Quantifying Large Numbers

I was having an interesting discussion with a few teachers about getting students to understand the value of large numbers. At 3rd grade, any number beyond 4 digits becomes an exercise in abstract art. They have tens, hundreds, and thousands pretty well, but really haven't had a lot of experience with more and unless you can count it, even by 100,000's, you really can't quantify it. 

I began to think about my own experiences with this. My family played a lot of board games when we were youngsters and one I remember vividly was called "Masterpiece". It was a game that involved selling and buying famous paintings. There would be auctions where you could purchase paintings, hoping to secure the one worth $1,000,000. Some were worth as little as $150,000, some more. The money came in denominations of $50,000/$100,000/$500,00 and $1,000,000. We had to make change and I think this is where I became familiar with 5 and 6-digit numbers-easily, without thinking about it. 

Many fond memories of buying and selling famous paintings

It was that great juxtaposition where math meets necessity. It is what we try to give children in the classroom. Effortlessly using math to do, to create, to solve, to communicate, to advance. 

Not only did I gain experience with large numbers, but who can forget Edward Hopper's Night Hawks, Edgar Degas' The Dance Class, or Grant Wood's American Gothic?

Busy Summer

Towards the end of every school year I can't help but think I am going to have a whole summer off to relax and play and just live day-to-day. Summer reading, flip-flops. Sounds heavenly - right? 


It just doesn't always happen like that. This summer is going to be my busiest math summer yet!

So a question for you - what do M&M's, paint, aquariums and cubes all have in common? These are the items that will be a part of our 3-act movies that my colleague and I are creating for elementary students. We love the Dan Meyer ideas floating out there for getting kids to problem solve odd and quirky "situations". We want to get something out there for elementary folks so they can push the mathematical practices. Along with this task, I am looking at creating some type of assessment for mathematical practices. There's not a lot out there so if you have any suggestions I would be happy to take them!

Washington State is trying to get their digital library up and running and are asking me to review items like crazy. Lots of good things going in there so be sure to take advantage. 

As always, writing math curriculum. I keep thinking to myself, what do teachers need? Since I visit Kindy through 5th grade on a daily basis throughout the school year, I have tons of ideas. 

We will be posting the video clips as soon as we have a few ready to go. Stay tuned......

Estimation Guesstamation

The 1st grade teacher held up a 1" by 1" (approx) linking cube in front of her class. She told her students that they were going to be measuring some things in the classroom. They got very excited. They were going to use the blocks to measure things - including the height of someone in their group. The excited chatter began.
"Lets start by estimating what Tommy's height is using cubes." Silence
"How tall do you think Tommy is?" Silence
"How many cubes do you think it will take to go from his toes to the top of his head?"

One student pipes up, "You mean like a guess?"
The teacher smiled. "Yes! A best guess."

Estimation
What are we really asking students to do with estimation? Are there different types of estimation that are used in different scenarios?

A primary student may think "best guess" is a random guess based only on an immediate number that comes to mind. When we begin to use strategies to make accurate estimations, students come up with amazing ideas.

• Put ten together and see about how many sticks of ten it will take
• Pretend you are holding a cube between your fingers and "walk" your hands up the side of the person
• Divide the person into "sections" and figure out how many tall the head, the leg, the arm is.

Why should we have students estimate? 

Primary students are still working on the idea of quantity, or the "largeness" of a number. More experiences with quantity will help them understand the magnitude of numbers. So, going back to compare their original estimate with the exact amount helps with this. 

Our elementary students often use estimation for reasonableness. The answer to 589 + 204 should be about 800.

A great resource for getting students to practice estimating is   ESTIMATION 180   This site has 180 days worth of quick estimating activities with pics.

So how many cubes would it take to measure the height of an average 1st grader? (About 60)