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I totally meant to share these problems a few weeks ago, but I wanted to try it out with my classes first. However, I got so distracted with doing my Capture & Recapture Lab that we never got to the worksheet. Yes, I did a Capture & Recapture lab for my Beginning Algebra Classes to help demonstrate how proportions might be used as part of a method of estimation. Several students told me that without the lab, they wouldn’t have really understood exactly why we even needed proportions. That made me happy. So, here we are after the semester has already ended and I never used these problems. But I thought that I would share them anyway.
2. McGraw Hill Game Zone Resources – This website is full of wonderful games that can be used in the classroom, such as this Measurement Relay Game. Essentially, this is one of those ‘I Have. Who Has?” Activities. But what I like to do with them is cut them out and have the students put the questions and answers together in domino-style format. The students really seem to enjoy this for the most part, it’s less chaotic than having everyone run around the room all at the same time, and it’s conducive to having the students work in small groups.
3. Ratio and Proportion weblinks – This is a list of weblinks that I found from Mathmammoth. If you hunt around their website long enough, you will also find a list of Integer weblinks, among others. I think tha these lists of weblinks would be perfect places to start in putting together a spectacular Web Quest for students. There were definitely resources on there that I hadn’t heard about in the past.
4. BBC Podcasts: A Brief History of Mathematics – Let me just say this… don’t you just love the British? And if a British Podcast doesn’t float your boat, try looking at some videos over at EduTube, this video of a math teacher rapping. Hey, it’s not great compared to some of the impromptu songs that I’ve sung during my classes in order to keep my students interested in the lessons. I’m a big fan of keeping students engaged in the classroom.
5. [removed by request]
6. Best Free Online Applications and Services – This is really great not only because I haven’t heard of many of these resources before, but because they are all on-line. This eliminates the need for pesky downloads and making sure that applications are compatible with various operating systems. I also liked that Wolfram Alpha is highlighted as being the Best Free Online Answer Engine. Any list that gives a shoutout to Wolfram Alpha is a respectable list in my book.
7. The History, Use, and Abuse of QR Codes – This is a fairly in-depth Slideshare that I found helpful in my quest to eventually integrate QR Codes into my teaching. I’m really thinking about putting QR codes on my syllabus, and homework assignments from now on just to try to alleviate some of the complaints that I often get from students about not being able to find an assignment that I’ve posted on the web. And by having to put the assignment on the web before even passing it out, I will also know that I haven’t sent students to a web resource that I might have actually forgotten to post. (It’s happened!)
8. 20 Free Web Apps for the 2.0 Student – I don’t think that all of these will work for every student, but there are a few good resources on the list that I would recommend for everyone, such as Phone Evite, a website that allows you to send out mass voicemails; Mikogo, a website that allows for remote desktop sharing; and Mint, free personal finance software. I’m actually considering using Mint myself since it’s part of the Intuit Brand, which I already highly respect since I’ve been using TurboTax for several years now.
Yesterday I came across this problem while planning a lesson on ratio and proportion:
"When I woke up this morning, I hit the snooze button and got 10 extra minutes to sleep. Every time I hit the button, I get 10 extra minutes. At this rate, if my alarm first goes off at 5:30 and I hit the snooze button 4 times before I actually get up, what time do I get up?"
After careful thinking, it turns out that I wasn't actually interested in this problem at all. I was actually interested in asking questions such as:
Does it make since to get 10 extra minutes every time you hit the button, or would it make more sense for the number of minutes to be related to the number of times that the button is hit?
Personally, I would love an alarm clock that gives me 10 minutes on the first hit, 8 minutes on the second hit, 6.4 minutes on the third hit, etc. Then I could use this situation to talk about the limit of the time approaching zero.
This problem came about because I was talking about solving the equation 4x + y = – 14 for y and there was a little confusion about how I could subtract 4x from – 14. Although this was really a problem with combining like terms, I figured that now was as good of a time as ever to reinforce the idea of combining like terms.
“Yaletta bought an unknown number of tomatoes at $4 each, but when she got home, she found out that all of the tomatoes were rotten. In addition, she checked her receipt and realized that the store had charged $14 to carry the tomatoes to the car. Write an equation to model Yaletta’s total losses.” (as a signed number)
The students seemed to come to the consensus that an appropriate answer would be y = – 4x – 14.
Then I asked these questions as well:
What does y represent?
What does x represent?
What does -4 mean?
What does -14 mean?
How much would Yaletta lose if she bought 25 tomatoes? (as a signed number)
What’s even more interesting about this problem for me is that later in the day I was talking about ratio and proportion and so I used this same problem to ask questions such as:
Do you think that it’s fair that the $14 dollar charge is fair? Why or why not?
Would it be more appropriate to have a charge proportional to the number of bags of tomatoes carried to the car?
What additional information would we need to know in order to make this change to the charge?