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| Although District 21 attempts to restrict
external links to web sites of appropriate educational content, neither
the school nor School District 21 is responsible for questionable
or controversial content found through links external to this site. |
Staff: Dr.
J. Beyersdorfer
Students: Grades 3 and 4 Gifted and
Talented Program for Math
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Studying Fruits and Vegetables
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Our Process for the Fruits and Vegetable Table:
We conducted a survey of three third
grade classes to find out about our friends' likes and dislikes
of 7 vegetables
(broccoli,
carrots, corn on the cob, green lettuce, mashed potatoes, pumpkin,
tomato) and 7 fruits (apricots, bananas, blackberries, grapefruit,
pineapple, tangerines, watermelon). We added a category called
"never tasted" to our "like" and "dislike" categories
so that students would not say they didn't like or did like
something that they had never tried. This would keep the number
of tallies (or votes) equal across the fruits and vegetables. We
re-surveyed
any student who did not complete the entire survey. We also arranged
to survey absent students at a later time. |
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| Fruits and Vegetables Survey Results--Katie,
Marissa, Rahul, Ryan, Jacob, Cameron and William |
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| Questions about the Fruits and Vegetables Survey |
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| 1. What vegetable is the favorite for all three classes?
Which vegetable is the least liked? Which vegetable have many people
not tasted? |
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| 2. If Mr Olson would serve a fruit salad for the class
picnic, which fruit would be his best choice to include in the mix? |
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| 3. Which class has the least experience with various
types of fruits? Which class the least experience with various types
of vegetables? |
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4. How many students are in third grade?
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| 5. What two fruits and two vegetables were equally
well -liked in Mrs. Cohen's class? |
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| 6. If 12 students liked broccoli and 4 students disliked
broccoli in Mr. Olson's class, how many never tasted broccoli? Write
your answer as a fraction reduced to the lowest common denominator. |
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| 7. What is the average number of third grade students
per class that dislike lettuce? |
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| 8. One student likes 3/4th of all 8 fruits and vegetables.
How many fruits/vegetables does she like? She dislikes 1/8 of them,
how many has she never tasted? |
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More Graph/Chart
Problems
Data taken from Scholastic Kid's Almanac for the 21st Century
Blackbirch Graphics Book
New York, NY 1999
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| Avalanches and Floods Data from
page339 highest number of deaths possible |
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| Questions by Cameron and Ryan
and Cameron |
| 1. When did the Bangladesh flood hit? |
| 2. Which two of the deadliest avalanches hit on the
same day of the month but in different years? |
| 3. How many more people died in the Huang Ho River
flood than in the Yungay, Peru landslide? |
| 4. How many died in all the avalanches? |
| 5. How many people died in the Bengal, India and the
Chang Jaing River floods in all? |
| Answers to Avalanches and Flood Questions |
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| Land and Marine Animals Data from page20 |
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Land Mammal
Elephant
Rhino
Hippo
Giraffe
Bison
Grizzly Bear
Camel
Moose
Tiger
Gorilla |
Weight in Pounds
11023
8818
4409
2646
2205
1720
1323
1312
661
485
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Mammal
10. Blue Whale
9. Fin Whale
8. Right Whale
7. Sperm Whale
6. Gray Whale
5. Humpback Whale
4. Baird's Whale
3. Southern Elephant Seal
2. Northern Elephant Whale
1. Pilot Whale
#11 is the total |
Weight in Tons
130.0
45.0
40.0
36.0
32.7
26.5
11.0
3.6
3.4
2.9
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| Questions by Katie and Marissa:
A zoo wants to send some of its animals by ship to a new home,
they need to know if their ship is the right size. They will need
a
bigger ship if the total weight is over 15,000,000 pounds. Do they
need a bigger ship? |
| 1. How much does an American Bison weigh? |
| 2. How much more does the Blue Whale and the African
Elephant weigh compared to the Giraffe? |
| 3. How much do 9 African Elephants weigh compared
to the weight of 5 Blue Whales? |
| 4. How much do the top 10 heaviest land
mammals plus the top 10 heaviest marine mammals weigh (in tons rounded
to the nearest tenth)? |
| Answers to Land and Marine Animals
Questions |
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| Tennis Data from page 306 |
| Men Players |
Austrialian Open |
French Open |
Wimbleton |
US Open |
Total |
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| Roy Emerson |
6 |
2 |
2 |
2 |
12 |
1961-1967 |
| Pete Sampras |
3 |
0 |
4 |
4 |
11 |
1990-1998 |
| Bjorn Borg |
0 |
6 |
5 |
0 |
11 |
1974-1981 |
| Rod Laver |
3 |
2 |
4 |
2 |
11 |
1960-1968 |
| Jimmy Connors |
1 |
0 |
2 |
5 |
8 |
1974-1983 |
| Ivan Lendl |
2 |
3 |
0 |
3 |
8 |
1984-1990 |
| Fred Perry |
1 |
1 |
3 |
3 |
8 |
1993-1936 |
| Ken Rosewall |
4 |
2 |
0 |
2 |
8 |
1953-1972 |
| Women Players |
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| Margaret Smith Court |
11 |
5 |
3 |
5 |
24 |
1960-1975 |
| Steffi Graf |
4 |
5 |
7 |
5 |
21 |
1987-1996 |
| Helen Wills-Moody |
0 |
4 |
8 |
7 |
19 |
1923-1938 |
| Chris Evert-Lloyld |
2 |
7 |
3 |
6 |
18 |
1974-1986 |
| Martina Navratilova |
3 |
2 |
9 |
4 |
18 |
1974-1995 |
| Billie Jean King |
1 |
1 |
6 |
4 |
12 |
1961-1981 |
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| Questions by Rahul |
| 1. Of the men and women athletes listed
here, who were better players between 1923-1959, men or women based
on their total winning matches? Who were the
better
players (men or
women)
between 1974-1998?
Were the men or the women the overall winners in all competitions
between 1923-1998? |
| 2. Margaret Smith Court won the following number of
matches: 11, 5, 3, 5. Ivan Lendl won 2, 3,0, 3 matches. What was
the difference between their averages? |
| Answers to Tennis Questions |
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| Sports Data from page310 |
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Sports
Walking
Swimming
Fishing
Cycling
Equipment
Camping
Bowling
Billiards/pool
Basketball
Boating |
Number
70794000
60277000
51992000
49818000
43784000
42932000
37356000
34000000
28191000
26400000 |
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| Questions by William and Jacob |
| 1. Bob wants to know the difference between the number
of people who walk for exercise and the number of people who bowl
for exercise? |
| 2. What is the total of people who like to play both
sports, billiards and boating? |
| 3. What is the population of people that go cycling? |
| Answers to Sports Questions |
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| Answers to Avalanches and Flood Questions |
| 1. November 13, 1970 |
| 2. Italian Alps and Huaras, Peru |
| 3. 3,682,500 To get this answer you had to subtract
3,700,000 from 17,500. |
| 4. 18,500 To get this answer you had to add together
all the avalanches, not landslides. |
| 5. 140,000 To get this answer you had to add 100,000
to 40,000 together. |
| Answers
to Land and Marine Animals A zoo wants to send some of its animals
by ship to a new home, they need to know if their ship is the right
size. They will need
a
bigger ship if the total weight is over 15,000,000 pounds. Do they
need a bigger ship? No, they do not need a bigger ship. |
| 1. 2,205 |
| 2. 268,377 The blue whale weighs 130.0
tons. You have to multiply it by 2,000. That equals 260,000 lbs.
You add
the African Elephants and the blue whales weight which is 11,023.
That equals 271,023 lbs. You subtract the giraffe's weight which
is 2,646 from 271,023. That equals 268,377 lbs. |
| 3. 12,900,793 The African Elephant weighs
11,023 so you times it by 9 which equals 99,207 lbs. Then you multiply
260,000
because that’s how much a blue whale weighs in pounds. You
multiply 260,000 by 5. That equals 1,300,000 lbs. Finally, you
subtract 130,000 lbs. from 99,207 lbs. That equals 1, 200,793
lbs. |
| 4. Add all the weights of the marine animals in tons.
They total 331.1 tons. Add all the weights of the land animals. They
tota 34.602 pounds. Convert that to tons by dividing by 2000 (the
number of pounds per ton). Then add the two totals. The final amount
is 348.4 tons. |
| Answers to Tennis Questions |
| 1. Women won more games between 1923-1959 than men,
Women won more games between 1974-1998, Women won more games in all
competitions between 1923-1998. |
| 2. Margaret Smith Court’s average
was 4 wins more than Ivan Lendl’s average. |
| Answers to Sports Questions |
| 1. 70,794,000 (exercise walking) -37,356,000 (bowling) =
3,438,000 |
| 2. 34,000,000 (billiards) + 26,400,000 (boating) =
60,400,000 |
| 3. 49,818,000 population who cycles |
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| The Project: To
complete the probability project, students analyzed
the structure of probability problems. They recognized that the
problem began by establishing a scenario that explained for whom
and why the problem existed. Often the when and where of the situation
was described. A restriction regarding the offered choices was
established. This framework served as the basis for the probability
problem they
designed. They illustrated
the use of this math concept in a specific
real world situation when they selected their
topics. For each of the three or more categories,
they listed a minimum of three options. |
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Kendell and her mom are searching
the Summer News for activities for her to participate in.
She knows she has three long summer
months ahead of her, and she wants to do something besides
relax, but still have some fun. She can participate in a
reading club,
join a basketball team, or take piano lessons. Each one will
take place either at the Park District, her friend Kiley’s
house, or at a camp. They can all last for either one, two,
or three hours. Kendell decides she doesn’t want to
take piano for two hours or basketball for three hours. Using
a tree diagram,
list the possible combinations of summer activities Kendell
can participate in. How many combination are possible given
her decision not to take piano for two hours or basketball
for three hours.
See Kaitlin's Tree Diagram
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Howard’s family wants to buy a new car because their
old car was in a car accident where the car got hit in a
parking lot. They have three different automobile companies
to choose
from Honda, Toyota, and Ford. After his family decides the
car company they will have to select the type of car such
as a mini van, SUV and a convertible. Once Howard’s
family picks their favorite manufacter and model car they
will have
to choose a color for their little car. the choices are red,
green and blue. The kids said they would not like a green
convertible from Honda. List the possible combinations using
a tree diagram. How many combinations are possible given the
family's decision not to purchase a green convertible from
Honda.
See Billy's Tree Diagram |
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You are going to the store to
buy supplies for your party next week. There are fourteen
people coming to your
party including you. The three stores that are nearby
that supply all you need are Walmart, Garden Fresh, Sam’s
Club. The foods you need to buy are vegetables, cereal,
candy, cheese, and fruit. The next item you need to buy
is drinks.
The drinks you need to buy are 7-Up, chocolate milk,
Pepsi, and Hawaiian Punch. Your friends will not choose cereal
with Pepsi. Give the number of total combinations possible.
List all the combinations
using
a
tree diagram
See Jim's Tree Diagram
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You are buying a birthday cake
for your birthday party at a bakery. You want a certain flavor
of cake, frosting,
and topping. They only have 3 flavors of cake. The flavors
are vanilla, chocolate, and confetti. They only have 3 flavors
of frostings. The flavors of frostings are vanilla, chocolate,
and mint. Lastly you are choosing the topping. They have
M&Ms,
peanuts, and sprinkles. But you can’t have vanilla
cake with vanilla frosting or chocolate cake with chocolate
frosting.
Give the total number of combinations of birthday cakes you
can serve to your guests. List the total number of combinations
using a tree diagram. Given that the cake cannot have vanilla
frosting with vanilla cake or chocolate frosting with chocolate
cake, what are the number of combinations available for
purchase.
See Brandon's Tree Diagram
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Check Your Probability
Answers |
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| Fruits and Vegetables Answers |
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| 1. Broccoli, Tomato, Pumpkin |
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| 2. Pineapple |
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| 3. Part One: Cohen Part Two: Henderson |
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| 4 .H 19, C 19, O 18; total 56 students |
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| 5. 2 Fruits: Pumpkin, Tomato Two Vegetables: Apricot,
Blackberries |
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| 6. 2/18 = 1/9 |
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| 7. 15 divided by 3 equals 5. |
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| 8. She dislikes 6 of the fruits and vegetables. She
has never tasted one of them. |
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| Probability Trees |
| Kaitlin's Tree: There are twenty-one cominations that
Kendall could choose. There are twenty-seven combinations possible. |
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| Billy's Tree: There are twenty -six combinations for
the family care without choosing a green Honda convertible. There
are twenty-seven combinations possible. |
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| Jim's Tree: There are fifty-seven combinations for
the party if you don't eat cereal with Pepsi. There are sixty combinations
possible. |
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| Brandon's Tree: There are eighteen combinations for
the birthday cake without making the frosting the same flavor as
the cake. There are twenty -seven combinations possible. |
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| Reviewed/Revised May, 2006 J. Beyersdorfer |
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