern fractions. Together, fractions and integers form the "rational numbers."

Type: Tutorial

Number systems evolved from the natural "counting" numbers, to whole numbers (with the addition of zero), to integers (with the addition of negative numbers), and beyond. These number systems are easily understood using the number line.

Type: Tutorial

Students will be able to see examples of addition of integers while watching a short video, and practice adding integers using an online quiz.

Type: Tutorial

The video demonstrates rewriting given numbers in a common format (as decimals), so they can be compared and ordered.

Type: Tutorial

This video provides sample questions about the concept of opposite numbers.

Type: Video/Audio/Animation