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2. Finding tessellation in nature 2. Finding tessellation in nature

a. Have students look through science magazines, informational books and/or online to find examples a. Have students look through science magazines, informational books and/or online to find examples
of tessellation in nature of tessellation in nature
3. Discussion: 3. Discussion:

a. Why is this helpful in nature? a. Why is this helpful in nature?
i. Efficient: there’s no wasted space or materials i. Efficient: there’s no wasted space or materials

b. Of triangles, squares and hexagons, what is the shape that uses the least amount of material make b. Of triangles, squares and hexagons, what is the shape that uses the least amount of material make
the biggest shape? the biggest shape?

i. Have students create individual hypothesis and then test it. i. Have students create individual hypothesis and then test it.
4. Experiment: 4. Experiment:

a. In groups of 3, have students investigate relationship between perimeter and area of triangles, a. In groups of 3, have students investigate relationship between perimeter and area of triangles,
squares, and hexagons squares, and hexagons

i. Investigation 1: i. Investigation 1:
1. Using 8 ½ X 11 paper, have students create triangular, square and hexagonal prisms 1. Using 8 ½ X 11 paper, have students create triangular, square and hexagonal prisms
by folding the paper into a tube. The face of each prism will have the same perimeter by folding the paper into a tube. The face of each prism will have the same perimeter
because they were created with the same size paper. because they were created with the same size paper.
2. Fill the triangular prism with cereal (or another large material). 2. Fill the triangular prism with cereal (or another large material).
3. Pick up the triangular prism and measure how many cups of cereal were needed to 3. Pick up the triangular prism and measure how many cups of cereal were needed to
fill it up. fill it up.

4. Repeat with square and hexagonal prism. 4. Repeat with square and hexagonal prism.
a. Alternatively, don’t measure the number of cups of cereal and just use the a. Alternatively, don’t measure the number of cups of cereal and just use the
same cereal to fill each prism. same cereal to fill each prism.
b. Discuss if each prism uses the same amount of cereal. b. Discuss if each prism uses the same amount of cereal.

5. What does this tell us about the volumes of the three prisms? Are they the same? 5. What does this tell us about the volumes of the three prisms? Are they the same?
What does this say about the relationship between the perimeter and the volume? If What does this say about the relationship between the perimeter and the volume? If
we took a cross section of this prism, so we had a 2D shape instead of a 3D one, what we took a cross section of this prism, so we had a 2D shape instead of a 3D one, what
would the relationship between its perimeter and area be? would the relationship between its perimeter and area be?

ii. Investigation 2: ii. Investigation 2:
1. Provide worksheet with regular polygons with the same area and have students find 1. Provide worksheet with regular polygons with the same area and have students find
the perimeter using rulers the perimeter using rulers
b. Create ratio of perimeter:area b. Create ratio of perimeter:area

c. As a class discuss what this ratio tells us. c. As a class discuss what this ratio tells us.
i. A ratio is “values comparing,” i.e. comparison between two numbers. i. A ratio is “values comparing,” i.e. comparison between two numbers.

ii. If an animal wanted to make something with the biggest area but smallest perimeter, which ii. If an animal wanted to make something with the biggest area but smallest perimeter, which
shape should it choose? shape should it choose?

iii. Show picture of bee making wax and tell students how its made iii. Show picture of bee making wax and tell students how its made
1. Wax is made from honey (If available, pass around samples of beeswax so students 1. Wax is made from honey (If available, pass around samples of beeswax so students
can see that wax smells sweet like honey) can see that wax smells sweet like honey)
2. It takes almost 10 pounds of honey to make one pound of wax. This makes wax very 2. It takes almost 10 pounds of honey to make one pound of wax. This makes wax very
expensive for bees to make, which is why they want the smallest perimeter to area expensive for bees to make, which is why they want the smallest perimeter to area
ratio when making honeycomb. ratio when making honeycomb.
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