## Tuesday, January 26, 2016

### What I'm Looking For

Last year Jo Boaler's multiplication task How Close to 100? caught my eye. I decided to bring it to our grade 3 teachers, and it quickly found its way into the rotation.

 Roll two dice.  Use the numbers as factors and generate corresponding rectangular arrays.  Place them on a 10 x 10 grid, and see how close you can get to filling it up.  I liked color coordinating the equation with the array.  Colored pencils worked best.

Although designed to build fluency with basic multiplication facts, we found the activity had other benefits.  In order to maximize your chances of filling up the grid, rectangles needed to be placed strategically.  Also, in order to calculate your final "score", you needed to do some computation.

 Students experimented with different computation strategies, from adding up all their products to subtracting the total number of blank squares from 100.

The activity provided inspiration for a number talk:

And when we experimented with a 20 by 20 grid, and dice that would generate higher factors, things got a bit more difficult...

And a little messier...

We also challenged the kids to find different ways fill up the grid using exactly 10 rolls:

The rectangles came in quite handy when we got to studying area and perimeter:

 There's really no escape from the scissors.
 We had them cut out the rectangles, find their perimeters and areas...
 ...and sort them based on their relationship.

I'm often asked, "What do you look for when choosing a game or activity to bring to a class?"  Once it passes through the first, most important test of might a kid who doesn't like math find  this engaging, I look for its potential to be extended or repurposed.  There's something about the idea of  becoming familiar with the way something works, then using that familiarity to build on or connect to something different, that appeals to my sense of how we grow and learn.  How Close to 100? is a good example of an activity that checked off those boxes.

1. I absolutely agree with your criteria for a good mathematics game, Joe, and you have shared some really great ones with us. It's great to have a game that you can then recommend to other year groups to play in a modified version; that the students might see again and build on.

1. Thanks Simon. I agree with you regarding games that can move vertically through grade levels as they increase in complexity. They're not always easy to find! I need to work more on this one and see what else can be done with it. Maybe something with decimals?

2. I really like how you have extended this game and I also like your criteria. Building this out, e.g., elaborating on the conversations/teacher moves involved, would make a great chapter in a book. Does that kind of writing interest you?

1. Thanks Linda! I appreciate your words of encouragement.

3. The fourth graders I'm working with loved the game. It was interesting to observe who had keen spatial sense for placing and who didn't. I'm interested to see what happens with more experience. Thanks.

1. Thanks for the comment Marilyn. I agree that the spatial component adds a very interesting layer. I believe it's the reason why some kids who are normally averse to anything resembling fact practice are eager to play this game.

4. I have to admit, comparing perimeter to area as in the last picture makes me uneasy, because the units are different. For example, I'm sitting at a table that is 2m x 1m. Is the perimeter larger or smaller than the area? In meters and sq meters, the perimeter is 6 meters, the area is 2 sq m, so I guess you could say P > A. In centimeters, the perimeter is 600 cm, the area is 20,000 sq cm, so maybe P < A?

For your rectangle packing activity, you can easily make this into a competitive game, if that's your style. We were introduced to it under the name Block Blobs.

5. As for comparing perimeter to area, I agree with you. In fact the very same issue had bothered me as well. In our Everyday Math curriculum the kids play a game where they are directed to find either the area or perimeter of a rectangle and accumulate points based on those values. On some plays you get to choose which to find, and on other plays you get to choose what your opponent finds. There is even a question on an assessment based on the game, the point being that the student needs to calculate both and determine which is to their advantage. Not that it makes it OK...
Thanks for directing me to Block Bobs. Looks good!

6. Hello! This post was recommended for The Best of the Math Teacher Blogs 2016: a collection of people's favorite blog posts of the year. We would like to publish an edited volume of the posts at the end of the year and use the money raised toward a scholarship for TMC. Please let us know by responding via http://goo.gl/forms/LLURZ4GOsQ whether or not you grant us permission to include your post. Thank you, Tina and Lani.