Scenario: Val’s Value from The Math Forum @ Drexel on Vimeo.

]]>The Algebra and Geometry classes at Mathland Hgh School are planning to play a game of Capture the Flag in the woods behind the school. They’ve been discussing how to fairly divide the woods into two territories.

They’ve drawn a map of the woods and added a coordinate plane. The Algebra class will put their base at (-8, 15). The Geometry class will put their base at (4, -3).

]]>I am 3 feet tall.

My dad is 6 feet tall.

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*Punxsutawney Phil and Suzanne with their shadows!*

Besides now having a special pass to use to pay only a dollar for my train commute into Philly, I’ve found myself having more than my normal amount of reflective thoughts. Recently I was thinking about my own Action Research with my students in ’99-’00. I was part of a Math Forum grant project and I was using the ESCOT Problems of the Week (*warning: there’s a lot of link rot within that group of pages but there are also still some interesting ideas/resources*) and I was interested in comparing my students’ standardized test scores from the previous year to their scores from the end of that school year. I remember when I looked up all of their scores from the previous year in anticipation of comparing them later, I noted both their literacy scores and their math scores. And, so, when I had the ’99-’00 scores for comparison I looked at both areas. The math scores were fine but it was the literacy score increases that were dramatic!

There were too many variables in play to only give credit to the problem-solving efforts I was focused on with these students. I was teamed with an excellent language arts teacher (Rick Hartwell) and, perhaps, their gains in literacy could be attributed to his effort … but … I think it was also because he and I used similar strategies and our combined efforts had a great effect.

When Annie introduced this slide into her Sense Making workshop and also used it in a Keynote she and Max delivered (and I know she’s used it in other talks recently, too) it just brought everything into focus!

While Rick was encouraging Strong Readers, I was encouraging Strong Mathematicians and the combination worked to the advantage of our students!

]]>In the wake of the recent tsunami, a company decided to donate to a disaster relief fund. The company started by pledging a certain amount of money.

To encourage their 60 employees to make individual contributions, the company pledge to also donate an additional fixed amount for each employee who made a personal donation to the fund.

The company treasurer determined that if one-third of the employees chose to make a donation, the company’s part of the total donation would be $7000. If 50% of the employees donated, the company’s part of the total donation would be $7750.

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Ethan, Fran, and Gloria have summer jobs at the local Dairy Freeze. They collect their own tips and then share them equally. One week Ethan collected $25 in tips, Fran collected $48, and Gloria collected $41.

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For some time I’ve been thinking about ways to gain minutes in classrooms so that students have more time to talk (and learn). Think-pair-share, turn-and-talk and other partner or group conversations help but invariably there seems to be a need to pull the whole class together for the whole discussion. Once we do that, though, we’re again having the “one person talk” mode — maybe it’s not the teacher doing the talking but it’s still just one voice.

BUT, here is the nugget that was suggested in the discussion post.

“**I’ve started to write down what I hear while I’m monitoring the class during their discussions and project them for all to see. Then students add any other thoughts that were discussed that I didn’t hear.**”

What a brilliant idea!

I responded,

“*As you record those comments and project them, do you find that your students refer to them? Do you still take whole class time to review those comments or might it (maybe with time and practice and suggestion) not need to be discussed as a whole? *”

Her response was,

“*I am noticing that as I post things and continue to monitor, others will say that they have the same thing. It actually seems to be encouraging discussion in groups and may be adding other ideas to continue their group discussions. I am not spending as much time on whole group discussion when I use this format.*”

I’m sure there are still moments where a whole class discussion is a good idea but this idea of projecting a compilation of ideas generated by the variety of pair/group discussants is a powerful idea!

If you try it or have already used this technique, we’d love to hear your stories!

]]>A regular hexagon and an equilateral triangle have the same perimeter.

]]>Did you know that there is a famous illusion associated with Lincoln’s “stove pipe” hat? The hat looks like it’s taller than it is wide, even when the height and width (including the brim) are the same. Let’s make a hat:

- Cut a circle with a radius of 5 1/2 inches.
- Cut a circle from the center of the first circle with a radius of 3 1/2 inches.

The smaller circle will form the tip of the hat, and what’s left of the larger circle will form the hat brim. If we had a rectangular sheet of paper of the right size, we could make the cylindrical part of the top hat.

]]>Mia drew a shape with exactly 4 sides.

It has 4 lines of symmetry.

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