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Egyptian Fractions (Investigation)

Lesson

Imagine that you're an ancient Egyptian, living around the time of 1650 BCE.  You're taking inventory of your pantry for tonight's meal.  Some of your food is partially used.  For example, you only have $\frac{2}{3}$23 of a fish.  

You need to write down the quantity of everything.  The trouble?  The fraction $\frac{2}{3}$23doesn't exist in your language.  You only know how to represent fractions like $\frac{1}{2}$12, $\frac{1}{3}$13, $\frac{1}{4}$14, $\frac{1}{5}$15, etc (we call these unit fractions). How will you write down the partial quantities in your pantry using only unit fractions?

Your Objective

  • With a partner or on your own, create an inventory scroll of $10$10 items in your pantry.
  • Use unit fractions to represent the quantity of each item.
  • Finally, present your scrolls in a class "museum" exhibit, where you interpret the ancient scrolls your classmates have made.

Materials

  • Paper, markers, colored pencils
  • Printed out fraction circles or other fraction manipulatives
  • Scissors

Create Your List

  1. Determine the $10$10 items that will be in your pantry.  If you like, you can research popular Egyptian food items on the internet to be more authentic.
  2. For each item on your list, determine the quantity you have available in your pantry.  Be sure the quantity meets the following criteria:
    • Each item must be partially used, so your quantity will be a fraction of the whole.
    • The quantity must be a fraction that is not a unit fraction.
    • Take note of the type of container or unit that each item would be measured in.  For example, your pantry could have $\frac{5}{7}$57 of a bag of wheat, $\frac{2}{3}$23 of a jar of honey, and $\frac{4}{5}$45 of a bar of gold (for trading later).

Represent in Unit Fractions

This is where you might want to use your fraction circles to help!

  1. Rewrite the fractions on your list in terms of unit fractions like the Egyptians would have done. For example, instead of writing $\frac{3}{8}$38, an Egyptian would have to write $\frac{1}{8}+\frac{1}{4}$18+14.
  2. Try and write the fractions with as few terms as possible (writing $\frac{1}{8}+\frac{1}{4}$18+14 takes fewer terms than $\frac{1}{8}+\frac{1}{8}+\frac{1}{8}$18+18+18).  Extra challenges: Represent fractions as the subtraction of two unit fractions or try using less common quantities like $\frac{11}{17}$1117.
  3. Once you've checked your maths, create a papyrus scroll to display your list as an artefact in the class museum.

 

Follow-Up Questions

1. Find a classmate with the same item as you in their pantry.  Compare the two amounts.  Who has more?   Explain how you found out.  

2. Which group had the most interesting quantity of something?  Why was it interesting to you?

3. What are some things you learned from this activity?

4. If you could go back and speak to an Egyptian from 1650 BCE, what would you tell them about fractions today?  How could you be sure they understood you?

Extension

Do some research on the Rhind papyrus.  In what other ways did the Egyptians represent numbers that are different to how we represent numbers today?

 

Fraction Circles

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