Here’s another number riddle for you to try. Post your answers with some explanation or proof for your answer.
1) The number is between 15 and 50.
2) The number is prime.
3) If you multiply the tens digit by 9 and add 4 you get the number itself.
Now it’s your turn to write a number riddle. You can post it here by commenting on this post. Remember there are some rules for these riddles.
At least 3 clues
Each clue contains some number theory vocabulary
No one clue can give the whole riddle away
No redundant clues (extra, unnecessary)
One and only one possible answer
This is the first problem of the year. Remember, when you comment on this problem you can’t give away the solution. Just write about your solution strategy or give some hints on how to get started for a student who may be having trouble. Dont’ give the answer!!!!
Mid-August is the time when many students are starting back to school or anticipating the start of school. Jansen’s school year begins in a couple of weeks. He figures that he has 13 more days to finish his summer reading books. When he had 18 days left to finish his reading, he figured that he needed to read an average of 23 pages per day. If he hasn’t read any pages since then, how many pages per day must he read now to finish the reading? Express your answer to the nearest whole number.
From: “Problem of the Week Archive.” MathCounts. 21 Jul 2006 .
I can see how the Web 2.0 tools are so much more interactive than what we’ve been doing. I’m excited about using the blogs with my classes to get my students to do more writing about their mathematical reasoning. Some of the things that I’m thinking of are having a class scribe to record daily notes on the class blog. That would be useful to all my students and particularly to anyone who’s been absent that day. I’m also thinking of posting a weekly problem that students will need to repond to. In the beginning it will be difficult for them to comment on the problem without giving away the whole solution, but they will get better at that. I’ll want them to concentrate on problem solving strategies, not on final answers.
Podcasting is another exciting application to explore. While many students already do slide shows or movies for presentations, a podcast would be different. Without the ability to have anything visual, students would have to work hard to be clear communicators using just speech. That would be hard in math, but worth trying.
This course has been great. I came in here on Monday thinking that I was pretty up on whatever technology was being used in schools today. I didn’t expect that I would learn many new things. It didn’t take long to discover how wrong I was. The first 3 things that we did, blogs, bloglines and del.icio.us accounts were all new to me and that was just Monday morning! Today, when we did iPhoto, was the first time that we did something that I would consider myself fairly proficient at.
My main difficulty has been trying to sit and work at something for such a long period of time. I guess that I’m in summer mode that way, but even during the school year, I rarely sit at my desk for very long. It’s been tough to spend so much time at the computer. Wednesday afternoon I was having a real hard time concentrating.
The only suggestion that I might make is to take a look at the course description that the PDC is publishing for this course. There is quite a range of experience in the class, and while that’s been fine, I know that some people were expecting a more basic “Using a mac computer” class based on the course description. I think it’s worked out fine, and I know that we’ve all learned lots. I know I have.
As I was reading this article (Executive Summary) I found myself wondering how my own children would have answered the questions and what their media diaries might have shown regarding their media habits. I’m sure their media habits are very typical with the exception of having cable tv and computers in their bedrooms. We never allowed that (so they probably just played video games there instead). My own media habits are also pretty much the same as the average teenager. I still watch about the same amount of tv as always, but we almost always record shows first to watch later sans commercials. I also almost always multi-task during tv watching, particularly if I’m watching in real time.
I also found myself reflecting on the amount of energy (electricity) being consumed with all these electronic devices running all the time. I recently read an article about the amount of energy that could be saved if we all unplugged our televisions and computers when we weren’t using them. It was considerable, but maybe we could start by simply turning them off once in a while! Generation M will have to solve the energy problem worldwide in order to continue their media habits!
This morning we learned about podcasting and audio emailing. I found a few math podcasts in the itunes store from a site called math grad. Listening to a few of them I found them to be engaging and mathematically accurate. I’d like my students to listen to and comment on some of the podcasts before trying their own. This could certainly be a new way for students to share their learning and in doing so reinforce that learning.
Right now I’m thinking that I would like to do something with podcasting in my math classes. I teach a sixth grade GT math class, two seventh grade pre-algebra classes and two eighth grade algebra one classes. I have the most freedom with my sixth graders so I will probably start with them. Our sixth graders will have laptops this year which is new.
I may start by having students listen to a few math podcasts that I’ve found through itunes. We’ll discuss them (maybe using my blog) and try to figure out what elements make them effective. The students could then take a topic from whatever we’re currently studying to make podcasts of their own.
It seems to me that the art or skill of critical thinking will become increasingly important for students to acquire. Part of the definition of critical thinking involves “analyzing, synthesizing, and/or evaluating information gathered from, or generated by, observation, experience, reflection, reasoning, or communication, as a guide to belief and action.” In the 21st century that information will be gathered from a plethora of sources unimaginable only a few years ago. While students have always needed to be careful regarding their choice of sources when doing research, today’s students must learn to distinguish what is valid information and what is bogus. They will need to learn how to tell fact from opinion disguised as fact.
There were several things that I liked about this article. First was the emphasis on the teacher’s role in student’s acquisition of critical thinking skills. The author makes it clear that students will not learn or apply critical thinking skills by accident. Teachers still need to plan lessons to teach, demonstrate and model these skills or students will not develop them. The fact that students may be practicing these skills in online chat rooms, blogs, or other collaborative learning situations is incidental to the teaching of the skills themselves. Participation in online discussion or collaborative learning alone will not produce critical thinking skills in students.
I also loved the list of Socratic questioning prompts. I will definitely plan to keep this list handy to serve as a reminder of the myriad of ways that I can ask students to clarify or extend their thinking. It’s great to have other ways of prompting students to “add something further to what they just said.”
Wow! We’ve done so much today that my head is spinning. There seem to be so many choices of how to do things–where do things go? Should I post it on my blog or subscribe to it in bloglines or tag it for my del.icio.us account? I am excited about the RSS feeds and will be looking for more sites to start to add them. I also want to show them to my husband; one of his responsibilities at work is to search daily for news stories related to his industry (telecommunications) and clip stories for his group to read. I don’t know how he does this now, but I can see that using bloglines to subscribe to various feeds will greatly simplify his work!
I’m still not sure what pieces of all this I’ll use in my math classes this fall. Certainly the students will benefit from sharing links in my del.icio.us account when looking for math help or references online. I like some of what I read yesterday from the AP Calculus class and will continue to think over whether I want to try something like that in my class.
