 # K12MATH006: Math Grade 6

Unit 5: Coordinate Graphing

Graphing on a coordinate grid helps label points in space. In this unit, you will extend the coordinate grid beyond quadrant I (x, y) and work in all four quadrants. This unit will cover some of your prior learning from earlier in this course by using negative integers and polygons.

Unit 5 Time Advisory
Completing this unit should take you approximately 5 hours.

☐ Subunit 5.1: 3 hours and 45 minutes

☐ Subunit 5.2: 1 hour and 15 minutes

Unit5 Learning Outcomes
Upon successful completion of this unit, you will be able to:

• Extend the coordinate axis in the plane with negative number coordinates.

• Understand that signs in a coordinate pair indicate the location of the point in a quadrant.

• Find and position pairs on a coordinate plane.

• Recognize the location of two ordered pairs that differ only by signs.

• Draw polygons on a coordinate plane when given coordinates for the vertices.

• Use sets of coordinate pairs to find side lengths for a polygon that is graphed on the coordinate plane.

• Recognize and solve real-world problems that involve graphing points in all four quadrants.

Standards Addressed (Common Core):

5.1 Understanding Four-Quadrant Graphing

Graphs are used to show trends, organize maps, and represent data. This unit will focus on extending the coordinate plane to include negative coordinates. When coordinates are negative mathematicians use what is called a four-quadrant graph. It is not different from the normal x-axis and y-axis that you are used to; it is just an extension of those lines in a negative direction.

It is very helpful if you have a stack of graph paper as you complete this unit. Graph paper can be found in most office supply stores as well as can be printed off the Internet if you have access to a printer.

5.1.1 Coordinates within the Quadrants

In subunit 1.5 you learned about integers (negative and positive numbers) and plotted them on a number line. Similarly, the quadrant graphing extends into the negative numbers, as well. In this subunit you will learn about the four quadrants involved in graphing.

• Explanation: CK-12: “Ordered Pairs in Four Quadrants”

Link: CK-12: “Ordered Pairs in Four Quadrants” (HTML)

Instructions: Read about Josh drawing a graph of where he lives in relation to school. Continue to read and take notes in the “Guidance” section. The basic graphing will probably be review for you. Do the example problems given to you.

One strategy to use as you work on graphing a coordinate pair is that you always “run before you jump/dig.” That means you will always move right/left along the x-axis with the first number given to you, before you will move up or down (jump/dig) along the y-axis.

Make sure you have the vocabulary words written down in your notebook. Watch the video and complete the “Guided Practice” section.

Taking notes, doing examples, and watching the video will take you approximately 30 minutes.

Standards Addressed (Common Core):

• Explanation: Khan Academy’s “Quadrants of Coordinate Plane”

Instructions: Watch the video and take notes about the different quadrants and how to graph pairs of integers. It is good to know the names (numbers) of the quadrants; however, it is more important to understand how to graph on a four-quadrant coordinate plane.

Watching this video and taking notes should take you approximately 15 minutes.

Standards Addressed (Common Core):

5.1.2 Plotting Pairs of Integers   - Explanation: Khan Academy’s “Plot Ordered Pairs”

``````Link: Khan Academy’s [“Plot Ordered

Instructions: Watch the video and take notes about how to graph a
coordinate pair. It is most important that you understand that the
first coordinate is the x-coordinate and the second coordinate is
the y-coordinate. One strategy to help with this is that “x” comes
before “y” in the alphabet.

Watching this video and taking notes should take you approximately
15 minutes.

Standards Addressed (*Common Core*):

-   [CCSS.Math.Content.6.NS.C.6c](http://www.corestandards.org/Math/Content/6/NS/C/6/c)

attributed to the Khan Academy.
``````
• Did I Get This? Activity: Khan Academy’s “Graphing Points and Naming Quadrants”

Instructions: This page provides a series of practice problems that you can answer and check online. Each question has a solution worked out step-by-step if you need hints along the way. Practice graphing coordinate pairs until you feel confident that you understand how to plot any coordinate pair (recommended a minimum of 10 minutes of practice).

Completing these practice problems should take you approximately 15 minutes.

Standards Addressed (Common Core):

• Did I Get This? Activity: Khan Academy’s “Points on the Coordinate Plane”

Link: Khan Academy’s “Points on the Coordinate Plane” (HTML)

Instructions: This page provides a series of practice problems that you can answer and check online. Each question has a solution worked out step-by-step if you need hints along the way. Practice the graphing questions until you feel confident that you understand how to successfully read any coordinate pair on a plane (recommended a minimum of 10 minutes of practice).

Writing activity: Write a letter to a sixth-grade pen pal who needs some extra help with graphing. Organize your letter with three short paragraphs.

• The first paragraph should explain how to graph on a four-quadrant plane. Make sure to use vocabulary such as x-axis, y-axis, quadrant, origin, and coordinate pair.
• The second paragraph should compare a number line to a four-quadrant plane. How are they the same and how are they different? Where do you find negative numbers on a number line versus on a four-quadrant plane?
• The final paragraph should be some real-world examples where a four-quadrant plane could be helpful or is used.

Completing the practice problems and writing a letter should take you approximately 45 minutes.

Standards Addressed (Common Core): - CCSS.Math.Content.6.NS.C.6c - CCSS.ELA-Literacy.WHST.6-8.2 - CCSS.ELA-Literacy.WHST.6-8.4

• Did I Get This? Activity: Howard County Public School System’s “Mathtastic Amusement Park”

Link: Howard County Public School System’s “Mathtastic Amusement Park” (PDF)

Instructions: Read the section titled “The Task” to understand how the Mathtastic Amusement Park is organized.

• Write the coordinate pair for each of the attractions at the Mathtastic Amusement Park.
• Answer the four bullet-point questions at the bottom of page 2.
• Plot the points under the “Extension” section on the top of page 3.
• Check your solution for the coordinates at the bottom of page 3.

Completing the questions and plotting the coordinates should take you approximately 30 minutes.

Standards Addressed (Common Core): - CCSS.Math.Content.6.NS.C.6b - CCSS.Math.Content.6.NS.C.6c

• Did I Get This? Activity: Khan Academy’s “Reflecting Points”

Instructions: In a previous unit, you learned about the opposite of a number. For example, the opposite of 3 is -3. The opposite of 10 is -10. In this resource, you will use opposites as you reflect coordinates over the x-axis or y-axis. When a coordinate pair is reflected over the x-axis, the x-coordinate remains the same while the y-coordinate is transformed into its opposite. More specifically, if you were asked to reflect (5, 9) over the x-axis, the result would be (5, -9). Reflect means to flip. A good hint if you forget the rules for reflections when graphing, simply fold your graph paper along the line of reflection (in this example the x-axis) to see where your new coordinate will be located. This will allow you to see what is happening to the coordinates and help you remember the rule.

This specific resource provides a series of practice problems that you can answer and check online. Each question has a solution worked out step-by-step if you need hints along the way. Practice the reflected coordinates questions until you feel confident that you understand how to successfully reflect a coordinate pair over an axis (recommended a minimum of 10 minutes of practice). It might be helpful to use your graph paper to graph the point given to you and fold your paper at the line of reflection; this will show you the resulting coordinate pair.

Completing these practice problems should take you approximately 15 minutes.

Standards Addressed (Common Core):

• Checkpoint: Howard County Public School System’s “Outdoor Education Map”

Link: Howard County Public School System’s “Outdoor Education Map” (PDF)

Instruction: Scroll about halfway down the page. In the last section of the sixth-grade standards, download “6.NS.8 Outdoor Ed.doc.” Read about how to set up the stations around camp. If you have access to a printer, print off page 3 of this document. If you do not have a printer, do your best to recreate the camp grid found on page 3 on your own graph paper.

• Plot the coordinates for the amenities, these are found on the bottom of page 1.
• Plot the stations using the considerations in the “Task” section on the first page.
• Answer the questions in the “Follow-Up Questions” section found on page 2. Note that although there are only questions numbered 1 - 4, there are often multiple questions for each numbered question. Be detailed when answering each question.
• Check your answer for the outdoor camp grid and follow-up questions on pages 4 - 6. If you have something incorrect, go back to your grid and fix it so that it is graphed correctly.

Plotting the coordinates, answering the questions, and checking your solutions should take you approximately 1 hour. Standards Addressed (Common Core): - CCSS.Math.Content.6.NS.C.6b - CCSS.Math.Content.6.NS.C.6c - CCSS.Math.Content.6.NS.C.8

5.2 Geometry on a Coordinate Plane

The coordinate plane and all four quadrants are often used to plot the corners, or vertices, of shapes. In this unit you will plot the coordinates to create shapes. You will also work the find the side lengths of the shapes by using the coordinate plane grid.

• Explanation: CK-12: “Polygon Classification in the Coordinate Plane”

Link: CK-12: “Polygon Classification in the Coordinate Plane” (HTML)

Instructions: Read about Josh using a coordinate plane as a map. In this resource you will graph the vertices of a shape on the coordinate plane and connect the points to create the given shape. Read through the “Guidance” section. Take notes and do the example problems on your own graph paper.

Check that you have all the vocabulary words written down in your notebook. Complete the questions in the “Guided Practice” section and begin watching the video. The video will be review, but it is helpful to listen/watch someone else explains in addition to reading about graphing. Feel free to stop the video at the 5:23 mark. The instructor continues on about graphing calculators. This is not a sixth-grade standard; however, if you are interested in learning more about graphing calculators, he does a good job of explaining how to use a calculator to plot coordinates.

Finish by completing the problems in the “Practice” section.

Taking notes, watching the video, and completing the practice problems should take you approximately 30 minutes.

Standards Addressed (Common Core):

• Explanation: CK-12: “Points in the Coordinate Plane”

Link: CK-12: “Points in the Coordinate Plane” (HTML)

Instructions: Read about Gina and Cameron on their quest to find a sunken ship. Continue reading and adding to your notes as you go through the “Guidance” section. Most of this reading will be review for you at this point. However, read closely as you may want to write down additional information or reminders.

Do the problems in the “Example” section, read through the vocabulary, and complete the questions in the “Guided Practice” section. You watched the video in the previous resource, so skip the video and continue with the “Practice” section.

Reading this lesson, taking notes, and completing the practice problems should take you approximately 30 minutes.

Standards Addressed (Common Core):

• Did I Get This? Activity: Khan Academy’s “Coordinate Plane Word Problems”

Link: Khan Academy’s “Coordinate Plane Word Problems” (HTML)

Instructions: This page provides a series of practice problems that you can answer and check online. Each question has a solution worked out step-by-step if you need hints along the way. Practice the graphing questions until you feel confident that you understand how to successfully read any coordinate pair on a plane (recommended a minimum of 10 minutes of practice).

Completing these practice problems should take you approximately 15 minutes.

Standards Addressed (Common Core):

`````` Instructions: Test your knowledge by completing this checkpoint.