Multiply Like an Egyptian

As we get to this point in the school year, I have more and more students who are achieving standards and are ready for a challenge.  Of course, I also have students who need intervention and much more support to get the big ideas they need to be successful in the next grade.  Because of this, I do more and more groupings as the year goes on.  I write about ideas for interventions all the time but I also think about the kids on the other end and how to keep them engaged when they are understanding all they are supposed to be learning.

I have turned to several books to challenge students and get them excited about math.  Math Detectives is one I wrote about several months ago that I use to challenge K-3 students.  Cool Math is another one I have written about that I use to challenge students in grades 3-6.

Today I want to share with you a new favorite book and a lesson I did with a group of students based on one of the ideas in the book.

Go Figure!: A Totally Cool Book About Numbers

Near the beginning of the book, there is a history of some of the ways numbers have been written in the past.  If you know any Egyptian or mathematical history,  you know the Egyptian numbers were quite complicated and required quite a few symbols to write each number.  

Because of this, multiplication was challenging for the Egyptians so they developed this great strategy for multi-digit multiplication based on the idea of doubling.  I showed their strategy to my students and they worked together to see if it always seems to work and to figure out why it works. 

Check out some of the problems

Look at the number on the left.  Start with the number 1 and double it until you get to the point where the next doubling would be bigger than the number on the left.  Take the number on the right and double it just as many times as you doubled on the left.  Find the numbers in the left hand column that add up to the number on the top left.  Cross out any numbers you did not use and the numbers across from them.  Add up the numbers left on the right.  

 Here is another one

This one made for easy doubling and easy addition!

Now that they had the process down, we started thinking about why it works

Here kids made the connection that the 188 across from the 4 represented 4 groups of 188.  The 752 across from the 16 represents 16 groups of 47.  

Now they pull it all together

Here is where students REALLY got what was happening and were able to write it out and talk about how it represented the distributive property.  I also had a student who was able to show how it connected to using an array.  

This lesson led to a great discussion about multiple strategies for multi-digit multiplication and how some strategies are more efficient than others and how the numbers in the problem change the efficiency of some strategies.  

How do you challenge kids who are ready for it? 

Looking for a great book on teaching multiplication?  Check out this post!

Here is a fun way to practice double digit multiplication.