I have this student. He is the perpetual honors kid. He was in a 4/5 combo last year and this year is a 6th grader in my 7th grade honors class. Over winter break he did, well, a million hours of Aleks (or like 75 hours over 9 days which is a lot!). Today I think I had a victory with him. Here’s the thing: My 6th graders were not huge fans of me at the beginning of the year. They assumed honors meant more homework and more grades. When I didn’t do that they were confused. “But Ms. G, you didn’t put that in the gradebook.”

I would always respond the same way, “because I want you to practice and learn. Do you feel like you’ve learned?”

They almost enviably said yes. So it became the way of it. I would read stuff and write comments and give it back with out ever putting anything in the grade book.

Today was amazing. David linked on twitter to some problems from Exeter website. I put this one on the board intending for it to be a Warm Up:

2. How long would it take you to count nonstop to one billion, if you counted by ones? First, write a guess into your notebook. Now try to solve the problem. One approach is to actually do it and have someone time you. There is another way to approach the problem,however. What do you need to know? What assumptions are you making?

I put a timer of ten minutes. Well that was silly we worked the ENTIRE period on it. There was a lot of talk of a billion seconds at the beginning. That turned in to this:

- How long does it take me to count to ten?
- How high can I count in 50 seconds?
- Does it take a different amount of time to count from 232132-232142 then from 1-10?
- Do you count at a constant rate?
- Can you figure it out by digits?
- How did you get shorter than me if you are counting slower? (this was cool*)

So, I made them write in sentences and list an assumptions they had to make. here are some things I got back:

“Some things I assumed today about this assignment was that it would take only weeks and a few days to count but than after doing the math i thought otherwise”

“It would take about 17 years. You need to know how many numbers per second the consitency and how long it takes to say to a number. For example, saying 352,495,021 takes longer than saying 2. I assume that however long it takes to count to 100 is 1 minute. Everytime I add another 100 numbers I would add 10 seconds to the periovous time. so counting 101-200 would take 70 second and 201-300 is 30 seconds. ” -he then ends up with 17 years… (some sketchy math but good thinking.)

” I did hard math.”

“Average of 1,000,000,000 seconds. If you count the amount of time it takes to say each number and times it by the amount of numbers you have you’ll find the amount of time it takes you to count to 1 billion. I can average 2 numbers per second from 1-1099 the about a second from 1100-9999. Then it’ll take longer and loner to say each number so here is the math I am thinking…” – there is a complex chart that follows. this student (due to lazy) has almost failed my class twice. today he said he did more math than he has in the last two years…. compliment? kinda.

Finally, I had the students rate the problem from 1-10… the mean was about 7 as was the mode. I did get one 14 and a -1. So there’s that.

Back to the beginning and my honors student. My victory was this:

He said, “Ms. G are you going to grade this?”

“Do you think I should?”

“Nah you should just read them and tell us what you think”

WINNER

*if you go from days to weeks to months to years you lose a lot of time (about 18-20 days because there are not 28 days in a month. makes a significant difference) better to go 365 days a year.

Your enthusiasm is contagious!

For pi day, I put a million digits of pi on my wall. I got into a discussion about how many sheets of paper a billion digits would take, and how much area that would cover. (We use A4 paper, so it was a nice number). I mostly enjoyed that my students and I feel familiar with and frequently see words like “million” and “billion” but we are typically surprised when presented with how big those numbers really are.

I think counting from 232132-232142 takes longer that 1-10 because there are eleven numbers to say instead of just ten. 😉

I like the student that added ten seconds per hundred for each additional digit. That’s a conjecture of logarithmic growth. It makes me want to time people counting. And I’ve never wanted to do that.