|
"I'LL TAKE THE COMBO!"
MASTER TEACHER Lori
Fleet-Morrison
GRADES 3-5
MATH
OVERVIEW
This lesson provides students with an opportunity to use logic
skills along with multiplication equations. Through interaction, students
explore various strategic methods to calculate the many possibilities when
combining items. Hands-on activities and video have been incorporated to
extend and reinforce the understanding that combinatorics (different
combinations) are commonplace in and beyond the classroom environment.
ITV SERIES
Math Talk: #109 Let Me Count the Ways: Counting with
Combinations
LEARNING OBJECTIVES
Students will be able to:
*define combinatorics
*find the maximum amount of different
combinations of given items
*create a mathematical equation that
correlates with different combinations of
specific items
*find the missing factor when given a partial
mathematical equation dealing with
combinations
MATERIALS
(per group)
poster board
markers
plastic bags each filled with cut-outs of shirts and pants
(per class)
video camera
bells or flags for game show
4 shirts, 4 belts
5 different styles of shorts cut-out of tag board (about 2
inches in size)
masking tape
cutouts of capes-1 each, red, green, yellow
cutouts of belts--1 each, black, brown, blue
VOCABULARY
combinatorics unknown
equation
PREVIEWING ACTIVITIES
(Prior to lesson, have students arranged in groups of four.)
Choose 5 students to come to the front of the classroom. Have four
students try on the shirts. Ask the students to guess at how many
different combinations of shirts and belts can be made. (Show students by
example by matching a shirt with four different belts.) Tell students it
is best when figuring out different combinations to draw a picture and label it.
(Draw Diagram on chalkboard, i.e.,
). Have students discuss how many combinations they could possibly come
across with the 4 shirts and 4 belts. Once each child's shirt has been
physically matched to each belt, make sure the drawing on the board is complete.
Ask students if there is a rule or a mathematical equation that can represent
this situation. Write down the mathematical equation 4x4=16. Ask
students if they think that multiplication would be a good way to find the
maximum combinations.
FOCUS FOR VIEWING
To give students a specific responsibility for viewing say,
"You are going to see a video that shows a young man talking about
combinatorics (have the word written on the chalkboard). I want you to
listen to what the young man has to say and when I stop the tape I want you to
be able to give me a definition of combinatorics."
VIEWING ACTIVITIES
Math Talk #109 Let Me Count the Ways: Counting with
Combinatorics
Begin tape as Maria Lopez (cartoon character) is saying,
"Lucy, you guys, take a look at this piece from Square One T.V., and I
think you'll begin to get the idea." Pause video with the
visual of Dweezil and the announcer states, " Combinatorics, it's not just
a word anymore." Ask students, "What do you think the word
combinatorics means?" (Combinations of items, different combinations
of items, the maximum amount of combinations you can get out of a certain number
of items) Write the various definitions of combinatorics on the
chalkboard. Tell students that now they are going to use combinatorics to
figure out how many different outfits Super Guy can wear.
Fast forward and begin tape with visual of gray WATER
WORKS sign; audio is an announcer saying, "Somewhere in metropolitan
Cityville, leaks were occurring in the local water works." Pause
tape after the announcer says, "Stay tuned for the continuing adventures of
Super Guy." Show students a drawing or tag board cutouts of capes and
belts. Ask volunteers to give their ideas on the possible amount of
combinations that can be made with the capes (Green, red, and yellow) and the
belts (black, brown, and blue). (There are nine different combinations)
Tell students that we are going to find out if Super Guy has found as many
different combinations as we have. Fast forward to Maria Lopez
stating, "Watch part two and you'll see combinatorics in action."
Pause tape with the salesman pointing to an empty space on the shirt
rack; audio is the salesman saying, "Wait a minute, wait a minute,
what, what goes here?" Ask students which combination is missing (red
cape with the black belt)
Resume tape. Pause tape when the salesman
states, "there are nine possible combinations. Ask the students, in
their small groups, to put their heads together and come up with a mathematical
equation that will fit this combinatoric problem. (equation- 3x3=9) Resume
tape to see if the students came up with the correct mathematical equation. Pause
tape with the visual of Super Guy and salesman; audio is the salesman saying,
"Wonderful!" Say, now students, let's listen for Maria's
definition of combinatorics.
Fast forward and begin tape with visual of
Maria Lopez ; audio is, "Do you see how combinatorics helped him
Lucy?" Pause tape with Maria Lopez; audio is Maria saying, "Combinatorics
is a way of organizing things so you can see how many possible combinations
there are." Ask students to name different things that can be
organized creating different combinations. (clothes, ice cream toppings, car
colors, etc.) Tell students that now we are going to look at combinatorics
differently. Remind students of the mathematical equations that we have
created. Tell students that sometimes we have unknowns in mathematical
equations and we have to logically figure out an appropriate answer. Say,
"I want you to listen carefully to the next combinatorics problem and see
if you can come up with a mathematical equation that will fit the problem."
Fast forward and begin tape with visual of
Maria and Buster; audio is Maria stating, "Let's look at this game show
question about combinatorics." Pause tape when the game show
announcer says, "Now, what is the smallest number of shorts that I would
need to make at least twenty different combinations of shorts and
T-shirts?" Ask groups of students to put their heads together and
come up with an answer and an equation. (answer is four pairs of shorts;
possible equation is 6xN=at least 20) Have cut-outs of different color
shorts about two inches in size to visually show students the correct answer on
the television screen.
Resume tape to figure out which game show player is
telling the truth. Pause tape with visual of the game show
announcer; audio is him saying, "Four shorts, there you go."
POSTVIEWING ACTIVITIES
Students should be divided into groups of four. Say,
"Today you are going to be game show question makers for the new television
show called "I'll Take the Combo." Each group needs to make up a
combinatorics question and draw a picture of the incomplete combo. Once
students have completed the task, have another class come into the classroom and
have a televised (video record) version of their own game show. (Students in each
group will need to conference with the teacher about their question or
questions. It is helpful for another teacher to do the same activity so
that your class may participate in the game show process.) Or involve
students in a creative scientific combinatoric activity. Discuss with
students the different types of beaks and feet that birds have.
ACTION PLAN
Arrange a field trip to an ice cream parlor. Have students
figure out possible combinations of ice cream toppings as a challenge. (Use
chocolate, vanilla, and strawberry ice cream and the various toppings available
at the store. Students may need to use calculators.)
Invite a florist to visit your classroom. Ask her/him
to show different combinations of flowers in a boutonniere arrangement.
EXTENSIONS
LANGUAGE ARTS
Arrange a mock vacation. Due to the space, students are
only allowed to take a few pieces of clothing. Students must come up with
a different outfit for each day. (i.e. a different outfit for 25 days)
MATH
In groups, have students cut out outfits from catalogs and make
problem solving questions for other groups. Place tag board backed pieces
in plastic bags along with problem solving questions.
ART
Have students draw and graph pictures of different combinations
of items.
SCIENCE AND MEDICINE
Ask the school nurse to share some information on genetics.
Have the nurse explain how humans have combinations of different colored eyes,
hair, etc.
TECHNOLOGY
Have students visit the internet. Students can ask Dr.
Math questions about combinatorics.
Create a Combo Creature
You need imagination, pencil, paper, and crayons.
1. using the pictures of different bird beaks and feet, you are
going to create an imaginary animal that is perfectly adapted to survive in any
environment you choose. Your bird must be able to survive without any help
pr feeding from you. In order to do this, you need to decide on several
things. Do this by answering the following questions. Be as
imaginative as you can?
*What does your bird eat?
*How does your bird get its food? What physical
adaptations (body parts) does it have to help it get this food? (For
example, an owl's sharp beak and claws help it catch mice.)
*Where does your animal get water? What physical
adaptations does it have to get this water?
*What predators does your animal have?
* How does your animal move? Are the wings on your bird
long or short?
2. Make sure that your draw your bird in its own
habitat.
3. Name your bird and write its name under its picture.
Combinatoric
Eun
With Animals
Birds use their beaks for catching and eating food.
Some use their beaks for tearing meat. Others use them for cracking seeds or
scooping water. Still many other birds use their beaks for spearing fish.
Birds have different types of feet to help them survive in
their various habitats. Some birds use their feet to swim and wade,
while others use their feet to climb and perch. Birds also their feet to
catch and eat food. A grasping foot allows a bird to catch their prey.
Using the four different beaks and the four different types
of feet, how many different types of birds can you create? Draw a picture
or use a special code to show how many different birds can be created.
Formulate a mathematical sentence that matches your picture.
Updated: April 01, 2008
|
