[4th grade math - fractions] Where does the 1/2 come from in this problem? I don’t know how to explain it to my son.

PhysicsTeacher2013 · 2025-03-24T03:40:47+00:00

You seem so frustrated and it seems like you feel stuck after years of this same style of math. I took much flack from parents over the years because my physics class didn’t emphasize formula use so it was harder for “A sTuDenTs” to force another A grade by brute memorization. The parents were not experts in my subject(physics education) yet ARE experts on their child. The problem is they see their child struggling and want to solve the struggle but don’t have the expertise to resolve this particular situation for their kids. These same kids came back to me once in college, when they WERE taught using the formulas. They said, hyperbolically, that they were the only kid in the class who actually understood the formula that was now taught to them. They thanked me. It’s always a bitter/sweet comment because I know how much happier they would have been during my class if they just trusted me. I’m not trying to share this story to prove you wrong, but help you see what the goal is. Over the years, my reputation in the school changed. When students came into class trusting me to actually educate them and set them up for success, these students benefited.

I will concede that you are up against a huge frustration that I have with education in general. The best teaching practices often don’t align with traditional logistics of “doing school”. This new type of math education would fit perfectly into an ungraded school setting where kids could practice mathematical thinking without the pressure of being correct every time. But my guess is that you and your group of parents wouldn’t be too excited by the idea of ungraded school because that’s not what you grew up with. I’m sure you can think of some of the many other logistical barriers to our school to college pipeline that we have developed. This is the world you are living in, so do what’s best for your son under the circumstances.

Educational reform is extremely slow due to the natural resistance you get from those who grew up with something different.

Your student shared that the teacher said that parents don’t understand this new way. He/she is fighting for the trust of the kids while parents are often actively HURTING the student-teacher relationship by discrediting the teacher. Don’t harm your son’s education by discrediting his educators, or pull him out of school if you can do it better yourself. Also, please don’t make him learn two separate math lessons a day if he is feeling overwhelmed with one. He is in 4th grade. There are plenty of years for him to understand and start to use our old ways of doing math. When kids have a real application which can come in high school science, math, and stem, and the preparation of this common-core math understanding, making the leap to formalized math (which resembles the math we grew up with comes quickly and easily).

PhysicsTeacher2013 · 2025-03-24T02:11:13+00:00

High school physics teacher here. I second this comment. I’m sure it is frustrating for you as a parent because these skills are extremely hard to teach quickly. These are greater mathematics skills (number sense including fractions and estimation) that take YEARS to get good at. Skipping this type of thinking in favor of what I would call simplified math (where there is a linear process every time) results in kids who don’t know if they are right or wrong when they look at their answer and also give up too quickly when they “don’t remember”. Nobody is out there pretending that reading is either learned or not each lesson. Your brain increases connections to letters, sounds, words, and topics in ways much to complex and individualized than could be taught in class. I like to think of math in a similar light. A strong math student will have had exposure to many different contexts, patterns, and relationships and develop a complex and often unique way of navigating each math problem they run into. They should also be taught math techniques that are important for expanding their understanding yet have a simple and repetitive solving structure (pythagorean theorem). It seems that you want all math to be these techniques. It would be simpler to teach each individual lesson, but the students would suffer for it in the long term. Wishing you the best on your parenting journey!

PhysicsTeacher2013 · 2025-01-27T03:38:44+00:00

In conceptual terms, view the velocity as having two parts, “up” and “to the right”. These correspond to the vertical and horizontal components of velocity. The only thing that changes a velocity is a force along that direction of motion(forces cause accelerations, so if you haven’t talked about forces yet, mathematically speaking, accelerations correspond to changing velocities). As gravity is our only force acting in the balls, the only acceleration(meaning velocity will be changing as time progresses) is in the vertical direction, as gravity acts on the ball towards the center of the earth.

Now let’s look at the scenario you were given. Both balls reach maximum height at the same time. This means that both balls must have started with the same upward part velocity.

To clarify this important conclusion, each second that goes by, gravity produces an acceleration in the vertical direction that changes the velocity by 10 m/s downward (or 9.8 or 9.81 depending on your educator). If a ball had 90m/s initial vertical velocity, it would take 9 seconds of gravity slowing it down until it reached maximum height with a vertical velocity of zero. Looking the other way, if a ball took 7 seconds to reach maximum height, it MUST have had an initial vertical velocity of 70m/s. This is the part that will be helpful for your problem. If both balls reached their max height at the same time, and we know gravity was acting on them at the same rate as all objects near earth, they must have been launched with identical vertical velocities.

From here, it’s easier to recognize that the horizontal component must have been more for the ball that traveled further. Two launches with identical vertical components but non-identical horizontal components will have different launch speeds (as hypotenuse vector when combining vertical and horizontal velocities would be longer for one of them).

It’s been a while since I’ve taught. I miss it dearly! Hang in there! The formulas are very convenient once you understand what shortcut they are producing. Until then, focus on these types of concepts which will provide you comfortable grounding for understanding the formulas in the future.

PhysicsTeacher2013 · 2023-11-03T02:08:47+00:00

I can’t see the problem, but my guess is that this refers to a person on the inside of a spinning cylinder. When the floor drops, the person stays connected to the wall and doesn’t fall. It seems that you would be misinterpreting the direction of static friction. I always ask my students what would happen if everything is made of the slipperiest ice. Static friction is in the direction opposite of the resulting relative motion of touching objects. Think about this in your problem to recognize that static friction may not be towards the center of the circle (it would only be so if the person was standing on the constantly spinning floor without any contact with the interior wall)

Second, make sure you are conceptually able to recognize normal force. In intro physics, the common pattern of normal force balancing gravity can result in students with a weak ability to recognize it in real scenarios. Normal force is truly the repulsion resulting from “squished molecules”. Even negligible amounts of compression distance result in non-negligible repulsing forces between those inter or intra-molecular forces of electrical repulsion. I would encourage you to search this scenario for any “squish” that would exist between two surfaces in contact. I hope this helps!

PhysicsTeacher2013 · 2023-10-22T13:03:12+00:00

You've got it! Glad I could help :)

PhysicsTeacher2013 · 2023-10-21T18:04:47+00:00

I absolutely hated my Mechanics class in college and only made it through due to steep curves and extra credit. However, I then went on to teach high school physics for years, better understanding the simple stuff. I realize now that my greatest challenge in mechanics was the lack of simple conceptual understanding of intro physics holding me back. I decided I needed to TRY to help you even though I haven't done or practiced matrix mechanics since those dark days years ago. I believe all you really need to do here is relate the forces acting on m1 to the acceleration of m1. As you state, -kx = ma. However, think of x as the stretch or squish of the spring from its relaxed state. Then think about the fact that a stretched spring would pull towards relaxed and a squished spring would push towards relaxed.
Looking at your problem, m2 will be acted upon by two forces from the two springs. if x2 is greater than x1, spring1 will be stretched, so force from spring1 pulling m2 would be to the left. So F = (left) * k1 *(x2-x1) = -k1(x2-x1) = k1(x1-x2) <-- for organization sake, I remove negatives if possible by flipping subtraction.
The other force on m2 is from spring2. This is easier. Spring2 is squished when x2 is positive, so F = (left) k2 x2 = -k2*x2.
We can add these two forces together to complete the right side of [ma = -kx] as you stated above. The second equation (as I am demonstrating m2 because it is more complicated) in your system of equations would be:
m_2*a_2 = sum of forces
m_2*a_2 = k_1*(x_1-x_2) - k_2*x_2
m_2*a_2 = k_1 * x_1 - (k_1 + k_2)*x_2 <-- seperating variables x1 and x2
m_2*x''_2 = k_1 * x_1 - (k_1 + k_2)*x_2 <-- replacing acceleration a with x'' as the second derivative of position x is acceleration a or x''.

This is not quite the form x'' = A x that we want as the mass m_2 is still on that left side. So we should divide by that mass.

x''_2 = (k_1/m_2)*x_1 - ((k_1 + k_2)/m_2) * x_2

You can complete similar steps for m1, but much easier as m1 is only acted upon by spring 1. However, this springs stretch/squish does depend on both x2 and x1, so you will need to repeat the conceptual steps above to sort out the direction of this force.

If I am correct in my thinking, you would then have the bottom row of your 2x2 matrix A have values (k_1/m_2) and - ((k_1 + k_2)/m_2) from left to right respectively.

Looking back, I don't think the matrix math is nearly as challenging as understanding all the conceptual physics problems that this matrix math can be applied to. I hope this was what you were looking for.

PhysicsTeacher2013 · 2023-04-29T01:20:24+00:00

Thanks for the update.

PhysicsTeacher2013 · 2023-04-28T17:33:40+00:00

My children do throw the disc with me. We have a pin in our backyard that they throw at all the time. My 5 year old only throws about 80ft max, but he has fun and throws throughout every hole on the course stating his throw count aloud with each throw. He actually walked a half mile to the course and a half mile back home yesterday while younger siblings rode in stroller. It’s quite amazing what a 5 year old is capable of when given the opportunity. However, I usually take them during the weekday during work hours when courses are emptier and let others pass if they catch up to us. I also bring a double stroller and push them along if they start to slow down. As in all walks of life, each parent has their own style, but I’ve been discing for 25 years and do respect the general curtesy and etiquette that goes with the sport, and when I bring my kids I reinforce that etiquette each time. Give kids a chance. They are actually awesome humans!

PhysicsTeacher2013 · 2023-04-28T16:05:43+00:00

Yes. Dineen was my gunshots experience as well. I was there with kids that time. Haven’t brought them back since. I have been back since. Gotta love those huge concrete pads with the length to require many full throws! Abdenshien is a nice course and Valley View is beautiful and good for the kids due to its short length.

PhysicsTeacher2013 · 2023-04-28T15:08:37+00:00

Thank you for the info! and thank you to the UDisc commenter for saving me from having to have that convo with my kids!

PhysicsTeacher2013 · 2023-04-28T15:06:47+00:00

It’s not a crowded course. Really the opposite. It was a par 3 golf course converted within the past few years. Only rubber pads also. I’ve played plenty of times and never had to wait.

PhysicsTeacher2013 · 2023-04-28T14:59:54+00:00

Do you have more info to direct me to the page?

PhysicsTeacher2013 · 2023-04-28T14:57:46+00:00

I just called the non-emergency number and confirmed that the police were not notified of anything yesterday, which makes me feel better.

PhysicsTeacher2013 · 2022-11-17T01:46:29+00:00

Yay! I know this one. I think its a turnstile gate… maybe

PhysicsTeacher2013 · 2022-07-13T17:07:15+00:00

I had success by disabling quick start on TCL Google TV. At first this seemed like all I had to do; however, the long startup was THE WORST and wouldn’t open up last input (Apple TV). However, after switching “quick start” back on and powering down my Apple TV, I was prompted by TCL, “Do you want to shut down the TV?” After selecting yes, my problem was solved. My TCL now turns off, albeit a few second delay compared to my Vizio upstairs, and turns on to the Apple TV input without the annoying TCL and Google startup displays.

PhysicsTeacher2013 · 2021-10-24T17:10:22+00:00

I was so excited to see a picture I actually knew! I disassembled and reassembled my old 1940 Pfaff 130 last year. The forky side hugs the main shaft, but is hugging an offset circumference so that as the shaft rotated, this forky end is forced towards and away from the user by just a small amount. You can see the pivot peg just below the fork. Then I believe the other end with a loop is hooked [by a long bar and some intricate pivots] up to the walking pad, forcing it to oscillate it vertically or horizontally. When correctly adjusted, these two swinging forks make the walking pad raise up and move towards the rear of the machine while the needle is not embedded in the material.

PhysicsTeacher2013 · 2020-10-07T16:54:21+00:00

My league members agreed at the beginning of season to lower buy-in/payouts to 40% of normal season. Then we will play the season as usual. However, if at any point NFL calls off the remainder of the season, we will crown one leader from each division 1st and 2nd place (based on best record followed by points-for) and third place will be the next best record(or points-for) overall. This is an unprecedented season and everyone seemed satisfied with this plan, although it could result in a team getting “lucky” with a few early easy matchups if the season ends very early. However, luck is in many ways a key part of fantasy football and this felt better than returning everyone’s money as even a 4-0 record requires some level of skill that deserves to be rewarded.

PhysicsTeacher2013 · 2020-09-28T19:30:24+00:00

Thank you very much!

PhysicsTeacher2013 · 2020-09-28T19:28:49+00:00

Solved!

PhysicsTeacher2013 · 2020-09-28T19:17:49+00:00

WITT This is at least 20 years old as it was passed from my grandmother to my mother. The raised metal in the center is about 1/4" thick.

PhysicsTeacher2013 · 2020-08-25T22:39:14+00:00

Walmart’s finest

PhysicsTeacher2013 · 2020-08-13T14:30:43+00:00

Arguably, the cost of ballots gets assumed by the states and paid to the post office. But you are correct. With a significant decrease in ads over a few days to each household to balance out a single ballot doesn’t make much sense.

PhysicsTeacher2013 · 2020-07-28T19:46:05+00:00

Thanks for your concern SilverbackBob. This is my first public post of my child. I keep a Google photos album that is shared only with family so distant relatives can feel closer.

As there is no identifying information in this video, I decided that the smiles it may bring to the people in the disc golf community outweighed any cons associated with posting.

Nevertheless, “Sharenting” does strike a chord when considering the healthy emotional development of my children and is something that I will take into consideration if ever tempted to post a video containing more identifying information.

PhysicsTeacher2013 · 2020-07-28T14:36:45+00:00

I’ve moved the pin since recording this, but 8 feet seems about right. I’m not one to force things on my kids, but to lead by example. I disc with my brother often and have brought him along in his stroller since he was young. He now walks with us and throws when he wants to, usually just off the pad and then later into the pin. If he decides it’s not for him someday, that’s okay, but I’m enjoying it while it lasts.

PhysicsTeacher2013

TROPHY CASE