DES Problem Solvers

K-2 Question 

Lines of symmetry exist in almost every part of our world.  Take a walk to discover some of them.  Collect, draw, or write about the lines of symmetry in our natural world.  Take these ideas back to class and create pictures with the lines of symmetry drawn.  What lines did your classmates find?  Who found the most lines?  Can you think of any natural object that has more than 1 line of symmetry?  If you are unable to go on a walk, visit this website for stunning pictures of leaves:

Euphorbia is a pretty flower with only 2 petals; the hibiscus has 5 petals; and dicotyledonous plants can have 10 beautiful petals.  Pretend you are designing a flower arrangement made with 30 petals, using only these 3 flowers.  What combination would give you the fewest flowers?  What combination would give you the most flowers?  Find as many combinations as possible using at least 2 flowers to produce 30 petals. 

3-5 Question

Honeybees make their honeycombs in a hexagon shape.  If we assemble 15 hexagon-shape pattern blocks, what is the largest perimeter we can get?  What is the smallest perimeter we can get?  What do you notice about the perimeter and the number of hexagons in the middle?  Honeycombs are built a specific way and in a hexagon shape for a reason.  What could some reasons be?  Can you explain?

California's giant Sequoia trees increase in height by an average of 4 ft. per year.  Imagine that you are monitoring 2 giant Sequoia trees.  Both trees are 200 ft. tall to start.  One tree receives more water and sun, better soil, and altogether more resources.  It grows 5 ft. per year.  The other tree grows an average of 3 1/2 ft. per year.  What will be the height of these trees in 5 years?  In 10 years?  Make a graph of their growth. 

Challenge Question

Africa’s forests are disappearing at twice the rate of those in the rest of the world.  Forests cover one-fifth of the continent, which loses 4.0 million hectares of its forests per year.  Knowing that Africa is approximately 11,670,000 sq. mi., determine how long it would take before all of Africa’s forests are gone.  (One sq. mi. is about 260 hectares.)  Explain your reasoning.

Whale sharks feed on plankton in the Gulf of Tadjoura in Djibouti from November to January.  Up to 40 m in length, whale sharks are massive, and yet they survive on the smallest organisms, filtering food through their teeth.  To support its energy needs, a 6 m whale shark spends 7.5 hours a day eating and can filter about 2.8 kg per day.  Assuming that the length of a whale shark is proportional to its food consumption, about how much must a 27 m shark consume in a day?  What would be the ratio of weight to daily food consumption if the whale weighed 13.05 tons?