21st Century Lessons

Graphing Polygons & Finding Side LengthsMrs. Thompson

Level 1

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Lesson Objective SWBAT graph polygons on a coordinate plane and calculate the side lengths by engaging in the “Polygon Initials” activity.

Lesson Description During this lesson, students will review the characteristics and definitions of polygons, other key vocabulary related to polygons and coordinate planes, and how to graph coordinates (if needed). Then, students will participate in a brief guided practice of graphing points to form polygons.

Once this launch is complete, students will be introduced to the main activity, “Polygon Initials”, during which they will draw their initials using only horizontal and vertical lines on a coordinate plane. Then, they will label the coordinates of their vertices and copy them on a separate sheet of paper. All students will then pass in those coordinate logs to be shuffled up and chosen at random by the students to graph on a new coordinate plane to figure out whose initials they received, and compare their polygon drawings to that student’s.

Lesson Overview (1 of 3)

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Lesson Vocabulary Polygon, coordinate plane, coordinate pairs, vertex/vertices, length, quadrant, distance, horizontal, vertical, x-axis, y-axis.

Materials 1 “Warm-up” sheet per student, 2 sheets of graph paper per student , 1 “Activity Guide” per student, 1 “Vertex Coordinate Log” per student, 1 “Exit Ticket” per student, pencils & rulers for each student.

Scaffolding Students will experience the content of this lesson through a multi-modal approach: using visuals, in writing, and tactile means to reach the objective. In addition to pre-teaching of vocabulary and some guided practice within this presentation, students requiring more help can access online tools via the links provided in “online resources for absent students”.

Enrichment Students who complete the lesson activity, and having demonstrated mastery of the objective to the teacher, will:

Take it to the next level! Find the perimeter and area of each letter in your initials on the coordinate plane, then explain your method for finding the perimeter and the area.

Students will also write a short reflection on why we used only horizontal and vertical lines, and what difficulty would they encounter by using diagonal lines to build polygon initials.

Online Resources for Absent Students

Review of coordinate plane:http://www.youtube.com/watch?v=xvEyE3_k1C4Review of graphing coordinates:http://www.mathopenref.com/coordplane.html; Practice: ittc-web.astate.edu/lessonportal/attachments/25-Activity.doc

Lesson Overview (2 of 3)

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Lesson Overview (3 of 3)Common Core State Standard

6.G.3: Draw polygons in the coordinate plane given coordinates for the vertices; use coordinates to find the length of a side of joining points with the same first coordinate or same second coordinate. Apply these techniques in the context of solving real-world and mathematical problems.

Before and After Students should have familiarity of polygons and their properties from previous instruction (from the Shapes & Designs unit that occurs in Nov-Dec in the scope and sequence), finding area and perimeter (from the Covering & Surrounding unit in Jan-Feb) as well as the basics of graphing and coordinate planes (from the beginning of this 3rd Common Core investigation on Integers and the Coordinate Plane, to occur in May).*

The skills exercised in this lesson will carry over to the many 7th grade investigations involving graphing and geometry, and eventually, to the 8th grade content (even the Pythagorean Theorem—the answer to the question “how can we find the length to a polygon’s side on a graph when the side is not perfectly horizontal or vertical?”).

Topic Background The word "polygon” comes from the Greek (polús) "many" and (gōnía) πολύς γωνία"corner" or "angle". Today we identify polygons in terms of the number of sides. The idea of polygons is an ancient one. The ancient Greeks understood the regular polygons, and such designs have been dated as early as 7th century B.C.! The Cartesian Plane was invented by French mathematician Rene Descartes in the 17th century, and it played a huge part in the development of higher math, including Calculus! This lesson on graphing polygons and using the coordinates to find the side lengths is an important step in math learning-- not only to further student skill with using Cartesian planes, but to help students make valuable connections between various strategies for finding area and perimeter.

Warm UpOBJECTIVE: SWBAT graph polygons on a coordinate plane and calculate the side lengths by engaging in the “Polygon Initials” activity.

Agenda

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On the “6.G.3 Warm-up” sheet, answer the following to get your brain ready for today’s activity:

1) What is a polygon? Explain using mathematical vocabulary and draw an example.

2) a. Make a coordinate plane and graph the points (0, 2), (4, 2), (0, -3), and (4, -3). b. Connect the points to make a shape. c. Is this shape a polygon? Explain why/why not!

WARM-UP: Review/Solutions

A polygon is a closed shape that is formed by line segments.

How did you describe a polygon? Raise your hand to share out!

1) What is a polygon again?

WARM-UP Review, Cont. 2)

X

Raise your hand if you would like to volunteer to show your work here on the board!

Y

How can we find the side lengths of the rectangle we made?

Solution!

Agenda:OBJECTIVE: SWBAT graph polygons on a coordinate plane and calculate the side lengths by engaging in the “Polygon Initials” activity.

1) Warm Up – (Partners) then review (ALL) 10 mins

2) Launch – Key Vocab & Intro (Teacher/ALL), 10-15 mins

3) Explore – “Polygon Initials” (Independent, Pairs), 35-40 mins

4) Summary – Identify your peer & Discussion (ALL), 5 mins

5) Practice – Homework 6.G.3

6) Assessment – Exit Ticket (Independent), 5 mins

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Launch

Agenda

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During today’s activity, you will be graphing polygons andfinding the side lengths of the polygons.

Then you will use given coordinates to graph objects and decipher what they are.

To prepare us better, let’s briefly review some key vocabulary terms!

Key Vocabulary

• Polygon • Vertex (s.) / Vertices (pl.)

the “corners” of any polygon,where the line segments meet.

• Coordinate PlaneA 2-Dimensional graph with anx-axis and y-axis. Pointscan be plotted on theplane. Figures or shapes too!*Let’s review how to use coordinate planes:http://www.mathopenref.com/coordplane.html

Vocabulary, cont.

• Quadrant: One of the FOUR equal sections of a coordinate plane!

Quadrant I

Quadrant II

Quadrant III

Quadrant IV

(+, +)(–, +)

(–, –) (+, –)

Do you notice a pattern with the signs in each quadrant?

Y

X

Explore ACTIVITY INTRO

Agenda

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Graphing “Polygon Initials”

Explore ACTIVITY SET-UP

Agenda

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You will need these tools to graph your “Polygon Initials”:

• pencil & eraser • ruler• handouts - 2 sheets graph paper - 1 coordinate log - checklist

LOOK AT YOUR CHECKLIST to Follow along!

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Explore: Graphing “Polygon Initials”During this activity, you will…

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Agenda

--------------------------------- 1st HALF of Activity -----------------------------------------1) Graph your initials as polygons on the coordinate plane using only horizontal and vertical lines. (3 mins)

2) Label the coordinates of each vertex and find all side lengths. (10 mins)

3) In order, write only the coordinates for all vertices in your initials on the Coordinate Log—DO NOT write your name on this sheet! (3 mins)---------------------------------- 2nd HALF of Activity ---------------------------------------4) Randomly choose a coordinate log of an unknown peer and graph their initials to reveal their identity! (10 mins)

5) Use the graph and coordinates of your peer’s initials to label the LENGTHS of all sides of their initials polygons. (5 mins)

Explore: KEEP IN MIND as you work…

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Agenda

> Use only the initials of your first and last name

> Draw each letter so that both fit onto the one coordinate plane on one sheet of graph paper & use all 4 Quadrants

> Use ONLY perfectly horizontal and perfectly vertical line segments to form your polygon initials. NO diagonal lines!

Example: a student named “Theresa Alvarez” may graph her initials like this

Need an exemplar? Take a look!

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Agenda

(-4, 4)

(-2, -4)

(4, 4)

|––––––– 6 un.–––––––|

Let’s Begin!

Do theFirst 3 Steps

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On this Sheet!

NEXT STEP…

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On your Coordinate Log

Write each vertex’s coordinates IN ORDER, as you ‘trace’ around one initial, then the next. You may use any vertex as the starting point for each letter.

(-3, 3)

-3 3

(0, 3)

0 3

FREEZE!Please pass in your completed

“COORDINATE LOGS”

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LAST STEPS!

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Do these 2 Stepsusing a peer’s “Coordinate Log”

On this Sheet!

Summary: Let’s wrap up and discuss!

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Agenda

• If you have not already, please identify whose initials you graphed, and compare your graph and measurements with theirs! Does your work and your peer’s work match? Why or why not?

• What did you find difficult during the “Polygon Initials” activity? What was easy to you?

• How can you find the side lengths of polygons using only the coordinates of the vertices? Explain and/or show!

Assessment: EXIT TICKET!1) On your “Exit Ticket” sheet, make an x- and y-axis, then plot the following points in order. Connect the points with lines as you go.

(-4, 8), (6, 8), (6, 5), (-1, 5), (-1, 3), (2, 3), (2, 1), (-1, 1), (-1,- 5), (-4, -5), connect back to first point.

2) Identify the polygon letter you graphed!

3) Label the side lengths of the polygon letter.

4) CHALLENGE! Finished early? Find the PERIMETER & AREA of the letter!

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Agenda

HOMEWORK

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Agenda

> For Homework, please complete “HW 6.G.3”, due by _________