WHAT'S FOR LUNCH? A COMBINATION SENSATION!
Grades K-2
The purpose of this lesson is to allow young students to explore
the concept of combinatorics, the science of counting and finding possible
solutions, to describe patterns of arrangements. The activity is designed
to allow students to use information they learned in previous lessons about
the food groups and healthy food choices. The activity plan assumes that
the students have already studied about food groups and are able to identify
some foods in each of the groups. Although it would be helpful to maintain
the continuity of the lesson by teaching it all in one day, this lesson
may require more than an hour to complete. If dividing the lesson into two
days, conduct Pre-Viewing activities on one day and Viewing and Post-Viewing
activities the second day.
Math Talk #109: Let Me Count the Ways: Counting With Combinatorics
Students will be able to:
- predict the number of possible combinations of food choices
- work together as a group to determine a reasonable solution for the
number of possible combinations.
- identify the food groups for a menu of food items.
- identify at least two different combinations of the food items by
following guidelines on food choices.
Texas Assessment of Academic Skills (TAAS), Grade 4 Math Objectives:
- Demonstrate an understanding of probability and statistics.
- Estimate solutions to a problem situation.
- Determine solution strategies and analyze or solve problems. Science
Objectives:
- Interpret scientific data and/or information.
- Make inferences, form generalized statements and/or make predictions
using scientific data and/or information.
Per class:
- poster or overhead transparency of Food Guide Pyramid and food items
- poster or overhead transparency of food tray and menu items
- yellow, red and green construction paper, 5 sheets each
- black, blue and brown construction paper strips, 5 sheets each
Per student:
- copy of the tray
- copy of food items
- scissors
- glue
- sticky note
- choice
- cereal
- milk
- food
- pasta
- fats
- food pyramid
- serving
- sweets
- food group
- fruit
- combination
- variety
- vegetable tray
- grain
- protein
- rice
- bread
- meat
- dairy
[Note: A major portion of this lesson will involve activities
done prior to the viewing of the ITV program. The segment from Math Talk
which is used in the Viewing Activities section of the lesson deals with
combinatorics and will help students organize their information and make
predictions about and verify the number of possible combinations of food
items.] Remind the students that they have been learning about healthy eating
choices and that people should eat a variety of good foods in sensible portions.
Bring to their attention a blank display of the food pyramid, which is something
the class has examined in an earlier lesson. Ask the students to identify
the food groups. As each group is identified, place a label or write the
name on the food pyramid. Show the students a picture of a common food item
from the school's cafeteria menu. Real food items might be used with younger
students. Have the students name the food item and identify the food group
to which it belongs. Place the picture of the food item on the blank food
pyramid. Continue until each of the food groups has several examples in
it. You may also wish to include some food items that are composed of food
from different food groups, such as pizza (bread, vegetables, dairy) or
enchiladas (bread, vegetables, meat, dairy). Choose the menu for one lunch
from the school cafeteria menu. You may wish to choose a recent lunch or
one to be served in the near future. Determine the food groups to which
each food item belongs. [Note: Many school cafeterias are allowing children
to make selections among a small variety of food choices. The following
activity is based on this idea. The students will select one meat/protein
dish from two choices and two fruit or vegetables from a selection of four
fruit or vegetable choices. Each lunch will also include a roll (one bread
is served, no choice) and milk (dairy, no choice). The activity could be
adapted to fit your school's cafeteria process. If this is not appropriate,
you may wish to place the activity within the context of making choices
at a local restaurant or cafeteria.] Show the students the display of the
cafeteria tray. Ask the students to identify where each of the food items
from the cafeteria menu would fit on the tray, in both space and food group.
You may wish to list the food items in a manner such as this. meat/protein
(1 choice): chicken, fish fruit/vegetable (2 choices): broccoli, salad,
apple, banana bread: roll dairy: milk Ask the students to use the paper
cafeteria tray and the pictures of the food choices to show one choice of
selections for lunch. The students will place one food item in each space
on the cafeteria tray. Students must choose one meat/protein selection and
two fruit or vegetable selections. They may choose either two different
fruits, two different vegetables, or one fruit and one vegetable. They cannot
choose two of the same foods (for example, two servings of oranges). Ask
the students to tell other students around them what choices they made.
Did everyone make the same choices? Why did this happen? Have two students
name the food selections they choose. Place these selections on the display
trays. Ask students to identify the similarities and differences between
the two meals. Discuss the concept of food preferences and how that will
effect the choices people make. What other factors might change the choices
you make? Have the students examine the food selections again and have them
make a final choice for the lunches they would like to eat. These selections
should be glued in the appropriate places on the food tray. [Note: With
some groups of students, you may wish to conduct this choice and pasting
activity in a small group to assist students in locating the foods correctly.
With a large group, you may wish to have the students work item by item
with you as you model. Your oral directions may be very specific to emphasize
vocabulary or to encourage the students to practice following directions.
You may say something like this: "Take a milk. Paste it in the space
next to the fork. Do you want to eat chicken or fish? Pick up one and paste
it in the space on the bottom next to the milk."] Have the students
examine the trays of others near them. Ask them to talk with their neighbors
about how their choices are the same and different. Ask the students to
tell you something they noticed which is the same about every person's tray.
The students should be able to recognize that every tray has milk and every
tray has bread. Tell the students that since each tray has both milk and
bread, those food items will not need to be considered when we begin sorting.
Ask the students to think of a way their trays could be sorted. Have the
students discuss how the trays could be sorted with the others near them.
For example, they might think of putting all the trays with fish together.
Ask the students to predict the number of possible ways the lunch tray could
be filled with different food selections. Give each student a small sticky
note. Have each student write the prediction on the note. Have the students
place the sticky notes on the wall or blackboard to make a graph of the
predictions. The graph may look something like this.
9 12 14
8 9 10 12 13 14 15
6 8 9 10 11 12 13 14 15
Tell the students that they will be viewing a short story that
is about making combinations and looking for all of the possible combinations.
Ask the students to listen and watch for ways Super Guy and the sales person
organize their information to find all of the possible combinations or ways
of putting things together.
Begin the Math Talk video when the black and white sign labeled
"Water Works" is shown. Show the segment through the explanation
of the problem at the Water Works and pause after Super Guy knocks on the
occupied phone booth, turns away and says, "What am I going to do?"
Ask, "What is Super Guy's problem?" (water is leaking from the
wall, he wants to help stop the water, he can't find a place to change into
his Super Guy suit) Tell students to watch the next segment to see where
Super Guy goes to change into his Super Guy suit. Resume the video to continue
through the segment where Super Guy goes into the clothes store to change
into his suit. The sales person points out that Super Guy has a problem:
he forgot his cape. Pause where Super Guy says, "I don't have time
to get a new one. Destiny calls!" Ask, "Where did Super Guy go
to change his suit?" (the clothes store) Ask, "What did the sales
person tell Super Guy?" (He forgot his cape.) Tell the students to
watch the next segment to see how Super Guy will fix his problem of having
no cape. Resume the video through the segment where Super Guy notices the
capes hanging on the rack. Pause after the sales person says, "Well,
they're all very nice capes, sir." Ask, "What did Super Guy see?"
(capes hanging on the rack) Ask, "What color capes did Super Guy like?"
(yellow, red, green) [Note: If students do not recall the colors of capes,
rewind through capes hanging on the rack and replay.] Display sheets of
yellow, red, and green construction paper to represent the capes. Tell the
students to watch the next segment to see what else Super Guy wants. Resume
video through the segment where the sales person shows the black, brown,
and blue belts and pause where Super Guy says, "Oh, I could wear the
blue belt with the yellow cape." Ask, "What else does Super Guy
want?" (a belt) Ask, "What colors are available in belts?"
(black, brown and blue) [Note: If needed, rewind and replay this segment
to remind students of the colors available in belts.] Display strips of
black, brown, and blue construction paper to represent belts. Ask, "What
combination does Super Guy think of first?" (yellow cape with blue
belt) Display strip of blue construction paper on across yellow construction
paper. Ask, "Do you think that's the only thing Super Guy could choose?"
(no) Ask, "What other combination of cape and belt might Super Guy
choose?" Allow students to name several different combinations and
use the construction paper and paper strips to display these. Tell students
to watch the next segment to see if Super Guy and the sales person can think
of different combinations of capes and belts as the students did. Rewind
briefly to where Super Guy is holding the green cape. Resume the video through
the segment where they talk about the number of combinations and pause where
the sales person says, "But we can figure it out." Ask, "How
many combinations do you think there will be?" (various predications)
Ask, "How do you think we could figure it out?" [Note: Lead students
to recognize that they could use the construction paper pieces and strips
to show the combinations.] Ask, "What combinations of one cape and
one belt could we make?" As students name a combination, use construction
paper and strips to display them. Their combinations may include duplicates
or not include some possibilities. Be sure to display these as this is part
of the learning to make combinations. Tell the students to watch the next
segment to see how many combinations Super Guy and the sales person make.
Resume the video through segment where the combinations are made on the
display rack and pause where Super Guy says, "Now, have we forgotten
anything?" Ask, "How many combinations did they make? (eight)
Rewind the video to the view of Water Works sign and people against wall.
Tell students to watch to see which combinations match the ones they made.
[Note: If students have not recognized that some combinations are duplicated
at this point, you may wish to lead them to see this before viewing the
next video segment.] Resume and pause where the sales person says, "Well,
let's see if we can get all of this in some sort of order." As you
watch the segment this time, remove the construction paper cape and paper
strip belt combinations from the display. Ask, "How many combinations
did we name that Super Guy and the sales person also found?" Count
those removed to determine how many were the same. Ask, "They had eight
combinations. Did they have some combinations we didn't name? Did we have
combinations they didn't name? How many?" Tell students to watch the
next segment to see how Super Guy and the sales person organize the capes
and belts and to see if they find all of the possible combinations. Resume
the video through segment where they move the combinations and pause where
the sales person says, "Wait a minute. What goes here?" Ask, "How
did they organize the capes?" As the students tell how all the yellow,
green, and red capes were put in different columns, put the construction
paper capes in columns on the display. As the students tell how all the
black, brown, and blue belts were put in different rows, put the combinations
in rows on the display.
yellow capes green capes red capes
black belts
brown belts
blue belts
Ask, "Can you figure out what is missing?" (red cape with a black
belt) Ask, "How can you figure this out?" Ask, "How many
combinations did you find?" (nine) Ask, "Do we have all the combinations?"
(yes) [Note: With younger children, it may not be as important that they
find every possible combination as it is that they realize that different
combinations are possible and that different choices can be made.] Tell
students to watch the next segment to see if they are right about the missing
combination and which combination Super Guy selects. Resume the video and
continue through segment where Super Guy puts on the cape and belt and stop
at the Adventures of Super Guy logo. Ask, "Were we right about the
missing combination?" (yes, red cape with a black belt) Ask, "How
many possible combinations were there?" (nine) Ask, "Which combination
did Super Guy select?" (red cape with a black belt) Ask, "Why
do you think he selected this combination?" (He liked it.) Ask, "Why
do people select things like clothes or food?" (They like them. They
taste good. They want them.)
Tell the students they can sort their food choices on their
trays in a similar way. Ask one student to identify food on his or her tray
and use this as a way to begin sorting. This could be something like all
the trays with apples and all the trays without apples. Have students place
their trays in one of these two groups on the floor or attached to a display
board. The trays will be in a formation something like this. Trays with
apples Trays without apples
Now ask another student to identify a different food on the trays, such
as chicken. Divide each of these two groups of trays into two groups. Trays
with Trays without apples
Trays with chicken
Trays without chicken (fish)
Have the students examine the trays to determine if any of the trays have
all the same food choices. If there are any trays with exactly the same
food choices, these can be stacked on top of each other. Have the students
count to find out how many different sets of food choices they see. Ask
the students if they think they have found all the different ways to choose
food selections for lunch. If they think they have, use the display to show
them a combination they did not choose. Have the students focus their attention
on the trays which have chicken. One group has trays with apples. What foods
could go with apples? Have the students sort the trays in a row. Record
these combinations either with food pictures or with letters to represent
the foods (if this will be understood by the students). Your combinations
may look like this. (c=chicken; a=apple; o=orange; b=broccoli; l=lettuce
salad)
C A B C A O C A L
Are there any other foods that could go with chicken and apples? (no) What
other food could you choose to go with chicken? (Students name one: broccoli,
for example.) Have students look at the trays to find possible combinations
with this food.
C B A C B O C B L
Is there one of these combinations that is the same as another we listed?
(Yes. CAB is the same as CBA.) Erase or put an X on that combination. Are
there any other foods that could go with chicken and broccoli? (no) What
other food could you choose to go with chicken? (Students name one: oranges,
for example.) Have students look at the trays to find possible combinations
with this food.
C O A C O B C O L
Are there combinations that are the same as another we listed? (Yes. COA
is the same as CAO. COB is the same as CBO.) Erase or put an X on those
combinations. The list of combinations should look something like this.
C A B C A O C A L
C B O C B L
C O L
How many different combinations are there when the meat/protein selection
is chicken? (six) What could you choose for meat/protein if you did not
choose chicken? (fish) If there are six choices with chicken, how many do
you think there will be if you select fish? Have the students examine the
trays with fish and see if they can sort them to see if they are right.
You may wish to show the students how they can change the list of combinations
with chicken above by changing the C to F.
F A B F A O F A L
F B O F B L
F O L
If there are six combinations of food selections with chicken and six combinations
of food selections with fish, how many different possible combinations of
food are there? (twelve) Do you have to know how to make them all? (no)
Review the main points of this lesson. When do we have food choices to make?
(in the cafeteria, at restaurants, at home, when shopping) What kinds of
foods should we choose if we want to stay healthy? (foods from all food
groups on the food pyramid) How do we know which food to choose? (foods
from food pyramid, foods we like) Is there more than one way to choose foods
in the cafeteria? (yes) How might we find out about different combinations?
(try it out, use pictures, write letters for the foods, list the combinations)
How would we know when we have all the combinations? (organize the information)
When else might we want to know about combinations? (making teams for games,
choosing clothes to wear, making things with different colors)
Have the students examine the local cafeteria menu. Does it
include healthy foods from all groups on the food pyramid? Does it limit
fats, salt and sweets? Students can write a letter to the cafeteria manager
or menu planner to suggest ways to improve the lunch menu. Use telecommunications
to communicate with classes in other schools in different parts of the state
or the country. Ask them to share how their school cafeteria allows students
to make food selections. Ask them to share a recent menu. How does this
menu compare with the one at our school? Do students have choices which
allow them to choose from all food groups on the food pyramid?
Writing: Have each student write a sentence to tell about his
or her food choices. The sentence may read something like: "On my tray,
I choose chicken, lettuce salad, an apple, a roll and milk." Have each
student read the sentence to the class. For younger students, they may use
their paper tray of food choices to talk about the food choices.
Science: You are planting a school garden. You have learned that there are
two kinds of trees and four kinds of flowers which are especially easy to
grow in your area. If you wish to plant one tree and two different kinds
of flowers in your garden, how many possible combinations would there be?
[Note: After doing this activity, some students may recognize this as the
same problem posed in the lesson with the food choices. There are 12 combinations.]
Health: The students will be provided the materials to make a trail mix.
There are five ingredients available and each student may select three of
these ingredients for the trail mix. How many different possible combinations
are there? (10)
ABC ABD ABE BCD BCE CDE
ACD ACE BDE
ADE
Health: Have each student prepare one day's food selections for the cafeteria
menu. When the food selections are prepared, have other students check to
see that a variety of foods from the food pyramid are available. Submit
the class menu to the cafeteria manager or menu planner.
Mathematics: Have the students investigate another instance of combinatorics.
For example, if Justine has four shirts (yellow, white, red, and green)
and three pants (black, brown, and blue), how many different combinations
of shirt and pants can she make? Have students use linking cubes to show
the possible combinations.
Social Studies: Have students use a map to locate five different cities
or sites which are within a relatively short distance of their home that
they would like to visit. List these places on the blackboard. If they were
able to visit two of these places on a vacation, which would they choose?
How many different possible combinations of two places would there be? Could
they visit both places they chose in one day?
NOTE TO TEACHER
For the esl learner: The student who is learning English as a Second Language
will have the opportunity to use many common words in this lesson. Many
of the vocabulary words are included with the pictures of the food items
the students will use to complete the activity. As you are reviewing the
food groups in the food pyramid, you may wish to explain or have students
identify examples of foods in each group to help clarify these words. Actual
food items for students to sort or pictures of food items for students to
place on a blank food pyramid could also help students relate the vocabulary
to real-life items. Try to include food items which are familiar to your
students. These could include foods served in their homes, such as rice
or tortillas, as well as foods they are familiar with from school, such
as local fruits and vegetables. Provide an opportunity for students to write
sentences about and read their combinations of food choices to others in
the class to support written and oral communication in English.
Background information on dietary guidelines: The USDA's Food Guide Pyramid
provides the following information about healthy food choices. Americans
above the age of two should eat a variety of foods, maintain a healthy weight,
choose a diet low in fat and cholesterol, choose a diet with plenty of vegetables,
fruits, and grain products, and use sugars and sodium in moderation. The
food pyramid emphasizes the five food groups located in the three lower
levels of the food pyramid. Each of these foods provides some of the nutrients
you need daily. Since no one food is more important than another, a variety
from each of the groups is needed for good health. The base of the pyramid
includes foods derived from grain, such as bread, cereal, rice, and pasta.
The most servings come from this group. The next level includes foods which
come from plants: fruits and vegetables. The third level includes foods
which, for the most part, come from animals and are sources of protein and
calcium. Meat, poultry, fish, eggs, beans, and nuts are in one group on
this level. Dairy foods, such as milk, yogurt, and cheese, are also on this
level. The foods at the tip of the pyramid, which include fats, oils, and
sweets, are recommended to be used sparingly.
Background information on combinatorics: "Combinatorics" is the
mathematics of counting. More generally, it is concerned with problems that
involve a finite number of possibilities and it attempts to answer one or
more of the following questions: - Does a solution exist? - How many solutions
are there? - Is there an optimum solution?". (E.W. Hart, 1991, p.70)
In this lesson, each student will find at least two combinations of food
items. (Does a solution exist?) After examining the combinations of others
in the class, each student will predict the total number of possible solutions.
(How many solutions are there?) Each student will paste one combination
on a paper tray to show a choice. (Is there an optimum solution?) A total
number of possible combinations may be identified.
Master Teacher: Wayne Gable
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