My (binary) family tree
July 5th, 2009This is a sketch for an Early Algebra activity from Math Clubs. Kids can draw their own family trees, use photographs, or clipart of their favorite characters.
Once the tree is built, it can be used for several activities. Start from common words, gradually moving to mathematical terms:
- How many grandparents are there? (point to the “grandparent” level on the tree). What about great-grandparents?
- We have one child, and we have two parents in the first generation from the child, and four grandparents in the second generation, and eight great-grandparents in the third generation… How many people are in the fourth generation? Fifth? How do you know?
- Mathematicians use the term “power” here. For example, we can say “grandparents” or “the second generation from the child” or “two to the second power.” Two to the first power (parents) is two. Two to the second power (grandparents) is eight. What is two to the third power? There is a symbol for it:
23=8
- What generation has eight people? What power of two makes sixteen?
Figuring out which generation each quantity means is a lot like logarithms.
We can say, “What generation has sixteen people?” or we can write:
log216=4 - Add up all generations up to a certain level, say, “grandparents”. Compare to the number in the next level. What do you observe? Is it always the case?
