| Code |
Description |
| MAFS.6.NS.3.5: | Understand that positive and negative numbers are used together
to describe quantities having opposite directions or values (e.g.,
temperature above/below zero, elevation above/below sea level,
credits/debits, positive/negative electric charge); use positive and
negative numbers to represent quantities in real-world contexts,
explaining the meaning of 0 in each situation. |
| MAFS.6.NS.3.6: | Understand a rational number as a point on the number line. Extend number line diagrams and coordinate axes familiar from previous grades to represent points on the line and in the plane with negative number coordinates.
- Recognize opposite signs of numbers as indicating locations on opposite sides of 0 on the number line; recognize that the opposite of the opposite of a number is the number itself, e.g., –(–3) = 3, and that 0 is its own opposite.
- Understand signs of numbers in ordered pairs as indicating locations in quadrants of the coordinate plane; recognize that when two ordered pairs differ only by signs, the locations of the points are related by reflections across one or both axes.
- Find and position integers and other rational numbers on a horizontal or vertical number line diagram; find and position pairs of integers and other rational numbers on a coordinate plane.
|
| MAFS.6.NS.3.7: | Understand ordering and absolute value of rational numbers.
- Interpret statements of inequality as statements about the relative position of two numbers on a number line diagram. For example, interpret -3 > -7 as a statement that -3 is located to the right of -7 on a number line oriented from left to right.
- Write, interpret, and explain statements of order for rational numbers in real-world contexts. For example, write -3 oC > -7 oC to express the fact that -3 oC is warmer than -7 oC.
- Understand the absolute value of a rational number as its distance from 0 on the number line; interpret absolute value as magnitude for a positive or negative quantity in a real-world situation. For example, for an account balance of -30 dollars, write |-30| = 30 to describe the size of the debt in dollars.
- Distinguish comparisons of absolute value from statements about order. For example, recognize that an account balance less than -30 dollars represents a debt greater than 30 dollars.
|
| 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.
|
This cluster includes the following access points.
Vetted resources educators can use to teach the concepts and skills in this topic.
| Name |
Description |
| Graphing Points in the Plane: | Students are asked to graph points given their coordinates and describe the coordinates of graphed points. |
| 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. |
| What Is the Opposite?: | Students are asked about numbers and their opposites. |
| Explaining Opposites: | 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. |
| South Pole: | Students are asked to interpret an inequality relating two temperatures. |
| 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. |
| Visualizing Absolute Value: | Students are asked to identify a number’s possible locations on a number line when given the number’s absolute value. |
| 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. |
| 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. |
| Submarines: | Students are asked to write integers to represent quantities given in context and to relate the integers with an inequality. |
| Positions of Numbers: | Students are asked to describe the positions of numbers relative to each other on a number line. |
| Absolute Altitudes: | Students are asked to compare two elevations and their absolute values and then interpret these comparisons within a given real-world context. |
| Relative Fractions: | Students are given positive and negative fractions and asked to explain their meanings within the context of a problem. |
| Relative Integers: | Students are asked to use numbers to represent gains/losses and to interpret the meaning of zero in the context of football. |
| Relative Decimals: | Students are asked to explain the meaning of positive and negative decimals within the context of a problem. |
| Rainfall Change: | Students are asked to interpret values given in a chart that represent positive and negative deviations from average rainfall. |
| Locating Quadrants: | Students are asked to determine in what quadrant or on which axis, points described algebraically, are located. |
| Graphing Points on the Number Line: | Students are asked to find the coordinates of graphed points and graph points with rational coordinates on a number line. |
| Garden Coordinates: | Students are given the coordinates of the vertices of a rectangle and are asked to graph the rectangle and find its perimeter. |
| 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. |
| Name |
Description |
| 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. |
| Too Hot, Too Cold-6th Grade STEM Lesson: | 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. |
| Positive or Negative? Does It Matter?: | 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. |
| The Layers of the Atmosphere, Guest Starring the Integers! : | 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. |
| 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. 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. |
| 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. 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. |
| 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. 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. |
| 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. |
| 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. |
| 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. |
| Understanding Integers: | 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. |
| 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. |
| Positive or Negative, It's All About Shopping!: | 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. |
| Positive, Zero, or Negative?: | 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. |
| 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. |
| Absolutely Integers: | 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. |
| 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. |
| Name |
Description |
| Above and below sea level: | 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. |
| Mile High: | Students are asked to reason about and explain the position of two locations relative to sea level. |
| Distances on the Number Line 2: | 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. |
| Comparing Temperatures: | The purpose of the task is for students to compare signed numbers in a real-world context. |
| Fractions on the Number Line: | The purpose of this task is to help students get a better understanding of fractions on a number line. |
| Integers on the Number Line 2: | The purpose of this task is for students to get a better understanding of the relative positions and values of positive and negative numbers. |
| It's Warmer in Miami: | The purpose of this task is for students to apply their knowledge of integers in a real-world context. |
| Jumping Flea: | 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. |
| Name |
Description |
| Comparing Rational Numbers: | In this tutorial, you will compare rational numbers using a number line. |
| Coordinate Plane: Word Problem Exercises: | This video demonstrates solving word problems involving the coordinate plane. |
| The Coordinate Plane: | Students will plot an ordered pair on the x (horizontal) axis and y (vertical) axis of the coordinate plane. |
| Coordinate Plane: | Students will become familiar with the coordinate plane. |
| Graphing Points and Naming Quadrants: | This video contains examples of plotting coordinate pairs and identifying their quadrant. |
| Negative Symbol as Opposite: | This video discusses the negative sign as meaning "opposite." |
| Decimals and Fractions on a Number Line: | Locate fractions and decimals on the same number line in this tutorial. |
| Ordering Negative Numbers: | Let's order negative numbers from least to greatest in this video. |
| Ordering Rational Numbers: | In this tutorial, you will learn how to order rational numbers using a number line. |
| Comparing Absolute Values: | In this tutorial you will compare the absolute value of numbers using the concepts of greater than (>), less than (<), and equal to (=). |
| Comparing Variables with Negatives: | This video guides you through comparisons of values, including opposites. |
| Sorting Values on Number Line: | This video demonstrates sorting values including absolute value from least to greatest using a number line. |
| Comparing Values on Number Line: | This video demonstrates evaluating inequality statements, some involving absolute value, using a number line. |
| Values to Make Absolute Value Inequality True: | This video demonstrates solving absolute value inequality statements. |
| Interpreting Absolute Value: | This video is about interpreting absolute value in a real-life situation. |
| Coordinate Plane: Quadrants: | Students will learn how to identify the four quadrants in the coordinate plane. |
| Opposite of a Number: | This video uses a number line to describe the opposite of a number. |
| 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. |
| Pre-Algebra - Fractions and Rational Numbers: | 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." |
| Pre-Algebra - Whole Numbers, Integers, and the Number Line: | 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. |
| Adding Integers: | Students will be able to see examples of addition of integers while watching a short video, and practice adding integers using an online quiz. |
| Ordering Numeric Expressions : | The video demonstrates rewriting given numbers in a common format (as decimals), so they can be compared and ordered. |
Vetted resources students can use to learn the concepts and skills in this topic.
| Title |
Description |
| Comparing Rational Numbers: | In this tutorial, you will compare rational numbers using a number line. |
| Coordinate Plane: Word Problem Exercises: | This video demonstrates solving word problems involving the coordinate plane. |
| The Coordinate Plane: | Students will plot an ordered pair on the x (horizontal) axis and y (vertical) axis of the coordinate plane. |
| Coordinate Plane: | Students will become familiar with the coordinate plane. |
| Graphing Points and Naming Quadrants: | This video contains examples of plotting coordinate pairs and identifying their quadrant. |
| Negative Symbol as Opposite: | This video discusses the negative sign as meaning "opposite." |
| Decimals and Fractions on a Number Line: | Locate fractions and decimals on the same number line in this tutorial. |
| Ordering Negative Numbers: | Let's order negative numbers from least to greatest in this video. |
| Ordering Rational Numbers: | In this tutorial, you will learn how to order rational numbers using a number line. |
| Comparing Absolute Values: | In this tutorial you will compare the absolute value of numbers using the concepts of greater than (>), less than (<), and equal to (=). |
| Comparing Variables with Negatives: | This video guides you through comparisons of values, including opposites. |
| Sorting Values on Number Line: | This video demonstrates sorting values including absolute value from least to greatest using a number line. |
| Comparing Values on Number Line: | This video demonstrates evaluating inequality statements, some involving absolute value, using a number line. |
| Values to Make Absolute Value Inequality True: | This video demonstrates solving absolute value inequality statements. |
| Interpreting Absolute Value: | This video is about interpreting absolute value in a real-life situation. |
| Coordinate Plane: Quadrants: | Students will learn how to identify the four quadrants in the coordinate plane. |
| Opposite of a Number: | This video uses a number line to describe the opposite of a number. |
| 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. |
| Pre-Algebra - Fractions and Rational Numbers: | 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." |
| Pre-Algebra - Whole Numbers, Integers, and the Number Line: | 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. |
| Adding Integers: | Students will be able to see examples of addition of integers while watching a short video, and practice adding integers using an online quiz. |
| Ordering Numeric Expressions : | The video demonstrates rewriting given numbers in a common format (as decimals), so they can be compared and ordered. |
Vetted resources caregivers can use to help students learn the concepts and skills in this topic.
