MAGICIAN OR MATHEMATICIAN?
Grades 6 - 8
Where do you see patterns? How are they connected to mathematics
and science? We will use the series Math Vantage to explore the concepts
of patterns used in magic tricks. Participants will have the chance to investigate
and create patterns. After viewing a magician's amazing card trick, students
will have an opportunity to create and perform "magic" tricks
of their own!
"Math Vantage segment: Patterns #101"
Students will be able to:
- Describe a pattern and explain how it works
- Continue a pattern and predict the outcome of a pattern
- Create and communicate a pattern using magic tricks.
1 per student
- calculators
- worksheet, "Mostly Magic?"
1 deck per group of students
1 per class
rabbit/carrot transparency
optional for teacher:
- magician's costume - top hat, tuxedo, magic wand, crystal ball
Ask students to, "Predict what the next numbers are in
this pattern '2, 4, 6,...'". After students answer, ask them "How
did you know the next numbers were 8, 10, 12?" Discuss that the pattern
is even numbers and that two was added each time. Say, "Now finish
this pattern, 1,3,5,7...". Discuss the students' answers, and what
patterns they see. Say, "We've looked at two patterns. Now I would
like you and your group to create a pattern for another group to try."
Direct students to work in small groups to create number patterns. Have
groups exchange patterns, and try to complete each others patterns. Class
discussion follows. Ask students, "Why do we use patterns?" Direct
the class to brainstorm why we use patterns. One student will record the
responses on the overhead while the other students record the responses
in their journals.
To give students specific responsibility while viewing, introduce
the video with the following directions: "Let's see if you predicted
all the functions of patterns. If you see one of the classes' responses
during the video, put a star by it. If you see a use for a pattern that
you don't have, add it to your journal."
START tape at the beginning when the commentator says,
"Ever notice how every morning the sun rises in the east, and sets
in the west?"
To underscore the point of why we use patterns, PAUSE the tape when
the commentator says "In fact, math has been called the science of
patterns. We use patterns to explain, create and predict." Ask the
students, "Why do we use patterns? " Class discussion follows.
Emphasize the uses of patterns: to explain, create and predict.
Give each student a calculator. Say, "I've been working on my magic
skills, and I want to show you a magic trick that I've discovered. Everybody
pick a number and write it down. Now I would like you to add 6 to the number
you picked. Next, multiply the sum you got when you added your number and
six, by 2. Take the answer that you now have and subtract 12 from it."
Check to make sure everyone is on task. "Take the new answer and divide
it by 2. Next, subtract your original number. Now look at the final answer
and don't say anything while I read your minds... (The teacher exaggerates,
acts as if she is reading the students' minds) Wait, I'm getting a picture...I
see the number zero!"
Wait while the students express their amazement (or skepticism), then say,
"Let's try another trick! Pick another number and write it down. Add
10 to your number. Has everyone picked a number and added 10 to it? Now
I would like you to multiply the answer that you have by 3. Does everyone
have that product? Next step, please subtract 30. Now, divide that answer
by 3. Next, subtract your original number. Ok let me get a reading, oh,
I am getting a strong reading of ZERO!"
Ask the class, "Do you think I'm really a magician?" Pause while
the students discuss the "magic" among themselves. Then say, "Maybe
I just know a pattern!" Turn on the overhead and say, "Lets look
for a pattern." On the overhead place a rabbit, and say, "Let's
let the rabbit represent the number you picked. Next, we added the number
6 to the rabbit, (place 6 carrots on the overhead). Then, we multiplied
this sum by 2 . What should we have on the overhead now? (put another rabbit
and 6 more carrots on the overhead). We then subtracted 12, which is the
same as 6x2 (take the 12 carrots off the overhead) and then, we divided
by 2 ("divide by 2", take one rabbit away, leave one rabbit on
the overhead). Next, we subtracted a rabbit (take the last rabbit away).
What do I have left? Do you see a pattern?" The students discuss the
pattern in their groups. A class discussion will follow about patterns that
were found in the problem. Say, "That's how I came up with zero, no
magic involved!".
Direct students to work in groups to discover a pattern for the second problem,
using the worksheet, "Mostly Magic?" "Work in your groups
and see if there is a similar pattern for the other "magic trick".
Give groups five minutes to find the pattern in the second magic trick using
the hand out "Mostly Magic?" Have the class discuss what patterns
their groups found.
To give students specific responsibility while viewing, ask the class, "Has
anyone ever seen a magician? Was it really magic? Now we're going to see
a magician perform a magic trick. When he performs the magic trick I want
you to watch closely to see if it's magic or if the trick is really a pattern."
RESUME the video, so that students can observe the magician and look
for patterns. To enhance students' observation skills, talk over the tape
when the magician appears and ask, "Do you think he's really a magician?"
When the magician starts laying out the cards, talk over the tape and say,"Watch
carefully how he lays out the cards." When the arrow points to the
ace of hearts, say over the tape, "We're picking the ace of hearts.
Notice there are three rows with four cards in each row. How many cards
are there? Watch how he picks up the cards!"
PAUSE the tape after the card trick, when the commentator says, "Hmmm
I think I see a mathematical pattern!", to allow time for students
to predict a pattern. Ask the students, "Did anyone see a pattern?"
Class discussion follows.
REWIND the tape to the beginning of the magic trick to provide time
for students to check their theories. Say, "Let's watch the card trick
one more time and see if your hypothesis works." Watch the trick again.
Remind students to watch how the magician picks up the cards.
PAUSE the tape after the card trick, when the commentator says, "Hmmm
I think I see a mathematical pattern!", to give students a chance to
test their theories. Give each group a deck of playing cards. Tell students,
"You will now have 5 minutes to experiment with playing cards to test
your theories and look for a pattern. Work in your group to discover the
pattern used in the card trick. Make sure you keep a record of which theories
work, as well as which theories don't work."
After students have had a chance to experiment using the playing cards,
have groups discuss with the class what patterns they found.
RESUME the tape to validate students' ideas and to allow students
to see the pattern. Say, "Lets watch the rest of the magic segment
to see if you're right."
Continue the tape through the explanation. PAUSE the tape to emphasize
the word explain when the speaker says "We see how patterns explain
things". Say, "In the card trick the pattern was used to explain
the magic!"
STOP the Video.
Working in groups of two, students will create a "magic
trick" using a pattern. The students will perform their magic trick
for the other groups, and see if the other students can discover their pattern.
Students will write a description of the "magic trick" they created,
and explain in their description how the pattern works. A book will be made
of the classes' different magic tricks, which will be placed in the school
library.
Students will take their "magic show" on the road!
The class will travel to a nearby elementary school and nursing home, where
they will perform (and explain) their magic! Also, students will perform
magic tricks at "parent nights", and during the annual Math Fair.
Mathematics
Have students create games which use patterns, like the game NIM. Using
calculators, have students create a game using patterns. Use a "Hundreds
Chart" to look for patterns. Have students create number tricks, and
use algebra to solve them. For example, the solution to the first "pick
a number" problem could be described as: [2( x+6)-12]/2-x
Science
Investigate patterns and shapes in nature. Students will create a news
report which uses patterns to describe weather. Investigate patterns found
in science, such as DNA. Students can explore patterns found in their finger
prints. Students can study the Fibonacci sequence, and discover how rabbits
"multiply".
Language Arts Write a story that uses a pattern to solve a mystery.
For example, a detective might discover that the numbers of all missing
math books are multiples of three.
Art
Investigate patterns used in Hopi Baskets and Navajo Rugs. Have students
create Hopi Baskets and Navajo Rugs using materials such as construction
paper or yarn. Use a computer to design patterns. Use patterns to create
tessellations.
Music
Have students use patterns and items found in the classroom to create a
musical composition.
Resources
The Nebraska Mathematics and Science Coalition's "Math Vantage"
segment: Patterns, contains segments which demonstrate patterns used in
music, sports, art, weather and games.
Zaslavsky, Claudia. Multicultural Mathematics, J. Weston Walch,Publisher
P.O. Box 658, Portland, Maine 04104-0658. Contains lessons on the patterns
found in Hopi baskets and Navajo rugs.
Reimer, Wilbert and Luetta. Historical Connections in Mathematics Volumes
I and II, 1993 AIMS Education Foundation, P.O. Box 8120 Fresno, CA. 93747-8120.
Contains "Number Tricks" and patterns such as square and triangular
numbers.
Family Math Contains lessons which use patterns, including the game "Balloon
Ride", a game similar to NIM.
MASTER TEACHER: Diane Weaver
Click here to view the
worksheet associated with this lesson.
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