"SHAPE UP!"

"SHAPE UP!"

MASTER TEACHER Lori Morrison

GRADES 3-4

OVERVIEW
This lesson provides students with an opportunity to explore geometric numbers. Students will learn that geometric numbers are numbers that can be represented by dots in arrays that form geometric figures. Students will also use T-tables to fill in the appropriate data that represents a geometric figure. Through interaction, students will apply the information gathered in an activity that validates a geometric pattern.

ITV SERIES
Math Talk: #120 What Shape Is Your Number?: Finding Number Patterns in Squares and Triangles

LEARNING OBJECTIVES
Students will be able to:
*Define triangular and square numbers
*Explore and document possible patterns in geometric numbers
*Fill in a T-table with data
*Apply mathematical pattern to real world situation

MATERIALS
(Per class)
poster board with dots in triangular/square shapes(See supplemental page one)
blank poster board
overhead marker (thick)
wipe off cloth
T-table worksheet

(Per group of 4)
small zip-lock bags filled with leaves, flower petals, wood pieces, etc.
4 pictures of animals in their environment
2 magnifying glasses

(Awards)
award ribbons for mini handshake Olympics (Amount according to participants)
award ribbons for classroom handshake Olympics (Amount according to participants)
award ribbons for Geometric Number Olympics (Amount according to participants)

VOCABULARY
triangular numbers - numbers that make a triangular shape (dot formations)
                               A number of the form n(n+1)
                                                                    2
square numbers- numbers that make a square shape (dot formations)
                          A number of the form n^2
consecutive- following one another in unbroken order; successive
whole numbers- A natural number
odd numbers- An integer that is not divisible by two

On-line Mathematics Dictionary- http://www.mathpro.com/math/glossary.html

PREVIEWING ACTIVITIES
(Prior to lesson, have students arranged in groups of four.)
Show students a poster with dots on it that are arranged in square formations and triangular formations. Ask students to discuss in their small groups what they see on the poster. (Students may suggest the total number of dots per triangular shape and square shape. List totals on the blackboard or poster board. Also, list any other student comments on the board. Analyze different student answers by making comparisons and contrasts.)

FOCUS FOR VIEWING
To give students a specific responsibility for viewing say, "You are going to see a video that explains how numbers can be represented as a geometric shape (like the poster board display). I want you to listen and watch the performance of Masterworks Theater. When the theater performance is over, I want you to be able to give me a definition of triangular and square numbers."

VIEWING ACTIVITIES
BEGIN Math Talk #120 What Shape Is Your Number?: Finding Number Patterns in Squares and Triangles tape as announcer is saying, "We take you now to the ancient city of Troy where the Great Trojan War has been raging for many months."; visual is sign- Masterworks Theater presents The Trojan Pie. PAUSE video with visual of two soldiers in front of pie diagram and soldier stating, "So, six is a triangular number." Ask students what the next triangular number will be on the pie (10).(If needed, draw dots with a thick overhead marker on the television screen.) RESUME tape, reminding students to continue to listen and look for the definitions of triangular and square numbers.

PAUSE tape with visual of Buster the parrot saying, "That's just what I was trying to say Sharon..." Ask students to give you their definition of a triangular number. (Accept reasonable answers. The triangular numbers are the number of dots in a figure that make a triangular shape. For example, the first dot represented a small triangle. The second triangle had three dots, the third had six dots, the fourth had 10 dots, and the fifth had 15, and so on. Students may give the actual total of triangular numbers. If the former happens, this would be a good time to make a T-table. In the T-table have n represent the nth triangle in respective order. (For example, n=3 is the third triangle, which contains six dots.) At this time, have students help fill in the T-table on triangular numbers (You may want to use the worksheet provided with T-tables already drawn so that students may be monitored for individual understanding of this concept.) Tell students that they are going to continue to listen for the definition of a square number and that they may want to use their T-table to write down any of the numbers that pertain to a square number. RESUME tape with visual of Buster the parrot saying, "The square numbers have the funny haircuts." ELIMINATE SOUND. Visual is screen divided into four squares with triangular shapes and numbers in the top two squares and square numbers and shapes in the bottom two squares.

PAUSE tape when the solid orange triangle is at the top of the screen and the yellow square is at the bottom of the screen. There will also be blue sparked lines all around the triangular and square numbers (Triangular- 1+2+3+4+5+6+7+8+9+10, Square-1+3+5+7+9+11+13+15+17+19) Discuss the mathematical pattern within triangular and square numbers. (Triangular numbers are made by adding consecutive whole numbers and square numbers are made by adding consecutive odd numbers.) RESUME SOUND and REWIND the tape to where Buster the parrot is saying, "The square numbers have the funny haircuts." PLAY the video with sound to show the formation of square and triangular numbers with sound.

PAUSE tape when triangular and square numbers are flashing on the screen and music is playing. Tell students that triangular numbers and square numbers occur in nature. Pass out plastic bags filled with items found in nature to small cooperative groups. (Bags may contain a number of items i.e., sea shells, flower petals, leaves, etc. Magnifying glasses may be used by the students to explore the bagged items and discover geometric shapes. Also, you may want to have pictures of animals in their natural setting.) Explain to students that long ago a famous mathematician named Fibonnacci studied shapes and patterns in nature to solve math problems. (Fibonnacci sequence-0,1,1,2,3,5...)

Tell students that now we are going to watch a sports program using triangular numbers to solve a problem. Tell students that you want them to watch the sports skit and listen for a way to solve the problem of how many handshakes will take place with a group of seven people.(Each person only shakes hands with the other individuals once.) Resume tape.

PAUSE tape with visual of sportscasters Paula and Peter saying, "Can we please come back and report a sport that somebody has heard of?" Ask students to discuss in their cooperative groups how   to come up with an equation that will fit the situation they just viewed. (Record all correct equations. Example-[Total number of people x (Total number of people minus one)] Divide the former by two = handshakes.
           n(n-1)=h Where n=number of people and h=number of handshakes.
               2

Tell students they will have their own classroom Olympics.

POSTVIEWING ACTIVITIES
Students should be divided into groups of four. Say, "Now students, you are going to have a mini handshake tournament in your group. But, before you shake your group members hands you must write out on a piece of paper the names of the people that you will shake their hands and figure out an equation that fits with the number of handshakes that will happen in your group. (Example- Adrienne, Jackie, Ian, and Robert-Adrienne/Jackie, Adrienne/Ian, Adrienne/Robert, Jackie/Ian, Jackie/Robert, Ian/Robert; total number of students (4), times the total number of students minus one (3), giving you twelve, divided by two, giving the answer of six total handshakes.

4(4-1)=6
2

Once students have had their mini handshake tournament, have a class hand shake tournament applying the equation and the information given about triangular numbers. Play sports music (i.e. Jock Jam) and give out ribbons for participation in the event.

After the Olympics, have students ask Dr. Math how to solve their tournament problems. Students write what happened in the classroom Olympics and make a problem solving question to pose to Dr. Math, asking him for the correct equation. Students can talk to Dr. Math at http://forum.swarthmore.edu/dr.math/

ACTION PLAN
Arrange a Triangular/Square Number Olympics with your entire grade level. Each classroom has an activity that correlates with a triangular or square number concept. Have the Geometric Number Olympics outside on your playground. Have each class present their event and equation to the entire grade level (Sports jerseys can be worn for team spirit). Students watch the different events and vote on the most creative. Have ribbons to give to each participant in the Geometric Number Olympics. (Examples; Big Toe Touch, Say Hey Yell, and Balloon Pop Drop.)

EXTENSIONS
Language Arts
Have students write in their math journals about the Geometric Number Olympics. Have students write about what they would rather be, a triangular or a square number, and why.

Math
In groups, have students explore triangular and square numbers on the multiplication chart. After exploration, have students share their findings with the entire class.

Have students come up with different geometric shaped numbers. (Hexagonal numbers, Pentagonal numbers, and Octagonal numbers) Once students have found the different geometric numbers, have them tell what the numeric pattern is by listing numbers on a T-table.

Art
Have students do geometric number art with dots, x's, lines, etc. Students may want to do geometric art with three dimensional objects. Have a Geometric Art Galley set up in the classroom for viewing.

Science and Health
Invite a doctor to speak to students about the patterns in mathematics as it relates to medicine. Have the doctor explain how a germ is transferred throughout a community of people (communicable diseases).

Updated: April 01, 2008