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How Many Monarchs in This Forty-acre Field?

Information we had to start with:

  • The field is 40 acres.
  • The monarchs are 8 feet apart.

Information we needed to look up:

  • One acre is 43,560 square feet
The steps we took to solve the problem:
  • We began with some graph paper so we could draw a picture and see the situation.
  • We knew there was one butterfly every 8 feet. We decided to let the length of each square represent one foot. We spaced the butterflies 8 squares apart.
  • Notice that there must be 8 feet between the butterflies in all directions. Here's our graph paper so you can see the spacing between the butterflies. (Click to enlarge.)
  • Because there are 8 feet between each butterfly, each butterfly is surrounded by 64 units (square feet) of space. In other words, there is only one butterfly for every 64 square feet.
  • You can click on the graph to count the 64 units (or "square feet") of space surrounding each butterfly.
  • We divided the 43,560 square feet in an acre by the 64 square feet needed for each butterfly and found there were 680 butterflies per acre. (43,560/64 = 680)
  • The field is 40 acres, so there are 27,200 butterflies in the 40-acre field!

More About Monarchs and Alfalfa
The 40 acres of alfalfa pictured above is a magnet for hungry butterflies. The monarchs are looking for nectar and alfalfa flowers are a good source.

When the monarchs travel through the Midwestern states they are surrounded by corn and soybean fields. In fact, as much as 90% of the land is now planted with crops where there was once prairie.

Only lucky monarchs find alfalfa in bloom. Farmers usually cut alfalfa before it turns to flowers. This is because farmers grow alfalfa for hay to feed their milk cows. The food value of the hay goes down when it's allowed to flower. (The plants use energy to make the flowers.)

Imagine you're a butterfly looking for flowers the next time you travel. What does the landscape look like to you? Can you find flowers easily?

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