MA.4.a Apply number theory concepts, including prime factorization and relatively prime numbers, to the solutions of problems.
MP.1 Make sense of problems and persevere in solving them.
MP.5 Use appropriate tools strategically.
The Learning Objective: Differentiate between prime and composite numbers
Quote of the Day: "Americans spend twice as much time on Facebook as they do exercising. And the younger the age, the worse the effects. The average college student spends three hours a day checking social sites. According to a USA Today report, the grade point average of college students who regularly use Facebook is a full point lower than their peers who do not...American workers are interrupted once every 10.5 minutes by things like emails, texts, or tweets. Once interrupted, it takes an average of 23 minutes for them to get back on task.” - Rick Pitino
Agenda:
The Assessment: My primary assessment to see where students stood against the objective was for students to classify the numbers 10, 25, and 29 as either prime or composite. I circumvented the room and they passed with flying colors.
That said, their minds were not pushed in the same way as they were when I asked what day of the year September 28th was. I rephrased this question several ways. How many days has it been since January 1st? How many days have there been in 2014? How many days in the calendar year have we had so far? Eventually they understood the question, but arriving at the answer was not even close to as easy as I would have imagined. I learned what months had thirty days when I was in second grade. And I'm pretty confident in saying that my classmates in second grade mastered this at the stage in their lives as well. I'm not saying that these kids aren't learning anything in lower grades either - in fact I feel the opposite. They are learning more and more sooner than I was at their age, but perhaps that's a problem. Finland's school days are shorter and their standards are fewer, but yet their mathematical achievements are much higher? Perhaps less is more. Perhaps the phrase "Thirty days have September, April, June, and November" is more important than estimating lengths to the nearest meter (both of these are second grade standards in Massachusetts but only the lengths to the nearest meter is a national common core standard).
Homework: This worksheet as well as our 2nd Weekly Quiz. The homework was deceptively difficult or as I would tell the students "filled with wolves." Students had the most difficulty with numbers like 121 and 57 because they are not divisible by the numbers with "easy rules."
My Glass Half-Full Take: It only takes one student. Today a student stayed after school that had not all year to complete a weekly quiz, homework, and help learn from mistakes made on the quiz from last week. The day was an overall struggle. Students did not know how to fill out the graph of their math quizzes, our self-assessment form is due to the administration team later this week, and I'm awaiting transcripts for credits from this summer and last summer after schools never notified me that my grades were in. I was in a bit of a funk from the first block on and every little obstacle I faced seemed much worse than it really was because of my mindset (so much for Day 18's quote of the day!). In any case it was good to have something positive come from the day at the very end of the day.
One Thing to Do Differently: In what I would deem a bad day for me, it's hard to pin this to one thing. Perhaps from the get go I should have put the students' quiz scores as a percentage (what they are used to) as opposed to leaving it as a fraction. They do not know how to convert from fractions to decimals yet. My partial goal in leaving these grades as a fraction of course is that they can learn this valuable skill and they see its use. My other goal is that they look not at the score of the quiz but turn to the parts they answered incorrectly or did not have the knowledge to answer at all.
That said, the amount of time it took for students to graph their results, look back at a quiz we took last week and graph that, and also just to do the journal entry about what went right and wrong with this quiz took long enough. I ended up spending 50 of our 100 minutes together today going over the quiz and the paperwork associated with the quiz (more time allocated to the ladder than the former). It was frustrating for me to waste this time that could have been spent on assessment of the objective, and obviously I did not deal with it well. Tomorrow I'm going to forget about it though and start fresh. There is still value in getting students to write how they can improve their study habits and in seeing what simple mistakes students were making to correct that in the future.
Link of the Day: I learned as much as they did.
The Learning Objective: Differentiate between prime and composite numbers
Quote of the Day: "Americans spend twice as much time on Facebook as they do exercising. And the younger the age, the worse the effects. The average college student spends three hours a day checking social sites. According to a USA Today report, the grade point average of college students who regularly use Facebook is a full point lower than their peers who do not...American workers are interrupted once every 10.5 minutes by things like emails, texts, or tweets. Once interrupted, it takes an average of 23 minutes for them to get back on task.” - Rick Pitino
Agenda:
- Self-Assessment from Friday's Quiz
- Journal about the quiz
- Create line graph from the three quizzes so far this year
- Review the quiz as a whole class
- Notes on prime and composite numbers
- Prime numbers challenge - what day of the year was yesterday (September 28th)? Is that day a prime number? How can you tell?
- Start the prime number homework and include a challenge.
The Assessment: My primary assessment to see where students stood against the objective was for students to classify the numbers 10, 25, and 29 as either prime or composite. I circumvented the room and they passed with flying colors.
That said, their minds were not pushed in the same way as they were when I asked what day of the year September 28th was. I rephrased this question several ways. How many days has it been since January 1st? How many days have there been in 2014? How many days in the calendar year have we had so far? Eventually they understood the question, but arriving at the answer was not even close to as easy as I would have imagined. I learned what months had thirty days when I was in second grade. And I'm pretty confident in saying that my classmates in second grade mastered this at the stage in their lives as well. I'm not saying that these kids aren't learning anything in lower grades either - in fact I feel the opposite. They are learning more and more sooner than I was at their age, but perhaps that's a problem. Finland's school days are shorter and their standards are fewer, but yet their mathematical achievements are much higher? Perhaps less is more. Perhaps the phrase "Thirty days have September, April, June, and November" is more important than estimating lengths to the nearest meter (both of these are second grade standards in Massachusetts but only the lengths to the nearest meter is a national common core standard).
In any case, it was fun as a teacher when I would go to the board after they struggled for a few minutes and they begged me not to tell them how many days there were. They worked in partners and continued to struggle. Eventually a couple students did get the answer. I was pleasantly surprised that using tools (yes the calendar above is a tool) came up in the lesson today.
All that being said the answer of 271 was my main reason for bringing this whole question up. I wanted the students to explain if 271 was prime or composite. By the time I asked them this question they were either spent from working out the previous problem or had no motivation to solve this one. They all guessed a simple yes or no. Nobody bothered to divide by seven until I commanded it. Nobody touched whether or not 11 or 13 or 17 went in. And this begs the question, did the students meet the objective?
Homework: This worksheet as well as our 2nd Weekly Quiz. The homework was deceptively difficult or as I would tell the students "filled with wolves." Students had the most difficulty with numbers like 121 and 57 because they are not divisible by the numbers with "easy rules."
My Glass Half-Full Take: It only takes one student. Today a student stayed after school that had not all year to complete a weekly quiz, homework, and help learn from mistakes made on the quiz from last week. The day was an overall struggle. Students did not know how to fill out the graph of their math quizzes, our self-assessment form is due to the administration team later this week, and I'm awaiting transcripts for credits from this summer and last summer after schools never notified me that my grades were in. I was in a bit of a funk from the first block on and every little obstacle I faced seemed much worse than it really was because of my mindset (so much for Day 18's quote of the day!). In any case it was good to have something positive come from the day at the very end of the day.
One Thing to Do Differently: In what I would deem a bad day for me, it's hard to pin this to one thing. Perhaps from the get go I should have put the students' quiz scores as a percentage (what they are used to) as opposed to leaving it as a fraction. They do not know how to convert from fractions to decimals yet. My partial goal in leaving these grades as a fraction of course is that they can learn this valuable skill and they see its use. My other goal is that they look not at the score of the quiz but turn to the parts they answered incorrectly or did not have the knowledge to answer at all.
That said, the amount of time it took for students to graph their results, look back at a quiz we took last week and graph that, and also just to do the journal entry about what went right and wrong with this quiz took long enough. I ended up spending 50 of our 100 minutes together today going over the quiz and the paperwork associated with the quiz (more time allocated to the ladder than the former). It was frustrating for me to waste this time that could have been spent on assessment of the objective, and obviously I did not deal with it well. Tomorrow I'm going to forget about it though and start fresh. There is still value in getting students to write how they can improve their study habits and in seeing what simple mistakes students were making to correct that in the future.
Link of the Day: I learned as much as they did.
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