If you have been following along, you know that I have been contributing to the teacherspayteachers.com website.
Monday and Tuesday (November 26 and 27), the site will be having a sale. Each individual seller can set up their own store on sale (up to 20% off) and then the TPT website has a code you can enter to get an additional 10% off!
If you have ever visited the site, you know that there are awesome ideas! There are projects, worksheets, and ideas galore - for every grade level and topic.
Take this opportunity to stock up on items that will make your teaching even more fabulous : )
Please visit my store to take 20% off anything in my store, and then use the code given in the graphic below to get an additional 10% off.
I realized something about myself today...it's really weird...I count things. Yes, I know you are thinking a math teacher that counts things...of course you do! But, I realized that I count things without knowing I am counting them. Like, for example, when the copy machine is copying, I realize in the middle that I am on copy 47. Have you ever played the game where you have to guess how many things are in a jar? When I look at something like that, a number comes to me - I don't calculate anything, I just think of a number. I'm always pretty close to the number of things in a jar. Years ago, I had a student - Emily her name was - she is probably the best math student I have ever had. She could just see things that the other kids couldn't. She was also my student aide. She was in my office one day when she got out a box of tic-tacs. One of my other aides said, "Hey can I have one?" I watched Emily slowly - as slowly as she could, hand over the box of tic-tacs. She obviously didn't really want to share, but couldn't think of a reason not to. Later, after the other student left, she said, "Did you know that there are almost always 36 tic-tacs in a package? I usually try to eat them 4 at a time so that I will have an even number in each serving of tic-tacs." Therein lay the problem that she was faced with when she was asked to share - who knew how many tic-tacs the other person would take? If she didn't know, she was likely to end up with an odd number of tic-tacs at the end of the package. Not a comfortable feeling for her!
How many times have I thought that in the last 20 plus years of teaching? OK, not so many times in about the first 5 years because I really had no idea...but especially lately, I find myself thinking it sometimes. How many times do I have to show you how to factor? Why do you absolutely REFUSE to learn it? Maybe I'm just getting cranky : )
I hear it from my department members all the time - the PreCalc teacher says why didn't you guys teach trig well enough last year, the Algebra 2 teachers says why don't these kids know how to factor, the Geometry teacher says why don't these kids know how to simplify a radical, and the Algebra teacher says why didn't those teachers in junior high teach these kids how to work with fractions??
Well, we each know that we could do it better - if WE were only the ones teaching those kids the year before, they'd know all these things! Until you do...until you know you're the one that taught them the year before - you know you taught how to factor a difference of cubes, and then when it comes up in calculus they look at you like you have two heads! You know you had these same kids in geometry, but bring up the relationship between the sides of a 30, 60, 90 degree triangle and blank looks glaze over those otherwise smiling faces.
What to do - how to solve this problem? To be honest, I have had several foreign exchange students over the years, and it seems like they never forget. They never have any computational trouble whatsoever, ask them to factor - no problem, convenient values of trig functions - right there on the tip of their tongue.
When you're a math teacher, you need a bag of tricks that you can reach into for those moments when some part of the lesson went faster than you imagined - or maybe there was an assembly scheduled that was suddenly cancelled and you are left with your class for 90 minutes (instead of the usual 45 you are used to)...that happened to me last week!
Sometimes you might just be able to continue with the lesson on the fly depending on where you are, but sometimes you just have to reach into you math teacher bag of tricks. Here is one of my favorites that usually takes freshmen or sophomores at least 20 minutes before they want to give up or someone finally gets it. (Junior high students can mathematically do this problem too).
One day I went to visit my friend George who is a mathematician. I went inside and had a nice visit. I saw a picture of his three children hanging on the wall. I asked him, "How old are your children?" He said, "The product of their ages is equal 72." I said, "That doesn't give me enough information to tell how old they are." He said, "The sum of their ages is equal to my house number." I went outside to look at the house number. I scratched my head and went back inside - I said to George, "That still isn't enough information." He said, "You're right, I should also tell you that the oldest one likes ice cream sundaes." I said, "Oh, now I know, their ages are..." There are several variations of this problem, but the idea is that the students have to list the possible ages of the children that could yield a product of 72. Then, they must realize that if you list all the possible sums of those products, there are two that yield the same sum. The piece of information about the ice cream sundaes is only there to help the students know which possible set of products and sums they need to use. (The two possible products that have the same sum are 3, 3, and 8 and 6, 6, and 2. Students must choose the one that only has one oldest child). Final answer is 3, 3, and 8. Have a great weekend!
I absolutely love that I can do constructions that used to take a ton of time in just a few minutes. I can ask better and deeper questions because the students don't have trouble making the things I am asking them to make.
I had another terrifying experience while teaching Geometry this week.
I was working through a problem in our book and the last question was to find the area of a triangle with specific vertices. We had already found the coordinates of all three of the vertices and the lengths of the sides of the triangle. Our last step was to multiply 1/2 * 9 * 12. I immediately wrote 54 on the board and started to go on to the next thing...when several of the students started to say wait how did you get 54 so fast? I said well, half of 12 is 6 and 6 * 9 is 54.
They were amazed that you could multiply like that - they all wanted to pull out their trusty calculators and type it all in. In fact after I explained that you could take 1/2 of either number and then multiply that by the other number, they continued to be amazed. Some of them were convinced that you need to take 1/2 of both 9 and 12 and multiply that together.
Wow, this is a real problem! Wish I had a solution...
Halloween Joke a Little Late: I was walking in the hall this week behind one of my fellow math teachers and I was listening in on a conversation he was having with a student. The student said, Mr. H, what are you going to be for Halloween? Mr. H said, I'm going to be a fraction - everyone is scared of them!