Phantom Lake Math Challenge February 2016 Interacting with

Phantom Lake Math Challenge
February 2016
Interacting with Butterflies
*Levels adjusted, based on parent feedback (Thanks!)
These problems are generally in an order of increasing difficulty (A-L). Choose the one that fits your math ability
and solve the problem. People at home can help you. Usually, you’ll need to submit your answer using the
response form attached. You should turn in one form for each problem you solve. Occasionally a poster or chart
might be a better way to show an answer. Feel free to be creative. Please put the letter or title of your problem,
your first and last name and your teacher’s name on the form when you submit it. All solutions are due to Mrs.
Gaylord by, Monday, February 29th. Bring your completed form(s), charts, and posters to your teacher.
Students who successfully complete the challenge with the correct answer and a logical explanation of their
mathematical thinking will receive a certificate and their name listed in the PTA newsletter. Happy problem
solving!
A. Butterflies are insects
Butterflies are insects, and all insects have 3 pairs of legs. If one pair of legs equals 2 legs, how many legs
does a butterfly have? If you were walking through the playground one day and 3 butterflies landed on
your arm, how many butterfly legs would you see? Show how you calculated the total number of
butterfly legs. Explain your solution to a friend.
B. Read From Caterpillar to Butterfly:
Read from Caterpillar to Butterfly (Heiligan 1996) or another book about the life cycle of butterflies.
On pages 10-11, the book notes that butterflies lay their eggs on host plants that the caterpillar eat
when they emerge from the eggs. It also shows plant leaves that are being eaten by caterpillars.
Leaf A has 8 caterpillars on it. Leaf B and Leaf C each have 3 caterpillars on them. How many
caterpillars are on the plant altogether? If a caterpillar consumes 20 leaves before it makes it
chrysalis, how many leaves would you need to feed all the caterpillars? Share and discuss your
answers with a friend?
C. A caterpillar
A caterpillar, which is also called a butterfly larva, changes into a butterfly through metamorphosis.
Pretend that 4 teachers in the school were raising butterflies: Mrs. Bramzel’s class had 3 Monarch
butterflies; Mrs. Carkonen’s class had 5 painted lady butterflies; and Mrs. Mitchell’s class had 4 painted
lady butterflies. If 17 butterflies were being raised in the school, how many butterflies was Mr. Kim’s
class raising? Create a display to show the number of butterflies in each class.
Write 3 statements about your data. Here are some ideas using the words most, least and combine.
1. Class --- has the most butterflies
2. Class --- has the least butterflies.
3. If class --- and --- combine their butterflies they have---butterflies.
D. Butterflies are symmetrical
Draw an image of a butterfly with the following body parts: 1 head, 1 thorax, 1 abdomen, 2
antennae, 6 legs, 4 wings, and 2 eyes. Fold your paper or draw a line to represent a line of symmetry
on your butterfly. Why do you think symmetry helps this insect fly? Name three other living things
that have a line of symmetry.
E. Most species of butterflies
Most species of butterflies lay approximately 100 eggs. If 27 different butterflies each laid 100 eggs in
the same garden, how many eggs would there be altogether? The garden is made up mostly of
milkweed plants, a monarch butterfly’s favorite nectar. If 2/3 of those were monarch butterflies and 1/3
were painted lady butterflies, how many of each would be in the garden? Show your work, and illustrate
your solutions.
F. National Geographic’s Growing up Butterfly video
(http://www.natgeotv.com/ca.great-migrations/videos/growing-up-butterfly)
This National geographic video notes that once a butterfly egg is laid, it spends 4 days in the egg stage.
Then the egg hatches, becomes a larva (caterpillar) for 14 days, and transforms into a chrysalis (also
known as the pupae stage) for 2 weeks. If it lives as an adult butterfly for 3 weeks after emerging from
the chrysalis, calculate its full lifespan, beginning with the egg stage. Create a graph to show this life
cycle. Write two observations and a question about your data.
G. The largest butterfly species
The largest butterfly species in the world is the Queen Alexandra’s birdwing butterfly. It has a wingspan
of 32 centimeters (cm). The smallest butterfly, the Western Pygmy Blue butterfly, has a wingspan of only
1 ½ cm. What is the difference between the wingspans of the worlds, largest and smallest butterfly
species? What would be the wingspan of a butterfly whose wingspan is exactly between that of the
Queen Alexandra’s birdwing and the Western Pygmy Blue butterfly? Draw a picture of your solution.
H. Scientists tracked
Scientists tracked a butterfly colony for a week as it migrated south. Using the data that the scientists
collected (in the chart below), find the total distance the butterfly colony traveled through the week.
Based on its flight patterns, make conjectures about the number of miles it could travel on the following
Monday and Tuesday. How many total miles could it travel during the following week? Show your work.
Day
Miles
Monday
89
Tuesday
84
Wednesday Thursday
79
74
Friday
69
Saturday
64
Sunday
59
I. National Geographic Kids
The National Geographic Kids website about monarchs
(http://kids.nationalgeographic.com/animals/monarch-butterfly/) states that during migration,
butterflies travel from Canada and North America to Central Mexico. They migrate to warmer areas
before winter because they cannot survive in cold climates. They fly during the day and roost at night to
rest and stay warm. Monarch butterflies can travel more than 2000 miles during their migration. If a
monarch butterfly travels 2200 mils in 8 weeks, on average, how many miles could the butterfly have
traveled each day? If the butterfly continued to fly at that average speed each day before resting, how
many days would it take to travel 1000 more miles? Show your strategy and write a description of your
steps for solving.
J.
Butterflies are Primary Consumers
Butterflies are primary consumers which means that they are also food for predators. In the
wild, butterflies have a 2% survival rate for many reasons, such as their access to food and
exposure to predators that feed on them. Four butterflies laid eggs: Butterfly A laid 200
eggs, Butterfly B laid 150 eggs, Butterfly C laid 100 eggs, and Butterfly D laid 175 eggs.
On the basis of the survival rate, predict how many of each butterfly’s offspring would
survive the full life cycle. How many total offspring would survive? Show your work and
share your responses with a partner.
K. Butterfly & Moths
Read the butterfly and moth section of Children’s Guide to Insects and Spiders (Johnson 1996) or some
other resource that tells about hawk moths. The Children’s guide states that hawk moths are the most
powerful fliers of all moths and butterflies. If they can fly up to 30 miles per hour (mph), how long would
it take a hawk moth to travel 56 miles at maximum speed? If a monarch butterfly flies at 12 mph, how
long would it take for it to fly 56 miles? Show your work.
L. Butterfly Habitat
Your class is creating a butterfly habitat in your classroom, and your teacher orders chrysalides. You
decide to do some research and discover that if the chrysalides are kept at room temperature
(70˚F), they will emerge 7-10 days after they pupate. Your class tracks the temperature for 5 days to
determine the average temperature of the room over the 5-day period. What is the difference
between the average temperature and the temperature needed for the chrysalides to emerge?
Day
Temperature ˚F
Monday
67.4
Tuesday
68.2
Wednesday
69.3
Thursday
68.6
Friday
71.1