King Euler’s Blueprint
Hector says to Larissa, “If you give me $2, we will have an equal amount of money.” Larissa responds, “That’s true, but on the other hand if you give me $2, I will have twice as much money as you.”
Scattered around the house are 100 nuts in 5 bowls.
After Tom’s mother drops Tom off at school, she has to stop at the drug store, the supermarket, and the post office before heading home.
Those lazy, hazy days of summer are just starting in the Northern Hemisphere! Don’t you look forward to doing what Lee is doing in this free scenario? (What is he doing, anyway?) What do you notice in the story below? What are you wondering about? Leave a comment to tell us your thoughts!
Specialist Lee Alejandre, who is 6 feet tall, had leave time from the Army, some of which he spent basking in the sun at Swarthmore College in a couple of different chairs:
|dimension||larger chair||smaller chair|
|width of seat||57 3/4″||21″|
|length of arm||80″||29 1/2″|
|front leg||26 1/8″||9 1/2″|
The Supreme Court of the United States is the highest court in the country. It consists of a Chief Justice and eight Associate Justices.
The Court begins each term on the first Monday in October. Suppose that on that first day, each Justice greets every other Justice by shaking hands exactly once.
A closed rectangular box whose dimensions are 8 feet by 5 feet by 3 feet has 5 feet of water in it.
We talk a lot about the problem-solving process here at the Math Forum and try to develop resources that will help teachers help their students get better at problem solving. We discuss how to encourage students to share their thinking (such as through Noticing and Wondering) and how to cultivate classrooms that value those thoughts and ideas as much as answers. But if we take a look at our own “problem solving” product, the Problems of the Week, we have to acknowledge that there isn’t so much support for process, starting with the “Compose Answer” button that appears at the bottom of each problem. Oops!
We have considered a number of possibilities, including an option (chosen by the teacher) to show just the scenario for a problem and then have fields in which students can submit their Noticings and Wonderings. That sort of thing would require some significant programming time, so while we are working on putting it in place (I’ll blog about it more before we get too far), we are first going to support the PoW process through some wording changes in the submission process. We’ve come up with some possibilities and wonder if anyone has alternative ideas.
On a problem page, it says, “Compose Answer”, which of course implies you have “an answer”. We’re thinking of changing that to “Submit Ideas”, which seems a bit more welcoming to submissions that might not actually contain an answer yet (or ever).
Once you get to the “submission” page, there are four spots we’re suggesting alternative wording:
What do you think? Would these sorts of changes convey “process” to your students? Do you have any other suggestions?
During the February 26th MoMath Masters Tournament, @MoMath1 tweeted, “No googling – how many sides on an enneagon?” We thought, “Hey! We know enneagons!” If you don’t, maybe this scenario from a problem we first used in 1998 will give you some hints (as well as some ideas for something you could do with one).
Extend the sides AB and ED of the regular enneagon ABCDEFGHI until they intersect.