This week was weird. For starters, it is a four-day week given Monday is the day we observe Labor Day. Wednesday I had a funeral to attend and therefore had to produce busy work for my students, Thursday is the start of Rosh Hashanah and had kids absent, and Friday, Muslims celebrate Eid. In other words, there was not much in the way of normalcy this week.
Tuesday 09/07/2010:
Went through the Sailor And The Coconut problem from Friday's worksheet. having students explain at the Promethean board what they knew and why they knew it. The discussion lasted about 35 minutes which then left 15 minutes to (finally) cover the syllabus.
Wednesday 09/08/2010
I was gone this day for a funeral and therefore had to come up with some busy work for the students to do while the sub was here. I found my resources in the Algebra with Pizazz book and gave the students pages A-8 and A-9 to work on in my absence. Both sheets have students practice order of operations and evaluating expressions for given values of the variables. A number of them thought the worksheet was beneath them, but the sub reported that a number of them struggled to find the answers.
Thursday 09/09/2010:
I thought to look at http://www.mathalicious.com/ as a source of inspiration. Since we had recently studied The Order of Operations, I found a unit called "Calories In, Calories Out". I noticed the unit has students use their knowledge of order of operations, unit conversions, evaluating expressions and analysis of functions while discussing the Basal Metabolic Rate, (BMR), to determine the amount of calories needed in a day to maintain ones weight. It looked as if it would take 4 days to go through the activity but the mathematics in the unit seems rich in analysis, computation and disguises the math within an interesting problem. The central problem is this: There are two formulas which are used to determine one's BMR. The students find the two formulas can give different results and are asked to determine for which persons would one formula be better suited than another?
Along the way, I was able to digress and discuss the interconnectedness of the units of length, volume, mass and temperature within the metric system. We only got through the first page of the unit. Clearly, I have to speed things up. I feel we should have been able to get through more material than this during the first day.
Friday, 09/10/2010
We continued with the Calories In, Calories Out unit. On page two the students have to crunch some numbers, analyzing which inputs, (Gender, Weight, Height or Age) have the greatest affect on the BMR. Students also must convert pounds to kilograms and inches to centimeters, determine if there is a difference between the two BMR formulas, determine which formula seems to make the most sense for various types of people. Students are also given the task of error analysis as there are asked to find the error and determine why the computation is wrong. (order of operations).
The last part of this page has students convert the formulas, which are inconveniently written in Kg and Cm, into equivalent formulas using pounds and inches. All-in-all there is a lot of good math buried in this unit.
6.9.10
Week ((((6 + 2) / 4 * 3 / 3) – 7 + 6 + 5 )/ 3 – 1 )* 1
Blather: I thought I would send out my overview of how I spent my first week in designing and implementing curriculum for the course we titled, College Prep Math.
I used the first week to cover order of operations, (with some success). I figured the topic is a foundational topic and is necessary for nearly everything else that will be taught. Unfortunately, the computational skills of many are quite low and as such, many were able to show knowledge of which operation to do when but still ended up with the wrong answers. I also noticed a profound need for me to cover integer arithmetic. If I had it to do over again, I would have started there.
One bright spot in the week was to have the students work on the 10-operation expression that appeared in the now infamous Survivor episode. The expression was:
For most, it took 40 minutes until the expression was reduced to 6 1/6. But what joy it was to watch the emotion on their faces when they watched the Survivor Episode where one contestant starts the problem by writing “PEMDAS” before even beginning to simplify and the “winner” evaluates left to right and gets the answer of “1”! I had students who were literally ANGRY with the injustice of it all!
In one final flash of pedagogical brilliance, the next day, (Friday) I asked my students to pretend to be consultants for CBS and write out the expression in such a way that the answer would be evaluated left to right, simplifies to 1 and yet adheres to the order of operations. Many students came up with
But one math buck argued that this expression would also work and uses fewer parenthesis:
Clearly, this young man has a deep understanding of the order of operations. He is also thinking on a completely different plane as the other students in the class. I also have been in contact with the developer of the www.mathalicious.com site, Karim Logue. He is looking for feedback on the lessons he has posted on his site. Unfortunately, he did not have anything posted about The Order Of Operations that I could use. After writing to him of the exploits of my classes, he made an activity around the Survivor episode.
I finished off Friday by having the students do a unit conversion, (stoichiometry). I broke the students up into groups of four and each group was to determine how fast a fingernail grows in miles per hour. We started by agreeing that a fingernail grows 1/8 of an inch every 2 weeks and I let the students take it from there. I intended to Just let them fly with it but had to abandon this crazy notion as I was being called to each of the groups to give them some hints as to how to start the conversions. Thus, the activity quickly turned from student-centered to teacher-centered. This has always been one of my bones of contention with student-centered activities, they only work when either the students possess the foundational knowledge that support the activity or the activity is so structured that it guides them through the activity but the student never really has an opportunity to think for themselves. Nevertheless, I ended class with a worksheet containing two problems from a worksheet I got from the files of my predecessor, John Triscari. It asks the students to use the fact that Usain Bolt was able to run 100 meters in 9.58 seconds and state how fast this is in miles per hour. The second problem on the worksheet has the students find the number of coconuts originally in the pile if each of three sailors in turn wake up and divide the piles up into thirds, take their third, leave two thirds and throw the one remaining coconut to a monkey. In the morning, the three wake up and notice a much smaller pile. When the piles are divided, each sailor would get 7 coconuts, but there would be one left for the island’s monkey. The intent of this problem is to get the student’s to use the working backward problem solving strategy. Since most of the students have the computational skills to solve this problem, it will be interesting to see on Tuesday (we are off Labor Day) just how many actually had the desire to work on this problem long enough to find the answer.
Wince: I still don’t have a clear direction for this class. I feel it is up to me to design my own curriculum and carry it out. I am putting way more time into this one class than I am in preparing for my two precalc classes. I feel as though it is both unfair and unwise for the district to expect their teachers, who are specialists in curriculum implementation to also serve as curriculum writers. While some teachers have the skills and time to write quality lessons and activities from my experience, most lack are at a lack for some combination of time and skill. Both teaching and curriculum writing are full-time jobs. I fear I will do both jobs poorly if I try to wear both hats. It also seems strange that each school has one teacher teaching this course and we are left to work on our own developing our own curricula. To put the importance of this course into perspective, John Triscari taught five sections of this class last year in his first year of teaching at Southwest. Last year, Southwest missed making AYP by the closest margin to date. According to SW Principal, Bill Smith, we missed AYP by just one ELL student on the math test. Imagine…Just one student! The SW math department credits the work of John Triscari and the work he put into developing both the curriculum as well as the curriculum’s implementation. It would be an understatement to say I don’t feel the weight of expectation on my shoulders now. I contend that this class and its curriculum should be of the highest priority. It seems odd that we have books and curriculum maps for all of our math classes except the one that will most help us meet AYP.
Blather: I thought I would send out my overview of how I spent my first week in designing and implementing curriculum for the course we titled, College Prep Math.
I used the first week to cover order of operations, (with some success). I figured the topic is a foundational topic and is necessary for nearly everything else that will be taught. Unfortunately, the computational skills of many are quite low and as such, many were able to show knowledge of which operation to do when but still ended up with the wrong answers. I also noticed a profound need for me to cover integer arithmetic. If I had it to do over again, I would have started there.
One bright spot in the week was to have the students work on the 10-operation expression that appeared in the now infamous Survivor episode. The expression was:
6 + 2 / 4 * 3 / 3 – 7 + 6 + 5 / 3 – 1 * 1
For most, it took 40 minutes until the expression was reduced to 6 1/6. But what joy it was to watch the emotion on their faces when they watched the Survivor Episode where one contestant starts the problem by writing “PEMDAS” before even beginning to simplify and the “winner” evaluates left to right and gets the answer of “1”! I had students who were literally ANGRY with the injustice of it all!
In one final flash of pedagogical brilliance, the next day, (Friday) I asked my students to pretend to be consultants for CBS and write out the expression in such a way that the answer would be evaluated left to right, simplifies to 1 and yet adheres to the order of operations. Many students came up with
((((((((((6 + 2) / 4) * 3) / 3) – 7) + 6) + 5) / 3) – 1) * 1) = 1
But one math buck argued that this expression would also work and uses fewer parenthesis:
((((6 + 2) / 4 * 3 / 3) – 7 + 6 + 5 )/ 3 – 1 )* 1 = 1
Clearly, this young man has a deep understanding of the order of operations. He is also thinking on a completely different plane as the other students in the class. I also have been in contact with the developer of the www.mathalicious.com site, Karim Logue. He is looking for feedback on the lessons he has posted on his site. Unfortunately, he did not have anything posted about The Order Of Operations that I could use. After writing to him of the exploits of my classes, he made an activity around the Survivor episode.
I finished off Friday by having the students do a unit conversion, (stoichiometry). I broke the students up into groups of four and each group was to determine how fast a fingernail grows in miles per hour. We started by agreeing that a fingernail grows 1/8 of an inch every 2 weeks and I let the students take it from there. I intended to Just let them fly with it but had to abandon this crazy notion as I was being called to each of the groups to give them some hints as to how to start the conversions. Thus, the activity quickly turned from student-centered to teacher-centered. This has always been one of my bones of contention with student-centered activities, they only work when either the students possess the foundational knowledge that support the activity or the activity is so structured that it guides them through the activity but the student never really has an opportunity to think for themselves. Nevertheless, I ended class with a worksheet containing two problems from a worksheet I got from the files of my predecessor, John Triscari. It asks the students to use the fact that Usain Bolt was able to run 100 meters in 9.58 seconds and state how fast this is in miles per hour. The second problem on the worksheet has the students find the number of coconuts originally in the pile if each of three sailors in turn wake up and divide the piles up into thirds, take their third, leave two thirds and throw the one remaining coconut to a monkey. In the morning, the three wake up and notice a much smaller pile. When the piles are divided, each sailor would get 7 coconuts, but there would be one left for the island’s monkey. The intent of this problem is to get the student’s to use the working backward problem solving strategy. Since most of the students have the computational skills to solve this problem, it will be interesting to see on Tuesday (we are off Labor Day) just how many actually had the desire to work on this problem long enough to find the answer.
Wince: I still don’t have a clear direction for this class. I feel it is up to me to design my own curriculum and carry it out. I am putting way more time into this one class than I am in preparing for my two precalc classes. I feel as though it is both unfair and unwise for the district to expect their teachers, who are specialists in curriculum implementation to also serve as curriculum writers. While some teachers have the skills and time to write quality lessons and activities from my experience, most lack are at a lack for some combination of time and skill. Both teaching and curriculum writing are full-time jobs. I fear I will do both jobs poorly if I try to wear both hats. It also seems strange that each school has one teacher teaching this course and we are left to work on our own developing our own curricula. To put the importance of this course into perspective, John Triscari taught five sections of this class last year in his first year of teaching at Southwest. Last year, Southwest missed making AYP by the closest margin to date. According to SW Principal, Bill Smith, we missed AYP by just one ELL student on the math test. Imagine…Just one student! The SW math department credits the work of John Triscari and the work he put into developing both the curriculum as well as the curriculum’s implementation. It would be an understatement to say I don’t feel the weight of expectation on my shoulders now. I contend that this class and its curriculum should be of the highest priority. It seems odd that we have books and curriculum maps for all of our math classes except the one that will most help us meet AYP.
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