Over April school vacation, we traveled to visit family. This was special for many reasons, not the least of which is that we have a relatively small family. (Catch the pun there? Ha!) The children no longer have grandparents from my husband’s side, and the uncle we were visiting does not have grandchildren. I was thinking about how nice it was to fill some of those empty spaces for each other, when it occurred to me that my kids had never seen a family tree. For family history and connection alone it is worth making a family tree with your kids, but, of course, I had to make it mathy.

I took out a piece of graph paper (just to make it mathy-er.) On it, I outlined one square at the bottom of the page and I told my 8-year-old that the square was him. Then I drew two lines coming out of the square connecting to two more squares that I outlined. That’s me, I told him. That’s your dad. Then I drew lines from each of our squares connecting to my parents and to his father’s parents. Then I handed the marker to the kid.

“Draw the next ones.”

He did.

Then we counted up how many people were at each generation.

“Mom, what’s a generation?”

Ah. Good question. So he learned what a generation is, then counted the number of people in each. 1, 2, 4, 8. (To make this activity work for what I was intending, we only drew in parents. No siblings or second marriages and such.)

“How many ancestors will there be in the next generation, kid?”

“What’s an ancestor?”

After learning what an ancestor is, he delivered the answer: 16. Then 32. He then busted out with the observation that each generation doubles as it heads back in time.

Now, if you’ve been reading my posts, you know my 8-year-old digs math. He likes to notice things and find patterns. So, he was excited to think about what the numbers would be at each level. If your child is not as interested or excited, or if your child is younger or doesn’t yet have the skills to notice the pattern or add/multiply the numbers…IT IS OKAY. This is about exposure. This isn’t a quiz. And it sure as heck isn’t a comparison or a competition. You are planting seeds of thought. Refer back to this previous post for a little bit more on that. It may be that though your child doesn’t seem interested in the growth of the family tree, they will have its image planted in their minds. Then later, when they see something similar, there will be a little bit of a foundation for understanding already laid. (Or roots already developed, if I’m to stick with my metaphor.)

Since the 8-year-old still seemed interested in what we were doing, I asked him another question.

“How many ancestors will you have at the 10th generation back?”

Whoa. There was no way we were going to draw our way to that level. That’s a lot of squares. At this point I decided I would lose his attention if I tried to coach him to figuring this out on his own. So I quickly showed him how each of the numbers he observed at each level could be found by repeatedly multiplying by 2 (which was connected to his observation that each generation doubles.)

2 = 2

4 = 2 x 2

8 = 2 x 2 x 2

16 = 2 x 2 x 2 x 2

and so on.

If we want to know the 10th generation, we multiply 2 repeatedly 10 times. Which is also a lot of work. But doable. And also worth pulling out a calculator for. Yes, I could have demonstrated how to use the exponent function on the calculator, but it seemed more appropriate and more valuable to simply multiply 2 by itself 10 times the long way. Eventually, the kid will get tired of the repeated button pressing and be ready to learn about calculating exponents. Just planting seeds…not trying to grow his “tree” too fast.

The answer, by the way, is 1,024. His eyes grew wide. I wanted to see them grow wider, so I showed him how easily we could figure out the 11th generation…and how huge that number was comparatively. Then we went off on a tangent, talking about how there must be overlap in ancestors (maybe with friends!) and this is one way to illustrate how we are all interconnected.

Below is the sheet of paper on which we did most of this activity. It looks awfully mathy, doesn’t it? If you or your kid is feeling less mathy, just do something like the teal colored parent tree we drew. Then start counting the number of people at each level. Then just let your kid lead you with their own questions and curiosity.

Next time, I’ll put the mathy part aside and focus on our actual family tree with all its unique branches!

(Mathematically…this is all about exponents and exponential growth. I do not recall where I read it, but supposedly toddlers more naturally grasp exponential concepts than they do linear concepts. That shifts as they are very purposely taught to count 1, 2, 3, etc. I’ll try to find that article so it doesn’t sound like I am making that up! Regardless, this activity plants the visual concept of FAST growth, or exponential growth. It is accessible for all kids in that anyone can begin drawing the picture of a family tree. How far and in what direction you take it depends on your kid.)

Feature Photo credit: AJC1 via Visual Hunt / CC BY-SA