Sunday, September 28, 2008

Homework That ROCKS!

The homework shown above (you can click on each image and it will enlarge) really shows what we are looking for in terms of effort in and out of the classroom!
The first thing that I notice is that ALL of the work is completed on separate paper. Bigger space means more ability to think outside of the tiny "box" provided on the page itself, and this is not optional. All students should be completing work on separate paper.
The second thing that I look for is work that was revised, enhanced, or merely recorded during our class review sessions. These sessions take about 20 minutes, and they are only valuable if the strategies shown are recorded. Again, this is not an option. Even if you had the same answer, you can record alternative strategies.
The last thing that I noticed was the level of detail in the review work. This student was so focused on our discussion that she recorded her answer in the same "surfer voice" that I was using during our review ("The length of Mrs. Phillip's porch is totally like 16 feet!") .
This work is totally rad and awesome! WORD!
Mr. R.
AKA T-Cubed
I should have mentioned that leaving a reply is pretty easy. All you have to do is click on the "comments" tab, type your reply (please don't use your name if you are a student), and then click on "anonymous" before you hit "publish". The post will come to me, and if it is appropriate, I will post it to the page.

Monday, September 22, 2008

Beijing Olympic Subtraction Example: Cool!

Take a look at this work from our Beijing Olympic Subtraction problem, and see if you are on the right track.

The work shown is very well constructed and efficient.

Please let me know what you think:-}

Sunday, September 21, 2008

Splitting Up Work Makes Life Easy!

I wish that I could make this uploaded work a bit more clear, but it still is great to emphasise my point.

This work comes from our last Mini-Quiz, and it is a great example of how organizing your work in a very simple way can lead to a great outcome. K did an amazingly simple but powerful thing when she drew lines to separate her problems. She made it easier for her brain to focus on the tasks individually. Separate spaces for separate thoughts. Simple but very important.

I also noticed something else really cool. K did not use ultra-small writing. While I like saving trees as much as the next teacher, I know that simply writing bigger and using more space often creates better results.

I also love love love love love love the expanded notation in the addition problem, the open number line in the subtraction problem, the generic rectangle in the multiplication problem, and the misconception corrected in the division problem. This work ROCKS!!!!!!

Monday, September 1, 2008

What is subtraction anyway? Difference or...?

We will be starting our investigations in the area of number sense tomorrow, and our unit starts with a look at subtraction. You know, where you find the difference between two numbers.

What if I changed that to read "find the distance between two numbers"? Does that sound any easier?

Here's my point: If I ask a kid to subtract 95 from 100, I hate to see the kids that are driven by traditional thinking as they line up their numbers in columns and subtract to find the distance. Wouldn't it be easier to just think about how far it is from 95 to 100? You can use an open number line if you wish as well, for all of you visual learners out there. Hopefully, you'll just think about the distance and know that the distance is five.

Many teachers that I talk to say "That's great for easy small numbers, but I don't want my kids to rely on that for bigger numbers!" I think that you might want to rethink that stance if you've taken it already.

Using an open number line or "counting up" works well with any numbers, and it prepares kids to make estimates far better than traditional thinking. We all know that "in the real world" folks will use calculators to deal with big numbers anyway. So why not build some audacious number sense now.

$1,000,000 - $257, 665 can be solved as follows:

257,665 +35 = 257,700 +300 =258,000 +2,000 = 260,000 +40,000 = 300,000 +700,000=

Bingo 1,000,000

So, if I add the numbers in bold that I "added on" I get a sum of $742,335 which is the distance between the two numbers. The beauty is that I did it in my head for the most part:-} Another beautiful thing is that there are an infinite number of ways to "add on". Kids choose the number combinations that they like. I would, of course, make sure to lead them into using landmark numbers (usually numbers that end in 0, 00, 000...) as targets to add up to.

Peace, and try it...

T-Cubed P.S. Do you know the man in the picture?