Egyptian Multiplication: Looking to the Past While Learning Forward
I am always looking for opportunities to make the math we’re studying more inclusive of cultures that are often overlooked in a more traditional American math curriculum. It’s important for students to know that math wasn’t invented in one place at one time, but rather, it was developed over time with contributions from many cultures all over the world. Mathematics is always developing and mathematicians are always looking to the past to better understand the discoveries they are seeking to make today.
The humanities curriculum in fifth grade includes an in-depth study of ancient Kemet (Egypt), so students are learning how to do research from primary source materials. Our current understanding of the way Egyptians used mathematics is largely thanks to the preservation of the Rhind Papyrus, the ultimate primary source document. Learning how Egyptians multiplied helps students understand that the algorithm we use today is only one of many ways of accomplishing the same goal. In addition, my father was born and raised in Egypt, so this was a great opportunity for me to share more parts of my own identity and build relationships with my students on a more personal level. It’s also a perfect opportunity to show them a picture of myself at their age riding a camel in front of the Sphinx.
While I was familiar with the Rhind Papyrus and the explanation of Egyptian fractions from a unit I taught many years ago, I had to do a little bit of research to find out the way they calculated multiplication. The students will also do a project about Egyptian fractions later in the year that will build on this introductory unit. I used a documentary made by the BBC called “The Story of Maths,” to better understand the method and then introduced it to the students with some additional scaffolding.
Prior to learning about Egyptian multiplication, students did an extensive exploration of several methods for multiplication calculation, including a place value area model, an extended algorithm and a traditional algorithm. They also studied number systems with different bases to further deepen their understanding of our base ten place value system. During “Big Time”, a long block of an hour and a half, students watched portions of the BBC video and discussed the ways Egyptians used their bodies to make measurements and the reasons that agriculture and taxation required calculations of area.
Then we shifted the focus to the Egyptians' method for multiplication. Students were asked to create a sample problem to show their understanding of the Egyptian multiplication method and to create a format to share their learning with the class. Some students created problem sets and companion worksheets while others created posters and presentations. Students were engaged and seemed to have a lot of fun. A few students mentioned the Egyptian multiplication lesson in their end of trimester self-reflection about their experience in math class. One student wrote, “The thing I enjoyed the most was Egyptian Multiplication. I enjoyed Egyptian Multiplication because it was fun to make the posters and it was cool to teach my family how to do it.” Another wrote, “The thing I found challenging this year in math was the Big Time about Egyptian multiplication. I found Egyptian multiplication challenging because in the example that you showed us the person was using the black and white disks that were representing the two sides, which was kind of confusing. But then when one of my classmates showed it, I understood it more. Now I can teach other people how to do Egyptian multiplication. Also Egyptian multiplication was my favorite unit because everyone in the grade didn’t know how to do it, so everyone was at the same starting spot. This helps me because no one knows more or less than you so it feels more equal that we are learning together.”
As the students are now deep into their humanities unit about ancient Kemet, I’m looking forward to doing another “Big Time” where students can learn how Egyptians used unit fractions to create non-unit fractions. Students will learn how to write any fraction as a sum of distinct unit fractions and the possible reasons the Egyptians chose to express them in that way. Framing our math inquiry with this historical lens not only draws students into the many varied ways that humans have developed and used math to tell the story of their experience, but also invites them to consider the relevance of math in our own lives and times. In this way, math becomes something more than the memorization of an algorithm and the corresponding computational processes; it becomes an invitation to critical and creative thinking in the context of solving authentic problems.