Saturday SAVY, Week 2, Secrets of the MoLi Stone (3rd-4th)
Hello SAVY Families,
We had another great day of Fall SAVY 2024: Secrets of the MoliStone. I was once again impressed by the SAVY Mathematician’s hard work and commitment to developing their knowledge of mathematics.
We started the day by reviewing our knowledge from last week including the generalizations of systems, place value, and the system we are most familiar with–the base ten system. While students are familiar with and fluent in the base ten system, we took the time today to talk through and externalize the number sense needed to understand what is happening when we “make groups of ten,” what each digit means, and what we are actually doing when we “borrow to subtract.” All of these concepts are encountered daily in a typical mathematics classroom, but it is not always easy to explain what is happening within each number. This knowledge was important to understand in order to transfer it to less familiar systems: the binary, or base two, system, and the base three system.
For our introduction to an unfamiliar system, we watched a video about a “two-to-one machine.” This machine showed a visual representation of the base two system and how to represent numbers within the base two system. After watching the video for a few minutes, students noted patterns in order to determine the code for what a given number would be in the base two system. We continued by demonstrating how we could use our fingers to count to 31 in the base two system and learning about how and why computers use the base two system. Finally, we defined what the word “base” actually means. While we hear “base ten” all of the time, the SAVY mathematicians were faced with a challenge in actually defining the word. We ultimately defined the word base as “how many are needed to make a group in a new place value.”
Next, our class moved to the “Land of Treble.” Here, we learned that everything came in a set of three, even the bases. Through a series of games, the SAVY mathematicians learned how to add, subtract, and manipulate numbers in the base three system. We used game pieces known as gickles (1), bickles (3), rickles (9), and trickles (27) to represent numbers and play math games in base three. This was definitely a highlight of the SAVY mathematician’s day. We ended this activity by having a debate on whether we should continue working in the standard base ten system, or if it would be beneficial to move to a base three system. Ask your SAVY mathematician what they think, and why? Finally, the SAVY mathematicians took a brain break in which they designed a pet shop where all of the prices were listed in base three prices.
The final numeration system we learned about today was the Egyptian hieroglyphic system. We learned about hieroglyphs last week, but only in the context of letters and words. This prompted a discussion about the importance of symbols and the symbols that we see every day. Then, we learned about the seven symbols that the Ancient Egyptians used to create numbers. We practiced writing, adding, and subtracting Egyptian numerals and debated how best to represent larger numbers such as one billion or one trillion. Finally, we noted that the Egyptian numeral system lacks a number zero. We talked about the pros and cons of this and ended the day with a fun activity: creating a “WANTED” poster to bring back the number zero. The SAVY mathematicians had fun creating reasoning to bring back the number zero. As always, we related all of our learning back to our generalizations of systems.
Discussion Questions:
- What is a “base?” What is the base two system? What is the base three system?
- Do you think we should remain in base ten, or should we transition to base two or three? Why?
- What are the pros of the Egyptian numeration system?
- How did today’s activities connect to our generalizations of systems?
I hope the mathematicians have a great week, and I am looking forward to working with them for one final day at SAVY Fall 2024.
Sincerely,
Ms. Anna Gruchot