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### Overview

If you grab a bunch of jump ropes and tell your kids you're going outside, you can trick them into thinking they are getting recess. Instead, you can surprise them with a math lesson about how to identify the points on the coordinate plane!

This is a College- and Career-Ready Standards showcase lesson plan.

## UP:MA19.5.20

### Vocabulary

• Coordinate system
• Coordinate plane
• Points
• Lines
• Perpendicular
• X-axis
• Y-axis
• Origin
• Ordered pair
• Coordinate plane
• Horizontal
• Vertical
• Intersection of lines

### Knowledge

Students know:
• Specific directions and vocabulary to explain ordered pair location.
• The first number of an ordered pair indicates how far to travel from the origin in the direction of one axis and the second number indicates how far to travel in the direction of the second axis.

### Skills

Students are able to:
• Graph points in the first quadrant.
• Interpret coordinate values in context of the problem.

### Understanding

Students understand that:
• graphing points on a coordinate plane provides a representation of a mathematical context which aids in visualizing situations and solving problems.

### Primary Learning Objectives

Students will be able to identify the four quadrants, point of origin, both the x and the y axis, and an (x,y) position on the coordinate plane--first on the playground, and then on paper.

### Procedures/Activities

1. WATCH A VIDEO

Share the following video with your students:

http://www.flocabulary.com/coordinate-plane/

It gives a great introduction to the coordinate plane, including the terms: origin, both the x axis and y axis (axes is plural for more than one axis), and ordered pairs. It also includes some memorable verses to remind your children which axis is which (since they understandably tend to confuse the x and y axes).

One shortcoming of the video is its neglect of all four quadrants. It deals solely with the first quadrant (the only all positive quadrant). One graphic shows the x axis going to the right (not showing it also goes to the left) and the y axis going up (not showing it also goes down). This is fine for an introductory lesson, so long as the teacher recognizes this shortcoming, and provides ample follow up regarding the dual directions both axes travel. The following lesson provides much of said follow up.

2. CREATE A COORDINATE PLANE

As you create a coordinate plane on your whiteboard or chart paper (doing each step as you instruct your students), have students create a coordinate plane on their graph paper, instructing them to first draw one line across the middle of their page. On the far right, under the line, have them label this line with a lower case “x”. Tell the students this is called the x axis.

Next, have students draw a line up and down in the middle of their page, intersecting the x axis in the middle. On the top right of this line, have them label this line with a lower case “y”. Say, “This is called the y axis.”

Next, have students draw a small circle over the point where the two axes intersect. Have them write the word “origin” next to the circle. Say, “Guess what this is called?” If students don’t answer correctly, check to see if they are asleep before continuing lesson.

Next, as you continue to do each step on the board that you have your students do on their paper, instruct them to put a Roman numeral I in the upper right quadrant. Explain that this is called quadrant one. Ask for volunteers to tell you which is quadrant two. Keep going until someone says the upper left quadrant is quadrant two, and put a Roman numeral II in that quadrant. (Keep in mind, this ordering is counter intuitive for many students, since is goes counterclockwise.)

Next, label quadrants three (lower left) and four (lower right) with Roman numerals III and IV.

3. OUTSIDE ACTIVITY

You’ve now labeled your coordinate planes, and it’s time to get out the jump ropes and whistle, and go outside.

Next, instruct your students to create an x axis with half the jump ropes. When completed, instruct them to create a y axis with remaining ropes. Hopefully, this will create a giant plus sign.

Once your giant plus sign is created, go stand at the end of one of axes and look to the origin. Have your students stand somewhat close to you and face the same direction you are. (Where you stand will be the bottom of your playground coordinate plane, as if you are looking at the graph papers that are currently sitting on your students desks.)

Say, “Can you tell me which axis I am standing close to?” They will hopefully answer “Y”.

Say, “What is the line called that intersects the y axis?” They will hopefully answer, “X axis".

Ask your students to stand as close as they can to the origin.

Ask for volunteers to go stand in each of the following four places: positive 10 on the x axis, positive 10 on the y axis, negative 10 on the x axis, and negative 10 on the y axis. (Keep in mind this is an intro lesson, you will have to place the students and you may have to spend considerable time helping them with this.)

Next, with the tens still in place, have volunteers stand in each of the following four places: positive 5 on the x axis, positive 5 on the y axis, negative 5 on the x axis, and negative 5 on the y axis.

With those 8 students still in place, have the rest come back and stand where you are, reminding them that they are to pretend they are looking at their paper that’s still back on their desks in the classroom. Quickly review where the origin and x and y axes are. Ask also where each of your eight volunteers is standing, reminding students to think of the number line as they do.

Next, pick four more volunteers to go stand in each of the four quadrants. Once they’ve done so correctly, ask the students what quadrant is "Sally" standing in, etc. (Repeat this until all students have had several opportunities to become part of the coordinate plane.)

Next, reminding them of the map they saw in the video, say, “I’m going to give you two numbers.  The first number will be the x and the second will be the y. This means that the x number is how far you move along the x axis—left or right. Once you’ve moved however far the first number tells you to, then you’ll move up or down along the y axis, according to the second number. So, for example (you’ll need to move from your spot now), I’m going to start at the origin, and say two numbers, (5, 5).  The first number is positive and is on the x axis (move to the middle of the positive x axis). The second number is positive and is on the y axis (move to the middle of the positive y axis). I’m now standing at (5, 5). Who wants to try the next one?”

Spend some time with this next step, as it’s the most important. Get volunteers to start always at the origin and to go stand on the coordinates you give them. Give them either your own coordinates or the following listed ones, teaching how to read the negative numbers as you go:

(0, 5)

(10, 0)

(5, 10)

(10, 5)

(0, 0)

(0, 10)

Continue with this until all children are placed. Repeat as many times as necessary, and to mix it up, you can have all the boys stand near one coordinate and the girls stand near another. Also, occasionally ask students to stand in certain quadrants.

4. INSIDE

Once you are back inside, write the previous coordinates on the board, asking students to find and label each. Give them a few minutes, and then put the coordinates on the plane you created earlier on the board.

Have students check each other’s work, and then have each group suggest extra points to plot. Once they’ve decided on a few and put them on their own papers, they can come to the board and write one or two of their coordinates next to the list you already put up there. Then the whole class can plot those points as well.

Last, when you are sure your students understand everything, have them work in groups and practice with http://www.ixl.com/math/grade-5/graph-points-on-a-coordinate-plane

1. WATCH A VIDEO

Share the following video with your students:

http://www.flocabulary.com/coordinate-plane/

It gives a great introduction to the coordinate plane, including the terms: origin, both the x axis and y axis (axes is plural for more than one axis), and ordered pairs. It also includes some memorable verses to remind your children which axis is which (since they understandably tend to confuse the x and y axes).

One shortcoming of the video is its neglect of all four quadrants. It deals solely with the first quadrant (the only all positive quadrant). One graphic shows the x axis going to the right (not showing it also goes to the left) and the y axis going up (not showing it also goes down). This is fine for an introductory lesson, so long as the teacher recognizes this shortcoming, and provides ample follow up regarding the dual directions both axes travel. The following lesson provides much of said follow up.

2. CREATE A COORDINATE PLANE

As you create a coordinate plane on your whiteboard or chart paper (doing each step as you instruct your students), have students create a coordinate plane on their graph paper, instructing them to first draw one line across the middle of their page. On the far right, under the line, have them label this line with a lower case “x”. Tell the students this is called the x axis.

Next, have students draw a line up and down in the middle of their page, intersecting the x axis in the middle. On the top right of this line, have them label this line with a lower case “y”. Say, “This is called the y axis.”

Next, have students draw a small circle over the point where the two axes intersect. Have them write the word “origin” next to the circle. Say, “Guess what this is called?” If students don’t answer correctly, check to see if they are asleep before continuing lesson.

Next, as you continue to do each step on the board that you have your students do on their paper, instruct them to put a Roman numeral I in the upper right quadrant. Explain that this is called quadrant one. Ask for volunteers to tell you which is quadrant two. Keep going until someone says the upper left quadrant is quadrant two, and put a Roman numeral II in that quadrant. (Keep in mind, this ordering is counter intuitive for many students, since is goes counterclockwise.)

Next, label quadrants three (lower left) and four (lower right) with Roman numerals III and IV.

3. OUTSIDE ACTIVITY

You’ve now labeled your coordinate planes, and it’s time to get out the jump ropes and whistle, and go outside.

Next, instruct your students to create an x axis with half the jump ropes. When completed, instruct them to create a y axis with remaining ropes. Hopefully, this will create a giant plus sign.

Once your giant plus sign is created, go stand at the end of one of axes and look to the origin. Have your students stand somewhat close to you and face the same direction you are. (Where you stand will be the bottom of your playground coordinate plane, as if you are looking at the graph papers that are currently sitting on your students desks.)

Say, “Can you tell me which axis I am standing close to?” They will hopefully answer “Y”.

Say, “What is the line called that intersects the y axis?” They will hopefully answer, “X axis".

Ask your students to stand as close as they can to the origin.

Ask for volunteers to go stand in each of the following four places: positive 10 on the x axis, positive 10 on the y axis, negative 10 on the x axis, and negative 10 on the y axis. (Keep in mind this is an intro lesson, you will have to place the students and you may have to spend considerable time helping them with this.)

Next, with the tens still in place, have volunteers stand in each of the following four places: positive 5 on the x axis, positive 5 on the y axis, negative 5 on the x axis, and negative 5 on the y axis.

With those 8 students still in place, have the rest come back and stand where you are, reminding them that they are to pretend they are looking at their paper that’s still back on their desks in the classroom. Quickly review where the origin and x and y axes are. Ask also where each of your eight volunteers is standing, reminding students to think of the number line as they do.

Next, pick four more volunteers to go stand in each of the four quadrants. Once they’ve done so correctly, ask the students what quadrant is "Sally" standing in, etc. (Repeat this until all students have had several opportunities to become part of the coordinate plane.)

Next, reminding them of the map they saw in the video, say, “I’m going to give you two numbers.  The first number will be the x and the second will be the y. This means that the x number is how far you move along the x axis—left or right. Once you’ve moved however far the first number tells you to, then you’ll move up or down along the y axis, according to the second number. So, for example (you’ll need to move from your spot now), I’m going to start at the origin, and say two numbers, (5, 5).  The first number is positive and is on the x axis (move to the middle of the positive x axis). The second number is positive and is on the y axis (move to the middle of the positive y axis). I’m now standing at (5, 5). Who wants to try the next one?”

Spend some time with this next step, as it’s the most important. Get volunteers to start always at the origin and to go stand on the coordinates you give them. Give them either your own coordinates or the following listed ones, teaching how to read the negative numbers as you go:

(0, 5)

(10, 0)

(5, 10)

(10, 5)

(0, 0)

(0, 10)

Continue with this until all children are placed. Repeat as many times as necessary, and to mix it up, you can have all the boys stand near one coordinate and the girls stand near another. Also, occasionally ask students to stand in certain quadrants.

4. INSIDE

Once you are back inside, write the previous coordinates on the board, asking students to find and label each. Give them a few minutes, and then put the coordinates on the plane you created earlier on the board.

Have students check each other’s work, and then have each group suggest extra points to plot. Once they’ve decided on a few and put them on their own papers, they can come to the board and write one or two of their coordinates next to the list you already put up there. Then the whole class can plot those points as well.

Last, when you are sure your students understand everything, have them work in groups and practice with http://www.ixl.com/math/grade-5/graph-points-on-a-coordinate-plane

### Assessment Strategies

In keeping with the introductory spirit of this lesson, a simple assessment is all that is required. So, in order to assess what they've learned, you should ask your students to do the following three things on their graph paper:

1) Draw and label a coordinate plane (this includes the x and y axis--labled with x and y; this also includes the point of origin and all four quadrants labled correctly).

2) Find and label the following four points on their coordinate plane: (4,4); (-4,4); (-4,-4);  (-4,4)

3) Connect the four points with straight lines.

The end result should be a square, making it easy for you to assess who needs extra help.

### Acceleration

After looking at the assessments, many students who are now fluent in the Primary Learning Objective will be anxious to create their own pictures using points on a coordinate plane. Have them do so, showing you a list of their points and a completed picture. If theirs is accurate, and if possible, post their points on your blog for other students in your class/school to try.

### Intervention

For the most basic remediation, I point to the tiles on my classroom floor, or the cinder blocks on the wall, and ask the students to identify numbers that I give them.

For example, pointing at a floor tile (origin), I ask them to count four tiles from the origin, like they would on a number line. When they've gone four tiles to the right, I'll ask them to count two tiles up.  Repeated practice with the floor tiles (something with which they are very familiar) is a great place to start.

Setting up yardsticks on the floor or a large piece of butcher paper to represent only quadrant one (all positive values for x and y) can help students who are still struggling. They can see the numbers on the yardstick--all positive numbers. Often, the concept of negative numbers is a sticking point, so focusing on the entirely positive quadrant on the coordinate plane will help students more easily understand how to use the coordinates to find a point. Also, this will very closely align with Content Standard 5-G2.

### Total Duration

31 to 60 Minutes

### Background/Preparation

Familiarity with a number line is very helpful, since the x axis is the untouched number line, and the y axis is the number line rotated 90 degrees counterclockwise.  And if your kids already know what the x and y axis are, they can set up the jumpropes for you!

### Materials and Resources

Graph Paper and Pencils/Pens--This is for when you finish up outside and come back into the classroom.

Jump Ropes--You will need as many jump ropes as you can find, since you are creating a "life-sized" x and y axis, and the bigger you can make it, the more room your students will have, and the less likely they will become clumped together, unable to move. (I use eight 16-foot jump ropes, 4 ropes for each axis.)

Whistle (recommeded, not required)--This is useful for corraling ten-year-olds who are super excited about doing a math activity instead of getting recess.

### Technology Resources Needed

Interactive whiteboard with a coordinate plane template (Otherwise, just spend a few extra minutes creating the biggest coordinate plane you can on your whiteboard, using different colors for the axis and for the points).