6.G.2 Find the volume of a right rectangular prism with fractional edge lengths by packing it with unit cubes of the appropriate unit fraction edge lengths, and show that the volume is the same as
would be found by multiplying the edge lengths of the prism. Apply the formulas V = lwh and
V = bh to find volumes of right rectangular prisms with fractional edge lengths in the context of
solving real-world and mathematical problems.
MP.1 Make sense of problems and persevere in solving them.
MP.2 . Reason abstractly and quantitatively.
MP.3 Construct viable arguments and critique the reasoning of others
The Learning Objective: Apply the operations of fractions in order to solve problems
Quote of the Day: “A professor stood before a class of 30 senior molecular biology students. Before he passed out the final exam, he stated, ‘I have been privileged to be your instructor this semester, and I know how hard you have worked to prepare for this test. I also know most of you are off to medical school or grad school next fall. I am well aware of how much pressure you are under to keep you GPAs up, and because I am confident that you know this material, I am prepared to offer an automatic B to anyone who opts to skip taking the final exam.’ The relief was audible. A number of students jumped up from their desks, thanking their professor for the linelife he had thrown them. ‘Any other takers?’ he asked. ‘This is your last opportunity.’ One more student decided to go. The instructor then handed out the final exam, which consisted of two sentences. ‘Congratulations’ it read ‘you have just received an A in this class. Keep believing in yourself.’”
Agenda:
The Assessment: The Fractions Test
Homework: Students were to answer these questions after watching this video and this video. The Weekly Quiz is also due tomorrow.
My Glass Half-Full Take: The Zombie Bridge was solved in one class and students tried hard to solve it another. Here were a couple examples of students trying to solve the problems:
One Thing to Do Differently: Fractions. Where to begin. This test did not have the desired results I was looking for especially looking back at my daily assessments and how students were meeting objectives. Although there were students that certainly met their potential, it is always emotionally draining when students are below their potential.
I could have given a quiz on adding and subtracting fractions. The students would have known what to do as far as always finding a common denominator and the word problems would have been much easier to guess at because they would only include two operations. The problem from my perspective with all of this is that it does not show true mastery. Thus the students mixed up the operations they did and made a handful of other errors. It is hardly to say that students were way off or that "they don't know fractions." Looking at their mistakes it was more often small details rather than a total lapse in a certain topic.
In the picture above, this student knew how to find a common denominator. The student also understood that to add you must add the numerators and not the denominators. The problem of course was that the problem was a subtraction problem.
In the problem above here, the student correctly put the whole number of one. This student also successfully changed the denominators. The problem was merely that they did not properly subtract four from twenty-one. Again not really an error with the fractions.
Finally, this last photo here uses a very high number of 42,000. There is no doubt that in our world today that an adult would bust out the iPhone and do this problem on the calculator. This student did just fine without the calculator. Except for the fact that the question says how many votes did the winner not receive. Now would an adult pick up on that detail after putting all the information into a calculator? I'm sure some would, but some also wouldn't. This is again an instance in which a student knows what to do with the fractions, but does not know how to solve the word problem.
As I looked at student errors, I came to the conclusion that perhaps I don't need to hit students over the head with fractions. There are those students that still need more practice of course, but in general the bigger issue here might be reading comprehension and just simple calculation mistakes. I have a plan in mind for working out this word problem issue. I might just put together a ton of word problems and in lieu of asking students to solve them, just ask students to find the operations they would need in order to solve them using analogous numbers. I also need to crack down harder on students that do not circle and underline the problems.
Link of the Day: Cool look at how to mislead people with graphs and statistics.
The Learning Objective: Apply the operations of fractions in order to solve problems
Quote of the Day: “A professor stood before a class of 30 senior molecular biology students. Before he passed out the final exam, he stated, ‘I have been privileged to be your instructor this semester, and I know how hard you have worked to prepare for this test. I also know most of you are off to medical school or grad school next fall. I am well aware of how much pressure you are under to keep you GPAs up, and because I am confident that you know this material, I am prepared to offer an automatic B to anyone who opts to skip taking the final exam.’ The relief was audible. A number of students jumped up from their desks, thanking their professor for the linelife he had thrown them. ‘Any other takers?’ he asked. ‘This is your last opportunity.’ One more student decided to go. The instructor then handed out the final exam, which consisted of two sentences. ‘Congratulations’ it read ‘you have just received an A in this class. Keep believing in yourself.’”
Agenda:
- Take the Fractions Test
- Work on WQ #7
- Zombie Bridge Problem (second part of class)
The Assessment: The Fractions Test
Homework: Students were to answer these questions after watching this video and this video. The Weekly Quiz is also due tomorrow.
My Glass Half-Full Take: The Zombie Bridge was solved in one class and students tried hard to solve it another. Here were a couple examples of students trying to solve the problems:
The activity does many things to make it a great lesson. Number one it is student driven. I read the problem and then I let the students do the talking - I only ask questions and give suggestions such as underlining what to find, draw a picture, or act it out. It's on the students to discover how to not get eaten by the zombies. It's the first time this year that I have spent an entire class with students trying to solve one problem and although only one student was ultimately able to derive the solution independently (and one teacher for that matter), the thinking and persevering is what makes it worthwhile from a learning perspective.
One Thing to Do Differently: Fractions. Where to begin. This test did not have the desired results I was looking for especially looking back at my daily assessments and how students were meeting objectives. Although there were students that certainly met their potential, it is always emotionally draining when students are below their potential.
I could have given a quiz on adding and subtracting fractions. The students would have known what to do as far as always finding a common denominator and the word problems would have been much easier to guess at because they would only include two operations. The problem from my perspective with all of this is that it does not show true mastery. Thus the students mixed up the operations they did and made a handful of other errors. It is hardly to say that students were way off or that "they don't know fractions." Looking at their mistakes it was more often small details rather than a total lapse in a certain topic.
In the picture above, this student knew how to find a common denominator. The student also understood that to add you must add the numerators and not the denominators. The problem of course was that the problem was a subtraction problem.
In this problem, again the student knew how to find a common denominator, knew to add the numerators and not the denominators, and even had the correct operation. The problem was that students ignored the fact that she ran around the track twice. My colleagues and I are constantly preaching to students to circle what you know and underline what you're trying to find out. That simple step here would have saved this student (and several more like this student) a simple error.
Finally, this last photo here uses a very high number of 42,000. There is no doubt that in our world today that an adult would bust out the iPhone and do this problem on the calculator. This student did just fine without the calculator. Except for the fact that the question says how many votes did the winner not receive. Now would an adult pick up on that detail after putting all the information into a calculator? I'm sure some would, but some also wouldn't. This is again an instance in which a student knows what to do with the fractions, but does not know how to solve the word problem.
As I looked at student errors, I came to the conclusion that perhaps I don't need to hit students over the head with fractions. There are those students that still need more practice of course, but in general the bigger issue here might be reading comprehension and just simple calculation mistakes. I have a plan in mind for working out this word problem issue. I might just put together a ton of word problems and in lieu of asking students to solve them, just ask students to find the operations they would need in order to solve them using analogous numbers. I also need to crack down harder on students that do not circle and underline the problems.
Link of the Day: Cool look at how to mislead people with graphs and statistics.
No comments:
Post a Comment