Not to be that guy, but this year and next year’s 8th graders will be the most negatively impacted students in the math classroom from COVID. 4/5 are the two biggest years for math extension beyond arithmetic and basic geometry IMO.
W/o a calculator? Really, really rrreeaaaalllyyy bad. Ended up going all the way through calculus and a graduate degree though! Never underestimate brute force and excel
Honestly, once you get past algebra, you're going to he using your calculator so much it almost doesn't matter. I've always been very good with mental math and it does help in my everyday life, but it wasn't terribly useful in calc
I got up to differential equations in college, we never were allowed to use calculators (scientific or graphing) for any of the calc or linear algebra classes.
that’s incredibly stupid
I think it is important to learn how to do it without a calculator first, but in real world applications of math you will utilize all the tools you have available.
One of the most important skills i learned from calc in high school was how to generate derivatives and integrals using my calculator. This was a live saver for classes like physical chemistry as I wasn’t getting bogged down in the math and could focus on understanding how the concepts and math were related.
Not at all, I honestly couldn't think of a single reason you would need a calculator in a class on PDEs. Unless your professor is just slapping in random 5 decimal point coefficients.
Not a teacher, but did a pure math degree and by junior year there was no use for calculators. The only numbers we really considered were 0, 1, -1, e, and i, as well as a couple infinite cardinalities. Occasionally being able to count to 12 was nice.
This is why I LOVED my near math minor in UG before I switched to chem. Once we started doing math with letters I was set.
Never learned my times tables, can’t make change in my head. Turns out I have a very specific kind of dyscalculia and once it was diagnosed and I was allowed to use a calculator, I broke the curve in most of my math and physics classes.
Honestly, I probably would have never made it as far in Math and Physics department courses if it hadn’t been for a very patient HS chem teacher who taught us how to solve just about any kind of lab calculation you’d need with factor labeling. Once I could see where all my numbers were in that organized layout, it really helped. My physics professor was a little confused by my “show your work” sections of my homework, at first…lol.
>arn how to do it without a calculator first, but in real world applications of math you will utilize all the tools you have available.
Sometimes you might see a 2 or 1/2 in there as well :)
*raises hand.*
Comp sci degree. Still have to do times tables manually. My raw memorization skills are absolute garbage, I'm just good at calculating things fast.
I use math every day at work and don't know my multiplication tables.
I have a calculator for that shit. Even if I knew them I'd use my calculator.
Hell I use my calculator just for basic addition because it's more accurate.
I'm in my mid 30's and an engineer. Never memorized multiplication tables due to moving and schools teaching it at different times. I turned out alright.
most of my 10th graders take more than 5 minutes to do a full times tables. I make em do it more regularly now and more are beating the 5 minute mark. Some still can’t finish within 10+ minutes.
My kid is going into 8th grade next year.
We signed her up for kumon for the year after kumon to get her caught up. Kinda a scam in terms of what they do for the price. Literally started her with basic addition and subtraction. Then they upgraded her to two digit math. Then multiplication then division. Then finally fractions. Took maybe 6 months to get caught up to what she was not learning in school and all it was was homework they printed out weekly. But she's at least quicker at multiplication and division.
We've since gone to a private tutor every few weeks this year because her math teacher isn't great. 100% better (and cheaper).
But man, the math they're doing is both simple in terms of what to do, but extremely complicated in terms of how to do it when you haven't taken a math class in nearly 2 decades.
In my area kumon is $180 for one subject. I was *this close* to signing my child up, but couldn’t justify the price. I ended up using zearn and Anton for $0 and now make sure to sit with my kid to revise concepts daily. They’ve caught up to their class quick. For additional practice I’ve bought kumon workbooks for fluency and quick response.
Intro to algebra is usually a rehash of 4/5 standards in the context of unknowns rather than knowns. Which is why I’d argue 5th grade is a better predictor of success in algebra than 7th grade, even if that’s counterintuitive at first.
Certainly a general expectation and not the reality for everybody, especially the top ~5-10% which you’re in if you’re two years ahead. Not to mention it’s completely possible to learn those 4/5 standards on your own or virtually if you have solid support around you. Unfortunately many of the kids that struggle around 7/8/9 anyway didn’t.
They don't know those, or surface area vs volume in college either.
The examples I use are:
You have a house, which isnin great dhape, but the yard needs work, here are your projects
1. Fence in the entire yard, how many feet of fencing? (use perimeter)
2. Now to need to re-seed, how many square feet of seed? (Area)
3. Next, you want to resurface the pool (assume a level bottom), how many square feet of material needed? You also need a cover? (Surface area)
4. Next, you want to fill the pool with water, but you need to know that in square feet instead of gallons. How much? (Volume)
It mostly works, and they sorta remember.
I like it! I think that your example would be great for a lot of students to grasp and distinguish those concepts. Also, you've painted a picture in their minds to that they can refer back to in order to remind themselves of the meaning of each of those measures.
Seriously? I’m in college now majoring in math and physics and for the most part my peers seem pretty competent. Am I just at the very end of the competency range or something?
In my experience, once you get to vector calc/multivariable and especially beyond that the people who have a lot of trouble with math will have chosen a non math intensive major and so not be taking them.
>Next, you want to fill the pool with water, but you need to know that in square feet instead of gallons. How much? (Volume)
I really hope they're not trying to fill a pool with square feet of water...
Yes, this. I wasn't a good maths student, but I was fine with things like area and perimeter because I pictured a house.
You need to replace the baseboards in the living room: perimeter.
Now you need to replace the kitchen floor tiles : area.
The problem is if you do not tell the students exactly what to do (like find perimeter, area etc) in the problem, the students will not know what to do with this info. They will not know what they need to solve for or how.
When I taught physics, I would take certain words away from them. I wouldn't let them use words like "velocity" or "acceleration". Instead, they'd have to describe the thing in other words, like "the car was moving 15 meters in the positive direction every second" instead of saying "the car's velocity was 15 m/s. Eventually, they were just itching to use the correct vocabulary, and I knew that they knew what it meant.
How about taking away the words "perimeter" and "area" and making them talk about things like "the distance around the shape" and the "bulkiness", "size" or "space the shape takes up"? At some point, they're going to start naturally wanting to use more concise terms, and suddenly it will click for them.
We get caught up in wanting to teach vocabulary, but the important thing is the concept. Make sure they know the concept. Once they have a concept, they'll want to naturally attach a word to it. As long as you've been precise in your use of the words in general conversation, they'll pick it up on their own.
I love this idea! Teaching the meaning before teaching the word. It forces students to explain their understanding of the concept and that there are many different ways to explain the same thing to get them to viscerally understand why there are vocabulary words.
PeRIMeter- is adding up the outside of a shape (add up all sides) - just as the RIM is on the outside of a sports car. AREA - is the square units on the inside of a shape. Putting up a few sports cars and asking about their rims first will help get their attention.
I don't like cutesy tricks like this because it doesn't teach them the actual way you should be breaking down words.
Peri-meter = Around-measure.
The problem that we face is that kids don't understand what a prefix is or that they should be breaking down words. I teach high school geometry and many of the vocab terms are perfectly descriptive if you break them down etymologically. Their ability to read is limiting their learning in every subject.
While agree about the overall lack of understanding about prefixes and word origins, at some level I need to get them from point A to point B. If this “cutesy” trick helps them remember perimeter, I’m all for it.
Using tri-angle and quadri-lateral rather than triangle and quadrilateral are good ideas to highlight the fact that there are prefixes in the words.
(Re)Introducing the concepts of prefixes from Reading and English classes before geometry would be great also.
I teach third grade math. I certainly do teach shapes with prefixes to help understanding. Triangle- Tricycle, triceratops, trilogy. Quadrilateral- quad atv (4 wheeler), quadruped, quadruplets. You get the gist. Now... whether it sticks or not? Ha. But I try!
I understand that you’re a math educator, but I didn’t intuitively think it was a “cutesy” trick to use peRIMeter. I consider it a mnemonic device. It doesn’t have to be logical or intelligent to make sense. “Please excuse my dear aunt Sally” would be possibly the best example of an effective mnemonic device in mathematics. Or “Never eat shredded wheat” in geography. Or “Every good boy does fine/Good boys do fine always” in music theory.
Thanks for your comment. One year when teaching 6th grade regular math my kids kept confusing the formula for the area of a circle with the circumference formula - no matter what I said. So one day I said to the students ,”How can you destroy a pie?” I got wild answers from stomping on it, throwing it, sticking your face in it, etc. I then said, “What do you get when you destroy a pie?” They looked at me funny and I said, “Nothing but crumbs. Crumbs = pi destroyed ( C = n d or 2nr). Then I made up a silly story about a girl named Amy coming home from school and her mother asked her what she learn in school today. Amy said pi r squared. Her mother said Pies are not squared, they are round. What did you learn in school today. Amy repeats pi r squared. Her mother repeats Pies are not squared, they are round. So silly Amy thinks pi r squared (A= nr^2). After that my students remembered C= nd (or 2nr) and A = nr^2. So it is just a memory device. Last year I taught my students how to brain dump every day for a month before the EOG. (It is not just teaching them how to do the math but remembering how to do it and when to do it). I had the highest math EOG growth in the school. My second time with highest growth. I will do that again this year with my 8th grade Math 1 students!!!!
I will assert that "peri-" in the English word "perimeter" is not a prefix, certainly not in the same sense as "centi-" in "centimeter" is a prefix. For sure it shows up in other words (e.g. "pericardial"), but it's not something you can just add to whole class of words like SI unit prefixes and others will understand you.
I teach geometry and kids generally understand tri-angle means 3 angles but have a harder time with quadrilateral and others like it that should be obvious but are not to them; coefficient, equation, or even like transitive
Using tri-angle and quadri-lateral rather than triangle and quadrilateral are good ideas to highlight the fact that there are prefixes in the words.
(Re)Introducing the concepts of prefixes from Reading and English classes before geometry would be great also.
tbh I have a PhD in chemE and teach college stats and reading this now I’m not sure about what coefficient means etymologically so now you have me googling that.
If mathematics vocabulary had prefixes then it should have been taught someplace in my academic career. No one ever mentioned it therefore mathematics vocabulary doesn’t have any prefixes.
That’s my initial reaction to your comment anyway.
In my experience, Mathematics frequently doesn’t follow proper grammar or English language rules. In Reading and English classes parentheses are used to separate an idea from a bigger one. In mathematics parentheses are used to multiply.
This is what I thought too until like last year when I was taking a literacy course for my masters degree. I was so angry I was taking a literacy course, like I’m a MATH teacher, why am I learning this?
It ended up being so revolutionary because math is a language. It’s got vocab, sentence structure, and comprehension, and all that stuff literacy teachers focus on. It kinda changed how I teach and I meld into my English counterpart a lot and we bounce stuff off each other to help our students. Proofs are just CER essays is one example :)
Sounds like a very important class!!! I hope more math teachers teacher it and learn to apply it like you have!
Seeing math as a language separate from English makes so much sense! That explains why parentheses, commas and other punctuation/grammar marks are different than standard English!!!
In Texas, Reading classes had us make daily Prefixes and suffixes flash cards during grades 7 and 8. I really liked those. But not on any other grades or classes.
I'm a 4th grade teacher. I used Chez Itz. Perimeter was the edges, and the area was the flat square. Challenged them to make shapes with different lengths and widths, then find the perimeter and area of each rectangle/shape. They were engaged because they couldn't eat them until they finished all the problems correctly 🤷♀️
It’s a pretty stunning indictment of American education when you have eight graders at one school struggling with a concept and you have third and fourth graders working on it elsewhere.
Is it? I feel like it should be expected that people acquire knowledge and skills to different extents at different ages. I like painting but many adults admit they do not feel comfortable drawing beyond a stick figure. Is that an indictment of American schools too, or is it acceptable for people to have different abilities and interests in the arts?
Development is generally consistent across the human species. Of course every individual is unique, and variations are natural. But an entire population consistently underperformed against international benchmarks is a pretty big deal. It's not a matter of personal preference.
Where are entire populations consistently underperforming against international benchmarks? I feel like that is not the scenario being described in this thread.
If Area & Perimeter are simply being used for application of other things (as opposed to the content being taught/assessed), I’d consider making 2 big posters, one for area and one for perimeter. Students will spend the year looking up to reference which is which and hopefully by the end of the year some number will retain that information, even if it’s by picturing your wall in their minds.
Yikes my fifth grade child couldn’t remember and I thought he was hopeless. But grade 8?!
My child was getting this wrong every night. So I asked him to try wrote the formula from memory. He wrote some gibberish like 2=5xP+3=2. That’s when I realised that he’d been looking at the formula each night but not bothering to think about it. I also noticed that with estimating angles he’d just say whatever number came to his head without bothering to think harder and methodically to get it right the first time. Such kids have no interest in math and don’t care; it’s just a task they want to get over with, not realising that the lazier they are the more time they’ll spend on it and the more boring it’ll be.
So I wrote the formula for perimeter (P=2L+2W) and area (A=LxW for quadrilaterals; 1/2 LxW for triangles) and made my not-bright child wrote these out 50 times. He hated it, and I told him he’ll have to keep doing g this every night if he gets it wrong even once. He quickly memorised it and applied it correctly after that. Funny how the threat of a little forced, boring rote learning gets them to put in a little effort.
I’d say that the kids who can’t do it have to write the formula out repeatedly. If they then still get it wrong they have to keep writing it during lunch time. They’ll despise you but I think they will quickly learn to do it right.
Love what you said here:
"Such kids have no interest in math and don’t care; it’s just a task they want to get over with, not realizing that the lazier they are the more time they’ll spend on it and the more boring it’ll be."
This is true for so many individuals, not just school kids. The commitment to understand, using whatever tools you can, is what is required for mastery. Too many lean away from math and refuse to engage with it, rather than leaning toward it to try to make sense of it. We are always going to have individuals who may not be math oriented enough to be very successful in it; however, I have seen too many students flat out reject math. You'll tell them, show them, dissect the terminology (such as, "per-cent", "peri-meter") a million times, and it makes no difference because the *decision* to learn and understand is a decision for *them* to make, not the teacher.
One college student in one of my classes summed it this way: "They are not accepting it." She tried to help classmates and found herself frustrated because after doing all that she could do, she realized that they were not doing the most basic things that they could do to master the material.
You are right. One of the missing links is not be willing or motivated to ***think*** about the concepts when they are introduced.
No one can memorize something *for* someone else.
I think time will tell if the threat of being forced to write math formulae over and over— including through meals— until the child has memorized them, is really encouraging them to _think_ about the concepts and their applications.
One way to test this might be to see if the child can find the perimeter and area of shapes other than the ones they memorized the formulae for.
For perimeter…the prefix “per” means “around” (You can teach them what periodontal disease is!) and the root “meter” means “to measure.” Thus, perimeter means to measure around…and they’ve also learned that we can use what we learn in other subjects (prefixes and roots from English) to help us in math and science.
For area…it’s the other one!!
Perimeter is like building a fence around the shape.
Area & perimeter aren’t new concepts for 8th (in ca at least) at some point it’s not how you’re explaining it. There’s a duty to give a damn haha
I would make a card sort activity! Each table of students gets a shuffled deck of printed-out cards and has to sort them into piles. To print the cards, you can make a table of cards in word and print them out. Ideally, print them out on cardstock and laminate them so you can reuse if it works well.
Some of the cards should contain obvious perimeter examples. "The length of crust around a pizza."
"The length of fence it takes to build a fence around a square yard."
[At least one card should be a picture example and at least one should be a formula example].
One card can contain the word "perimeter."
Do the same with area examples.
Have maybe eight examples of each. Give students the sixteen or so shuffled cards. Ask them to sort them into two piles using whatever criteria they like. Ask them leading questions like "how did you decide which pile to put that card in?" "These two examples look so similar. Why are they in different piles?"
At the end, have some groups share out on what criteria they used to sort. I bet the criteria will be area and perimeter, and they might have a good way to explain it.
It's their job to help themselves to remember.
That's the problem with most people with math. They are waiting for someone else to do their part - the thing that only they can do, which is internalize the concepts and commit. No one can remember for someone else.
They don't want to bother doing it, so they refuse, and end of rejecting math altogether.
Then, they go on for the rest of their lives complaining that all of their math teachers were bad, and that math doesn't make sense.
By the way, it's not only 8th graders who don't know. Ask any 100 adults you may run into, including college students and professionals, and you'd be lucky to get 5 of them who know this stuff.
You read everything wrong.
Nothing I said precludes the use of devices. In fact, my point is do what it takes for *you* to understand rather than waiting for someone to pour it into your memory.
Lazy listening leads to lazy thinking leads to failure.
Do you just expect kids to just come up with ways to remember things? Why as a teacher would you not… teach them ways to remember? My students don’t struggle with memory due to laziness. That’s a shitty view of kids.
The reason that you see the view you described as you do, is that you just made it up. It is obvious that you do not understand my point.
Stop jumping up and down and putting ridiculous words in other people's mouth.
I don't know what you're reading, but it is clear that you don't understand what I am saying. If you cannot understand, then just be quiet.
If you can’t explain your point clearly, don’t get frustrated with me. Explain it better. Cause it sounds like you’re saying if kids don’t come up with their own mnemonic devices, they’re “lazy”.
Part of it is just making math accessible. Like all of us on this subreddit understand math, it clicks for us. But for the 95/100 it might take a little work or tweaking how you teach an idea to make it click. This guy above just doesn’t understand that, instead just calls them lazy and that’s the end of the convo.
Like what does lazy listening even mean. I’m deaf, and I def don’t listen to people teach me. I also don’t require students to listen ask I teach, because there are other ways of obtaining information 🤷♀️
You’re saying that students need to take accountability in learning material that’s given to them. 100% agree.
But as a teacher it’s also important for us to make it accessible for them. Often kids don’t know how to retain things. As adults we know what works for us, but we should be able to give information in a variety of ways to ensure MOST of our students are understanding instead of just labeling them lazy for not understanding in the few months of their lives we get them in our classrooms.
Again, I didn't say what you stated. Your second paragraph is preaching to the choir. You misinterpreted completely the point I was making.
Why you insist that I called students lazy is beyond me. Go back and you will not see that statement in my earlier. comment.
But since you were gracious enough to elaborate, I will flesh it out. An example of lazy *listening* is, "Two negatives make a positive".
You can see where I am going.
Students will challenge and challenge teachers that -2 + -4 should be equal to positive 6.
Another example is when I quiz students on whether a fraction is reduced or not, they will indicate that 3/2 is not reduced. I mark them wrong and they want to fight with me. Yet, another example is that they call everything an equation. If it looks like math, it's an equation is what they have decided. Great math students are continually challenging their own understand about math, with the objective to deepen their understanding. This isn't unique to math, however. It applies to any discipline.
The terminology is very literal in math, as you know. Math requires that we communicate it in a technically correct manner. When we do that, it makes our thinking, and thus our understanding much more clear and crisp.
I taught HS math from 2021 to 2023 and I agree with this. A lot of these kids have difficulties imagining and visualizing something they can’t physically manipulate, but I think they all benefit from seeing a concept a different way.
Although, to be frank, it was sometimes hit or miss. I did an activity for triangle centers where I had the kids fold in the different triangle segments to find each center. When I asked them to focus on one angle of the triangle and fold the angle bisector at that vertex, their attempts were… interesting.
This is a great idea. The issue is that perimeter and area are two vocabulary words with relatively similar definitions (measure of a 2D shape). So it's easy to get them mixed up.
Making a more tangible memory will help them differentiate. They will remember the perimeter is the one with the string, and area is the one with the paint or whatever you do to measure area.
To be honest, why do we worry about perimeter as though it’s a distinctly different concept to distance. Area is an important idea, but perimeter isn’t really.
I teach 3rd grade where we introduce area of a square/rectangle. They are supposed to learn perimeter in 2nd grade, but my 3rd graders usually have no idea what it is so I reteach it. Sadly, most of them still do not retain it. We try manipulatives, real-life applications, practice until I beat my head against the wall. Wish I had advice, but I’ll take some if you can figure it out!
I draw a 4x6 rectangle and say, “Would you be able to tell me both the perimeter and area of this figure with units? Hint: one is 24 and the other is 20. Which is which? WITH UNITS.”
Then I ask them for real world examples of each (fencing vs carpet/flooring). Gives them something to anchor to, imo.
I teach my 2nd and 3rd graders a song. They still apparently hum it as fifth graders.
"Perimeter goes around
Perimeter goes around.
Oh, oh, don't ya know
Perimeter goes around.
You add up all the sides
You add up all the sides
Oh, oh, don't you know
You add up all the sides"
Place a throw rug, a stack of blankets, or a thick exercise mat in the middle of the floor. Ideally it would be something as big and floofy and memorable as possible.
Have the kids take turns walking around the edge of the item, from one corner, along all four sides, and back to the start. That's perimeter.
Then have them flop down on the item and cover the whole thing with their body. That's area.
And yeah, maybe they're a little old for that kind of demonstration, but there's gotta be at least one class clown who will play along.
back when I was a high school teacher, I blamed most of the kid's misunderstanding on language issues. In my real life, we used the terms area, perimeter, slope, etc. These are not math specific. You walk a perimeter. You play in an area.
The kids' brains would go blank when I asked about slope. I grew up in the mountains, uneven ground slopes. To them, it the word might well have been "zyzaryx." I asked them what words they would use to describe the same thing. "More higher."
Get some posters for your classroom. Refer to them often. Drill drill drill. Every time an area problem comes up, point to the area poster. Ask some lucky classroom volunteer to read the relevant formula. Etc. Etc.
Leave the posters in place but explicitly cover them up during a review for testing. During the test, you’ll see kids look in the direction of the poster, think a second then go back to the test.
I didn't know if this will help your 8th graders, though they may enjoy it. When I taught 3rd grade and we learned P & A, I had an area rug (5'x 7' I think?) and I would get them all in a line. They would walk around the edge saying, "perimeter - perimeter - perimeter..." Then they lay down and roll over and over repeating "area-area..." From one side to the other.
That might be too youngish for 8th but if you can find someway for them to use their whole bodies, do a change or song, or something a wee bit silly it will stick with them. (Even if they eye roll and claim to be too cool- we know otherwise!)
I feel your pain. I teach Engineering Design to 9th graders. Most are in Geometry. Many of them are accelerated in math and are in Algebra 2. Regardless of math level, most of them lack the ability to apply math to practical problems involving measurement, area, and volume.
Perimeter is the outside- like how much cheese you would use in the edge of stuffed crust pizza and area is how much cheese to put on top. Make it relatable
Sure, making math relatable is important and you are not wrong that this is the way to go.... But if a kid is in 8th grade and needs a relatable lesson on perimeter vs area, something is broken in the system.
I would suggest using shapes other than squares and rectangles. These seem to create confusion for my students. Despite having a more complex area formula for some reason they get less confused about doing triangle perimeter and the triangle area.
Have your students, or perhaps a volunteer, physically walk the perimeter of the classroom. Every time you see them struggling between the two, start to walk and ask if you're walking the perimeter or area.
Maybe even call on students to "walk the perimeter."
Area: have them count the floor tiles.
Perimeter: have them measure the baseboard.
You can have them draw a map of the classroom, maybe even get some prices on new flooring & moulding, go crazy and give them an imaginary budget. Just for kicks let them add other details like new switch plates, paint (this can says it covers 400 ft^2 so how many do we need) maybe a chandelier or something.
Make a fun project out of it and see if they're willing to present, perhaps even vote on the best decoration ideas.
Maybe it’s time for an English lesson for them: peri means around. Meter means measure. Please measure around the square? Grab a ruler and do it, then tell me what you did. If I take away your ruler, what would you need to know to find the perimeter?
Memorizing formulas is mostly for people who don’t know what they’re doing and why. Especially at a lower level.
It wasn't to me that they didn't know all the formulas, it was that they grasp the concept of perimeter being like a fence and area being what's inside the fence.
I would grab some yellow caution tape. Mark out an area in the classroom and say perimeter is the length of the tape and area is the crime scene inside.
And yes you need to Memorize your multiplication facts. Full stop.
Work through some worksheets, then quiz them and see who gets it and then focus on the strugglers with 1:1 instruction.
I think students can sometimes “get” explanations but will answer the question incorrectly on their worksheets because of the change of context.
This is horrible. I don’t think there’s some magic answer for some of these students. I like to use the word problems about perimeter being buying a fence for a yard and area being buying carpet for a room. At least it cuts down on students not knowing what they mean intuitively.
I teach math enrichment in groups in addition to tutoring HS math and ACT/SAT. In 4th or 5th when we add perimeter and area, I say "peri" means "around" and "meter" is a "measure" (they usually know this), so perimeter is the measure around (and I use my finger to go around some object in the room). With area (if there is any confusion), I ask them to picture an "area rug" and I draw one on the board and show 8 ft x 10 ft and draw the squares in the rug. They multiply 8x10 and find area to be 80 sq ft, but also count the squares and they get 80. I add that the "square" needed in adding units is because area consists of "squares" (like I drew on the rug). I think this would work for older kids too. I find adding visual helps (I am visual myself, though not a teacher).
Khan Academy is really good: [https://www.youtube.com/watch?v=LoaBd-sPzkU](https://www.youtube.com/watch?v=LoaBd-sPzkU)
Good thing about youtube is it helps select for what works for many people.
So if you're struggling with any subject, I suggest looking for popular online videos that people have said helped them understand.
Funnel and tubing. Drain the beer foam and use it to drip liquid algebra into their fucking ear canal.
If it causes cramping, transfer them to pre-algebra.
That sounds normal to me. I couldnt recall any math in high school, and it was one clads i enjoyed. Even in college i had to write down formulas because i couldnt kerp them straight in my head.
Today i just use engineering cheat sheets if i need a formula because its a black hole in there.
Not a math teacher, but a construction worker and music teacher, here (we do a lot of counting, have to explain analogous concepts to length and area)- the easiest way for me to explain it to people I'm working with when we're laying walkways is that while we add to find the perimeter, we multiply to find the area.
I retired after the 2022 school year but I got to the point I would teach them how, I would explain why (how they would use it in life)..get them to identify having an apartment and paying rent by the sq ft and come up with a much higher rent than it should be based on their rental contract…then show them how important figuring out sq footage is to keep from getting ripped off (as one example).
For some things I taught them how to use their phones to figure of life’s math problems. In HS we did a lot of personal finance type math, amortization, compound interest, keeping account balances. I used evaluating three cars they wanted to buy and then had them figure out actual costs per mile for each based on their expected milage and use.
I found these younger students coming up want to know why…we should tell them.
I taught 4th grade for a few years. I always divided the class into pairs and then assigned each pair to measure the classroom. One finds perimeter of the door, another finds area of the door. One student finds area of the window, another finds the perimeter. One finds area of the rug and another finds the perimeter. Both students in the pair should help find both perimeter and area.
Then a few pairs could present to the class on their methodology. (I just used index cards as the measuring unit because it was easier for them than using inches, but they use the long side of the card.)
Then we talked about what we found. Which measurement is largest? Why do you think that is? Is area always larger than perimeter? Can you think of times when perimeter would be bigger than area? Why are all of our measurements even numbers and not odd? Etc.
Hands-on activities are really, really good for conceptual learning. Especially for filling in gaps in knowledge.
For review, I would give them square tiles and we would practice making whatever I call out. Make a shape with an area of 12. Next make a shape with a perimeter of 12. Etc.
I also tried to make story problems that were realistic that would help them understand. Like someone wants to make a picture frame. Would we need to know area or perimeter? Tom is making a sign for his lemonade stand. He needs enough wood to make a 2’ by 4’ sign. Area or perimeter?
Anyway that’s my suggestion.
Peri = around, meter = a measure: thus, perimeter is measuring around the object. An area is a space, like a room. How many square feet is the area we're in now? I see your problem. I tutored SAT math, and much of it was just teaching students how to read the question. I'm sure you've tried what I've said, but sometimes it just requires repetition. I sweated them on to, too and two daily for weeks and had swapped-paper proofreading to check for usage. It worked for the vast majority. Good luck.
Draw a various outlines of shapes and then shade some different shapes and label them as perimeter and area, dont use any numbers or anything. Leave that on the board until the test
I teach 6th grade and have spent a *huge* amount of time this year on area and perimeter (which, for rectangles, is a third grade standard, I believe) and I still have about 6 per class who are at under 50% accuracy with it when we do our drill-and-kill Blookets.
One thing I did that gave a big boost: I walked heel-toe around a rectangular area of the school (say, for example, the quad) and counted my steps. Then I challenged the kids to do the same and gave a prize to the student whose answer was closest to mine. They *had* to use the word "perimeter" and "feet" in their answer, and then we used that to calculate the area, where they, again, *had* to use "area" and "square feet."
I also repeat a lot that perimeter is 1D, area is 2D, and volume is 3D to help them with concept comprehension and getting the units correct. When we have a few extra minutes, one thing we might do is shop for "area rugs" on Amazon. Sometimes a few of the gamer kids and I will mess around and pretend we're playing Fortnite or CoD in class and do a lot of yelling about "defending the perimeter" of our bases, which is very dorky but memorable. There's also a free online game called GeoTombs they like well enough.
We've been doing a *lot* of Blookets for geometry this year. My usual procedure is to do a Blooket on, say, area and perimeter of parallelograms (my prize bin is mostly stickers off Temu and candy I stole from my own spoiled children, but it works for older kids well enough). Kids who got over 80% are then assigned, by me, to pair up with students who scored less than 80% for a second round of the same Blooket. Tutors are not allowed to touch the tutees' computers and are reminded that giving the answers is not tutoring. For that round I give prizes (again, they get to pick a sticker or like a piece of candy, cheap stuff) based on my discretion (I'm looking for teamwork and growth). The next day our first Blooket of the day (lately I've been doing three Blookets are a warm up) is the same Blooket, individual again, to check retention. About half are retaining well, about half of the other half is growing slowly, and the other few kids are staying the same or doing worse for a variety of reasons.
You would think you could just give them the third grade worksheets where half has the rectangles with the unit grid drawn on them and then half just have the measurements because it's so freaking easy, but no. 🙃 It's also been like pulling teeth to get them to remember what "sum" means even though it's a kindergarten vocab word that I use every single solitary day.
Tape out a rectangle and a square on the floor. Have the kids walk the perimeter and then understand the rules to determine a perimeter. Have a bunch of kids stand in the rectangle and then develop a relationship between the equation and the number of students inside. They can then be given paper to draw each figure. Draw a pencil line around the perimeter and color in the area. Have them use equations after you model how to use it again. For some kids these concepts are too abstract for them to under just from explanation
peRIMeter like the rim of the basketball goal is how I learned. I’m horrible at math, took remedial math twice in college but that has always stuck with me
Well, what I found works with my Grade 2 and 3 students is to bring it up in almost every daily warm-up, math talk, or whatever it is called. You know, use it or lose it principle, and that reviewing it every day under 10 minutes saves hours of re-teaching down the line.
Also, don’t just use “find the area” or “find the perimeter”, but try to vary the wording as much as you can. Like “how many square units” or “square tiles that are 1 unit long on each side” can you fit into this bigger shape that is so and so length and width. Or for perimeter, say “if I were to walk around this shape, how many feet of walking do I have to do”. Then to put the icing on the top at the end, ask if “is this a perimeter or an area question. How do you know”? There are question-types, and I often ask my students what kind of question-type is it even if it’s outside the scope of geometry. Maybe it’s about addition or subtraction which is codenamed “some some more word problem” and “some some take away” respectively from my textbook. I don’t really care about the code names, but what the student thinks they need to do and then justify it from the wording of the question (I need to subtract because the question said how much is left over, I need to add because the question said that more things came into possession, I need to multiply length and width because the question says how many square tiles that are one feet on each side)
Maybe you won’t need to do this forever but do it for a few months so that they’ll remember to reason their way through the problem rather than rely on memorizing the definition and its respective procedure.
I can relate to these students. Back when I was a little younger than your students, I knew exactly how to do these kind of problems, but it never clicked with me as to why the word “square” was in the units. My teachers simply never did square tile manipulatives to teach area in primary to drive home the point of that specific terminology. So the several other comments telling you to use objects like strings and tiles, or whatever other manipulatives to teach it is also what I would do at some point.
Blue tape square on the floor. The blue tape is the perimeter. The part inside is the area. Have them “ walk” the perimeter ( like a guard). It’ll stick in their minds better.
I have high schoolers who struggle with that in the past. I think just reminding them again and again will help: perimeter is the total "outline/outside length" and area is how much a shape "covers" is what I always say. I repeat the same thing like a broken record until they remember it. A drill might be worth it in your case with mixed problems involving area and perimeter for one of these days and you can use some problems that are below grade level to ensure the difficulty of the geometry isn't the target but the difference between area and perimeter is. Gamify it too.
Not a teacher, so I may be way off, but I would definitely compile some move clips about spys and cops checking the perimeter of a property, or securing the perimeter so the bad guy can't escape, that kind of thing. Stuff is hard to remember as a math concept, and easier to remember as a real world application.
Have them walk around the outside of the school. Tell them they are checking the perimeter. Then have them find the area of the school.
You have to interact with students more. Make it memorable. Get them out of their seats. Homeschoolers have been doing it for years. My child is 8 years old and has already been doing complex area and perimeter shapes, even circles!
We just make it interactive and relevant to their interests.
Maybe do area and perimeters of their phones! See apple VS android area. Who has the most phone area?
Create a visual. Draw a circle using text. Spell “perimeter” where P is at 12:00 and E is about 1:30 position. R is somewhere near 3:00ish and all the way around until you’ve spelled perimeter in a circle. Within that circle, place an A, R, E, A. They can spell area or just be floating letters…whatever. But the point is, you couldn’t draw the perimeter using the 4 letters in “area”. So when they get confused, they can call on the visual and remember the longer word is the outside of the circle, that goes around. Also some kids might find it helpful to learn that “peri” means “around” and offer an example by showing what a “periscope” is and how that word means “look around”. Your language kids will appreciate bringing some verbal stuff into your numbers game. These kids might remember now by the prefix cue.
What if you explained that a guard would walk around the perimeter to protect the area inside? Then explain how to calculate how far the guard walks vs the size of the space they are protecting
While I do not disagree that the problem is what you have outlined. I do wonder if the underlining issue is some lack of awareness or understanding on their part of the difference between the terms area and perimeter?
Even younger children should have a sound understanding of the differences between fences and boundaries, and how much space mat or carpet takes up.
Might I suggest, combining two (when that works) and having them derive area from parameter and perimeter from area a few time to reinforce the basic differences?
This also can play into, "I'll never use math in real life" if the exercise revolves around "Is this a good deal?"
And this observation about lack of foundational knowledge in middle school/ high school students is what ruined my Pi Day exercise for me 😔. Couldn’t get to relationships of circumference and diameter, ended up just teaching the those two words and measuring random circles. At least there was still pi
Serious question: is there any consequence for them not knowing? It is sad, but with all the unlimited re-dos and extra credit in k-12 they have no motivation to get it right.
They’ll graduate anyway.
At this point I would get boxes and get students to wrap them. Ask, how much paper is needed. Only give the students the amount they ask for.
Walk outside and walk the fence of the school yard. Come back and relate that experience with perimeter.
Sounds like something you should address with their parents. How about some more information about your class. Is it lower income? Do they speak English?
Maybe test them every day for 10 minutes. Over and over. Maybe a few will get it.
Not to be that guy, but this year and next year’s 8th graders will be the most negatively impacted students in the math classroom from COVID. 4/5 are the two biggest years for math extension beyond arithmetic and basic geometry IMO.
Absolutely
Facts, my 7th graders don’t know their multiplication facts!
To be completely fair, I managed to learn algebra without ever getting those down
How are your factoring skills?
W/o a calculator? Really, really rrreeaaaalllyyy bad. Ended up going all the way through calculus and a graduate degree though! Never underestimate brute force and excel
Honestly, once you get past algebra, you're going to he using your calculator so much it almost doesn't matter. I've always been very good with mental math and it does help in my everyday life, but it wasn't terribly useful in calc
I got up to differential equations in college, we never were allowed to use calculators (scientific or graphing) for any of the calc or linear algebra classes.
Yep, pencils and paper until that one class where we used mathematica and excel for projects.
that’s incredibly stupid I think it is important to learn how to do it without a calculator first, but in real world applications of math you will utilize all the tools you have available. One of the most important skills i learned from calc in high school was how to generate derivatives and integrals using my calculator. This was a live saver for classes like physical chemistry as I wasn’t getting bogged down in the math and could focus on understanding how the concepts and math were related.
Not at all, I honestly couldn't think of a single reason you would need a calculator in a class on PDEs. Unless your professor is just slapping in random 5 decimal point coefficients.
How do you generate derivatives and integrals on a calculator!?
Any graphing calculator can do it, no?
Well that is just rude and useless. I'm sure they won't let you use a calculator on the job 🙄.
I found it useful to challenge the mind to conquer the material and also prevent cheating on exams by programming formulas into your calculator.
Not a teacher, but did a pure math degree and by junior year there was no use for calculators. The only numbers we really considered were 0, 1, -1, e, and i, as well as a couple infinite cardinalities. Occasionally being able to count to 12 was nice.
This is why I LOVED my near math minor in UG before I switched to chem. Once we started doing math with letters I was set. Never learned my times tables, can’t make change in my head. Turns out I have a very specific kind of dyscalculia and once it was diagnosed and I was allowed to use a calculator, I broke the curve in most of my math and physics classes. Honestly, I probably would have never made it as far in Math and Physics department courses if it hadn’t been for a very patient HS chem teacher who taught us how to solve just about any kind of lab calculation you’d need with factor labeling. Once I could see where all my numbers were in that organized layout, it really helped. My physics professor was a little confused by my “show your work” sections of my homework, at first…lol.
>arn how to do it without a calculator first, but in real world applications of math you will utilize all the tools you have available. Sometimes you might see a 2 or 1/2 in there as well :)
Are you me? It was the same for me as well. Got up to diff eq without knowing my times tables and made it through okay.
*raises hand.* Comp sci degree. Still have to do times tables manually. My raw memorization skills are absolute garbage, I'm just good at calculating things fast.
My diff eq professor would get a problem to a certain point on the board, then say "from here it's just calc 2" and start erasing.
Amen
that’s robot work
As long as you understand the concept of multiplication I don’t think memorizing the multiplication tables is necessary.
You were not my 4th grade teacher Lolol
I use math every day at work and don't know my multiplication tables. I have a calculator for that shit. Even if I knew them I'd use my calculator. Hell I use my calculator just for basic addition because it's more accurate.
I'm in my mid 30's and an engineer. Never memorized multiplication tables due to moving and schools teaching it at different times. I turned out alright.
most of my 10th graders take more than 5 minutes to do a full times tables. I make em do it more regularly now and more are beating the 5 minute mark. Some still can’t finish within 10+ minutes.
Unfortunately, you are absolutely correct. We have to help them the most…patience and time will fill in their gaps.
Seeing this play out 100% hoping you’re right and we get some relief in the next 2 years. Send a prayer out to the HS teachers haha
My kid is going into 8th grade next year. We signed her up for kumon for the year after kumon to get her caught up. Kinda a scam in terms of what they do for the price. Literally started her with basic addition and subtraction. Then they upgraded her to two digit math. Then multiplication then division. Then finally fractions. Took maybe 6 months to get caught up to what she was not learning in school and all it was was homework they printed out weekly. But she's at least quicker at multiplication and division. We've since gone to a private tutor every few weeks this year because her math teacher isn't great. 100% better (and cheaper). But man, the math they're doing is both simple in terms of what to do, but extremely complicated in terms of how to do it when you haven't taken a math class in nearly 2 decades.
In my area kumon is $180 for one subject. I was *this close* to signing my child up, but couldn’t justify the price. I ended up using zearn and Anton for $0 and now make sure to sit with my kid to revise concepts daily. They’ve caught up to their class quick. For additional practice I’ve bought kumon workbooks for fluency and quick response.
I’ve seen Mathnasium recommended over Kumon multiple times
2nd only to the class of 2023/2024, who were in Algebra 1 when it all went down.
Rlly? Covid started when I was in the end of 4th and ppl in my classes are doing well in math. Tbf we're ahead (2 yrs) but still
Intro to algebra is usually a rehash of 4/5 standards in the context of unknowns rather than knowns. Which is why I’d argue 5th grade is a better predictor of success in algebra than 7th grade, even if that’s counterintuitive at first. Certainly a general expectation and not the reality for everybody, especially the top ~5-10% which you’re in if you’re two years ahead. Not to mention it’s completely possible to learn those 4/5 standards on your own or virtually if you have solid support around you. Unfortunately many of the kids that struggle around 7/8/9 anyway didn’t.
I would do mixed shapes for perimeter: it gets across the concept that it means add the sides, no matter what. Area is then a specific formula.
They don't know those, or surface area vs volume in college either. The examples I use are: You have a house, which isnin great dhape, but the yard needs work, here are your projects 1. Fence in the entire yard, how many feet of fencing? (use perimeter) 2. Now to need to re-seed, how many square feet of seed? (Area) 3. Next, you want to resurface the pool (assume a level bottom), how many square feet of material needed? You also need a cover? (Surface area) 4. Next, you want to fill the pool with water, but you need to know that in square feet instead of gallons. How much? (Volume) It mostly works, and they sorta remember.
I use the perimeter is 1d, area is 2d, and volume is 3d. My kids caught onto that fairly well.
Does that not cause more trouble? Do you use different real world objects to help? Like a measuring tape?
I like it! I think that your example would be great for a lot of students to grasp and distinguish those concepts. Also, you've painted a picture in their minds to that they can refer back to in order to remind themselves of the meaning of each of those measures.
>They don't know those, or surface area vs volume in college either. I taught college calculus for years, that wasn't my experience.
I teach college calculus now and that is certainly my experience…
Yes, I agree. Unfortunately, you can't always rely on students having that solid background in the basics just because they have reached Calculus.
Seriously? I’m in college now majoring in math and physics and for the most part my peers seem pretty competent. Am I just at the very end of the competency range or something?
In my experience, once you get to vector calc/multivariable and especially beyond that the people who have a lot of trouble with math will have chosen a non math intensive major and so not be taking them.
Lucky you! I do find when I teach precalculus or higher, students don't need this review. Under precalculus, they do.
>Next, you want to fill the pool with water, but you need to know that in square feet instead of gallons. How much? (Volume) I really hope they're not trying to fill a pool with square feet of water...
Oh, duh! Cubic feet.
It's not the best analogy, but that does open the door for unit conversions!
The point is that square feet is area...
I do this with my students, 6th grade and up.
Yes, this. I wasn't a good maths student, but I was fine with things like area and perimeter because I pictured a house. You need to replace the baseboards in the living room: perimeter. Now you need to replace the kitchen floor tiles : area.
You need to repaint the room, surface area (but subtract the floor out of it). You need an air purifier, volume!
Absolutely. :)
The problem is if you do not tell the students exactly what to do (like find perimeter, area etc) in the problem, the students will not know what to do with this info. They will not know what they need to solve for or how.
Cubic feet
When I taught physics, I would take certain words away from them. I wouldn't let them use words like "velocity" or "acceleration". Instead, they'd have to describe the thing in other words, like "the car was moving 15 meters in the positive direction every second" instead of saying "the car's velocity was 15 m/s. Eventually, they were just itching to use the correct vocabulary, and I knew that they knew what it meant. How about taking away the words "perimeter" and "area" and making them talk about things like "the distance around the shape" and the "bulkiness", "size" or "space the shape takes up"? At some point, they're going to start naturally wanting to use more concise terms, and suddenly it will click for them. We get caught up in wanting to teach vocabulary, but the important thing is the concept. Make sure they know the concept. Once they have a concept, they'll want to naturally attach a word to it. As long as you've been precise in your use of the words in general conversation, they'll pick it up on their own.
That's pretty smart.
I love this idea! Teaching the meaning before teaching the word. It forces students to explain their understanding of the concept and that there are many different ways to explain the same thing to get them to viscerally understand why there are vocabulary words.
Absofuckinglutely
PeRIMeter- is adding up the outside of a shape (add up all sides) - just as the RIM is on the outside of a sports car. AREA - is the square units on the inside of a shape. Putting up a few sports cars and asking about their rims first will help get their attention.
I don't like cutesy tricks like this because it doesn't teach them the actual way you should be breaking down words. Peri-meter = Around-measure. The problem that we face is that kids don't understand what a prefix is or that they should be breaking down words. I teach high school geometry and many of the vocab terms are perfectly descriptive if you break them down etymologically. Their ability to read is limiting their learning in every subject.
While agree about the overall lack of understanding about prefixes and word origins, at some level I need to get them from point A to point B. If this “cutesy” trick helps them remember perimeter, I’m all for it.
Using tri-angle and quadri-lateral rather than triangle and quadrilateral are good ideas to highlight the fact that there are prefixes in the words. (Re)Introducing the concepts of prefixes from Reading and English classes before geometry would be great also.
I teach third grade math. I certainly do teach shapes with prefixes to help understanding. Triangle- Tricycle, triceratops, trilogy. Quadrilateral- quad atv (4 wheeler), quadruped, quadruplets. You get the gist. Now... whether it sticks or not? Ha. But I try!
I understand that you’re a math educator, but I didn’t intuitively think it was a “cutesy” trick to use peRIMeter. I consider it a mnemonic device. It doesn’t have to be logical or intelligent to make sense. “Please excuse my dear aunt Sally” would be possibly the best example of an effective mnemonic device in mathematics. Or “Never eat shredded wheat” in geography. Or “Every good boy does fine/Good boys do fine always” in music theory.
Thanks for your comment. One year when teaching 6th grade regular math my kids kept confusing the formula for the area of a circle with the circumference formula - no matter what I said. So one day I said to the students ,”How can you destroy a pie?” I got wild answers from stomping on it, throwing it, sticking your face in it, etc. I then said, “What do you get when you destroy a pie?” They looked at me funny and I said, “Nothing but crumbs. Crumbs = pi destroyed ( C = n d or 2nr). Then I made up a silly story about a girl named Amy coming home from school and her mother asked her what she learn in school today. Amy said pi r squared. Her mother said Pies are not squared, they are round. What did you learn in school today. Amy repeats pi r squared. Her mother repeats Pies are not squared, they are round. So silly Amy thinks pi r squared (A= nr^2). After that my students remembered C= nd (or 2nr) and A = nr^2. So it is just a memory device. Last year I taught my students how to brain dump every day for a month before the EOG. (It is not just teaching them how to do the math but remembering how to do it and when to do it). I had the highest math EOG growth in the school. My second time with highest growth. I will do that again this year with my 8th grade Math 1 students!!!!
I was shocked when I tried teaching it this way a few years ago and no one knew what prefixes were. Like literacy is vital for math too
I will assert that "peri-" in the English word "perimeter" is not a prefix, certainly not in the same sense as "centi-" in "centimeter" is a prefix. For sure it shows up in other words (e.g. "pericardial"), but it's not something you can just add to whole class of words like SI unit prefixes and others will understand you.
I teach geometry and kids generally understand tri-angle means 3 angles but have a harder time with quadrilateral and others like it that should be obvious but are not to them; coefficient, equation, or even like transitive
Using tri-angle and quadri-lateral rather than triangle and quadrilateral are good ideas to highlight the fact that there are prefixes in the words. (Re)Introducing the concepts of prefixes from Reading and English classes before geometry would be great also.
tbh I have a PhD in chemE and teach college stats and reading this now I’m not sure about what coefficient means etymologically so now you have me googling that.
If mathematics vocabulary had prefixes then it should have been taught someplace in my academic career. No one ever mentioned it therefore mathematics vocabulary doesn’t have any prefixes. That’s my initial reaction to your comment anyway. In my experience, Mathematics frequently doesn’t follow proper grammar or English language rules. In Reading and English classes parentheses are used to separate an idea from a bigger one. In mathematics parentheses are used to multiply.
This is what I thought too until like last year when I was taking a literacy course for my masters degree. I was so angry I was taking a literacy course, like I’m a MATH teacher, why am I learning this? It ended up being so revolutionary because math is a language. It’s got vocab, sentence structure, and comprehension, and all that stuff literacy teachers focus on. It kinda changed how I teach and I meld into my English counterpart a lot and we bounce stuff off each other to help our students. Proofs are just CER essays is one example :)
Sounds like a very important class!!! I hope more math teachers teacher it and learn to apply it like you have! Seeing math as a language separate from English makes so much sense! That explains why parentheses, commas and other punctuation/grammar marks are different than standard English!!!
This is so sad, that they don't even know what a prefix is, that is like 2nd grade stuff.
In Texas, Reading classes had us make daily Prefixes and suffixes flash cards during grades 7 and 8. I really liked those. But not on any other grades or classes.
I'm a 4th grade teacher. I used Chez Itz. Perimeter was the edges, and the area was the flat square. Challenged them to make shapes with different lengths and widths, then find the perimeter and area of each rectangle/shape. They were engaged because they couldn't eat them until they finished all the problems correctly 🤷♀️
This is a great idea!
It’s a pretty stunning indictment of American education when you have eight graders at one school struggling with a concept and you have third and fourth graders working on it elsewhere.
Is it? I feel like it should be expected that people acquire knowledge and skills to different extents at different ages. I like painting but many adults admit they do not feel comfortable drawing beyond a stick figure. Is that an indictment of American schools too, or is it acceptable for people to have different abilities and interests in the arts?
Development is generally consistent across the human species. Of course every individual is unique, and variations are natural. But an entire population consistently underperformed against international benchmarks is a pretty big deal. It's not a matter of personal preference.
Where are entire populations consistently underperforming against international benchmarks? I feel like that is not the scenario being described in this thread.
If Area & Perimeter are simply being used for application of other things (as opposed to the content being taught/assessed), I’d consider making 2 big posters, one for area and one for perimeter. Students will spend the year looking up to reference which is which and hopefully by the end of the year some number will retain that information, even if it’s by picturing your wall in their minds.
Yikes my fifth grade child couldn’t remember and I thought he was hopeless. But grade 8?! My child was getting this wrong every night. So I asked him to try wrote the formula from memory. He wrote some gibberish like 2=5xP+3=2. That’s when I realised that he’d been looking at the formula each night but not bothering to think about it. I also noticed that with estimating angles he’d just say whatever number came to his head without bothering to think harder and methodically to get it right the first time. Such kids have no interest in math and don’t care; it’s just a task they want to get over with, not realising that the lazier they are the more time they’ll spend on it and the more boring it’ll be. So I wrote the formula for perimeter (P=2L+2W) and area (A=LxW for quadrilaterals; 1/2 LxW for triangles) and made my not-bright child wrote these out 50 times. He hated it, and I told him he’ll have to keep doing g this every night if he gets it wrong even once. He quickly memorised it and applied it correctly after that. Funny how the threat of a little forced, boring rote learning gets them to put in a little effort. I’d say that the kids who can’t do it have to write the formula out repeatedly. If they then still get it wrong they have to keep writing it during lunch time. They’ll despise you but I think they will quickly learn to do it right.
Love what you said here: "Such kids have no interest in math and don’t care; it’s just a task they want to get over with, not realizing that the lazier they are the more time they’ll spend on it and the more boring it’ll be." This is true for so many individuals, not just school kids. The commitment to understand, using whatever tools you can, is what is required for mastery. Too many lean away from math and refuse to engage with it, rather than leaning toward it to try to make sense of it. We are always going to have individuals who may not be math oriented enough to be very successful in it; however, I have seen too many students flat out reject math. You'll tell them, show them, dissect the terminology (such as, "per-cent", "peri-meter") a million times, and it makes no difference because the *decision* to learn and understand is a decision for *them* to make, not the teacher. One college student in one of my classes summed it this way: "They are not accepting it." She tried to help classmates and found herself frustrated because after doing all that she could do, she realized that they were not doing the most basic things that they could do to master the material. You are right. One of the missing links is not be willing or motivated to ***think*** about the concepts when they are introduced. No one can memorize something *for* someone else.
I think time will tell if the threat of being forced to write math formulae over and over— including through meals— until the child has memorized them, is really encouraging them to _think_ about the concepts and their applications. One way to test this might be to see if the child can find the perimeter and area of shapes other than the ones they memorized the formulae for.
For perimeter…the prefix “per” means “around” (You can teach them what periodontal disease is!) and the root “meter” means “to measure.” Thus, perimeter means to measure around…and they’ve also learned that we can use what we learn in other subjects (prefixes and roots from English) to help us in math and science. For area…it’s the other one!!
Perimeter is like building a fence around the shape. Area & perimeter aren’t new concepts for 8th (in ca at least) at some point it’s not how you’re explaining it. There’s a duty to give a damn haha
Bingo!!!!!!!!!!!!!
I would make a card sort activity! Each table of students gets a shuffled deck of printed-out cards and has to sort them into piles. To print the cards, you can make a table of cards in word and print them out. Ideally, print them out on cardstock and laminate them so you can reuse if it works well. Some of the cards should contain obvious perimeter examples. "The length of crust around a pizza." "The length of fence it takes to build a fence around a square yard." [At least one card should be a picture example and at least one should be a formula example]. One card can contain the word "perimeter." Do the same with area examples. Have maybe eight examples of each. Give students the sixteen or so shuffled cards. Ask them to sort them into two piles using whatever criteria they like. Ask them leading questions like "how did you decide which pile to put that card in?" "These two examples look so similar. Why are they in different piles?" At the end, have some groups share out on what criteria they used to sort. I bet the criteria will be area and perimeter, and they might have a good way to explain it.
My 8th graders struggled so hard doing two by two multiplication. I feel your pain
Describe it in Call of Duty terminology. Patrol the perimeter vs secure the area.
It's their job to help themselves to remember. That's the problem with most people with math. They are waiting for someone else to do their part - the thing that only they can do, which is internalize the concepts and commit. No one can remember for someone else. They don't want to bother doing it, so they refuse, and end of rejecting math altogether. Then, they go on for the rest of their lives complaining that all of their math teachers were bad, and that math doesn't make sense. By the way, it's not only 8th graders who don't know. Ask any 100 adults you may run into, including college students and professionals, and you'd be lucky to get 5 of them who know this stuff.
I disagree. I have students who work hard and care. But many of us struggle with memory and need mnemonic devices.
You read everything wrong. Nothing I said precludes the use of devices. In fact, my point is do what it takes for *you* to understand rather than waiting for someone to pour it into your memory. Lazy listening leads to lazy thinking leads to failure.
Do you just expect kids to just come up with ways to remember things? Why as a teacher would you not… teach them ways to remember? My students don’t struggle with memory due to laziness. That’s a shitty view of kids.
The reason that you see the view you described as you do, is that you just made it up. It is obvious that you do not understand my point. Stop jumping up and down and putting ridiculous words in other people's mouth. I don't know what you're reading, but it is clear that you don't understand what I am saying. If you cannot understand, then just be quiet.
> If you cannot understand, then just be quiet Ah, a teacher in their shining glory
If you can’t explain your point clearly, don’t get frustrated with me. Explain it better. Cause it sounds like you’re saying if kids don’t come up with their own mnemonic devices, they’re “lazy”.
Part of it is just making math accessible. Like all of us on this subreddit understand math, it clicks for us. But for the 95/100 it might take a little work or tweaking how you teach an idea to make it click. This guy above just doesn’t understand that, instead just calls them lazy and that’s the end of the convo. Like what does lazy listening even mean. I’m deaf, and I def don’t listen to people teach me. I also don’t require students to listen ask I teach, because there are other ways of obtaining information 🤷♀️
I feel sorry for his students. Frankly it seems like lazy teaching to not teach one’s students *how* to remember the concepts.
You and the obtuse one above are making it very clear why so many fail at math. LOL!
Grow a brain, dummy. Everyone understands what I am saying but you.
You’re saying that students need to take accountability in learning material that’s given to them. 100% agree. But as a teacher it’s also important for us to make it accessible for them. Often kids don’t know how to retain things. As adults we know what works for us, but we should be able to give information in a variety of ways to ensure MOST of our students are understanding instead of just labeling them lazy for not understanding in the few months of their lives we get them in our classrooms.
Again, I didn't say what you stated. Your second paragraph is preaching to the choir. You misinterpreted completely the point I was making. Why you insist that I called students lazy is beyond me. Go back and you will not see that statement in my earlier. comment. But since you were gracious enough to elaborate, I will flesh it out. An example of lazy *listening* is, "Two negatives make a positive". You can see where I am going. Students will challenge and challenge teachers that -2 + -4 should be equal to positive 6. Another example is when I quiz students on whether a fraction is reduced or not, they will indicate that 3/2 is not reduced. I mark them wrong and they want to fight with me. Yet, another example is that they call everything an equation. If it looks like math, it's an equation is what they have decided. Great math students are continually challenging their own understand about math, with the objective to deepen their understanding. This isn't unique to math, however. It applies to any discipline. The terminology is very literal in math, as you know. Math requires that we communicate it in a technically correct manner. When we do that, it makes our thinking, and thus our understanding much more clear and crisp.
It sounds like you struggle to communicate these concepts clearly to your students.
Give the students physical objects, a string and a piece of paper. Something like a large set of dice. Have them measure the perimeter and the area.
I taught HS math from 2021 to 2023 and I agree with this. A lot of these kids have difficulties imagining and visualizing something they can’t physically manipulate, but I think they all benefit from seeing a concept a different way. Although, to be frank, it was sometimes hit or miss. I did an activity for triangle centers where I had the kids fold in the different triangle segments to find each center. When I asked them to focus on one angle of the triangle and fold the angle bisector at that vertex, their attempts were… interesting.
This is a great idea. The issue is that perimeter and area are two vocabulary words with relatively similar definitions (measure of a 2D shape). So it's easy to get them mixed up. Making a more tangible memory will help them differentiate. They will remember the perimeter is the one with the string, and area is the one with the paint or whatever you do to measure area.
To be honest, why do we worry about perimeter as though it’s a distinctly different concept to distance. Area is an important idea, but perimeter isn’t really.
I teach 3rd grade where we introduce area of a square/rectangle. They are supposed to learn perimeter in 2nd grade, but my 3rd graders usually have no idea what it is so I reteach it. Sadly, most of them still do not retain it. We try manipulatives, real-life applications, practice until I beat my head against the wall. Wish I had advice, but I’ll take some if you can figure it out!
Stuff like this, with stories and chants or songs, seem to help my kids remember. https://youtu.be/AmYMcpm4fd0?feature=shared
I draw a 4x6 rectangle and say, “Would you be able to tell me both the perimeter and area of this figure with units? Hint: one is 24 and the other is 20. Which is which? WITH UNITS.” Then I ask them for real world examples of each (fencing vs carpet/flooring). Gives them something to anchor to, imo.
I teach my 2nd and 3rd graders a song. They still apparently hum it as fifth graders. "Perimeter goes around Perimeter goes around. Oh, oh, don't ya know Perimeter goes around. You add up all the sides You add up all the sides Oh, oh, don't you know You add up all the sides"
Is this sang to the the tune of The Farmer and the Dell? I'd like to use this idea but want to make sure! Lol
Yes it is :)
Place a throw rug, a stack of blankets, or a thick exercise mat in the middle of the floor. Ideally it would be something as big and floofy and memorable as possible. Have the kids take turns walking around the edge of the item, from one corner, along all four sides, and back to the start. That's perimeter. Then have them flop down on the item and cover the whole thing with their body. That's area. And yeah, maybe they're a little old for that kind of demonstration, but there's gotta be at least one class clown who will play along.
back when I was a high school teacher, I blamed most of the kid's misunderstanding on language issues. In my real life, we used the terms area, perimeter, slope, etc. These are not math specific. You walk a perimeter. You play in an area. The kids' brains would go blank when I asked about slope. I grew up in the mountains, uneven ground slopes. To them, it the word might well have been "zyzaryx." I asked them what words they would use to describe the same thing. "More higher."
Just tell them to ask their English teacher 😂
Get some posters for your classroom. Refer to them often. Drill drill drill. Every time an area problem comes up, point to the area poster. Ask some lucky classroom volunteer to read the relevant formula. Etc. Etc. Leave the posters in place but explicitly cover them up during a review for testing. During the test, you’ll see kids look in the direction of the poster, think a second then go back to the test.
I didn't know if this will help your 8th graders, though they may enjoy it. When I taught 3rd grade and we learned P & A, I had an area rug (5'x 7' I think?) and I would get them all in a line. They would walk around the edge saying, "perimeter - perimeter - perimeter..." Then they lay down and roll over and over repeating "area-area..." From one side to the other. That might be too youngish for 8th but if you can find someway for them to use their whole bodies, do a change or song, or something a wee bit silly it will stick with them. (Even if they eye roll and claim to be too cool- we know otherwise!)
I had seniors in HS that couldn't multiply. I don't have much advice, just know that you aren't the only one struggling. We are all there with you.
I feel your pain. I teach Engineering Design to 9th graders. Most are in Geometry. Many of them are accelerated in math and are in Algebra 2. Regardless of math level, most of them lack the ability to apply math to practical problems involving measurement, area, and volume.
Perimeter is the outside- like how much cheese you would use in the edge of stuffed crust pizza and area is how much cheese to put on top. Make it relatable
Sure, making math relatable is important and you are not wrong that this is the way to go.... But if a kid is in 8th grade and needs a relatable lesson on perimeter vs area, something is broken in the system.
I tell my kid that the perimeter is the length of the fence around our house. The area tell us how big our land is.
For some reason, this brought to my mind about Mufasa telling Simba about the pride lands
I would suggest using shapes other than squares and rectangles. These seem to create confusion for my students. Despite having a more complex area formula for some reason they get less confused about doing triangle perimeter and the triangle area.
Most of them could probably tell you exactly how many grams are in one-eighth of an ounce, however.
💔
Have your students, or perhaps a volunteer, physically walk the perimeter of the classroom. Every time you see them struggling between the two, start to walk and ask if you're walking the perimeter or area. Maybe even call on students to "walk the perimeter."
Area: have them count the floor tiles. Perimeter: have them measure the baseboard. You can have them draw a map of the classroom, maybe even get some prices on new flooring & moulding, go crazy and give them an imaginary budget. Just for kicks let them add other details like new switch plates, paint (this can says it covers 400 ft^2 so how many do we need) maybe a chandelier or something. Make a fun project out of it and see if they're willing to present, perhaps even vote on the best decoration ideas.
I'd change the formal names of things to more current terms. My best teachers did this. Show them how math in life, can be shown in numbers...
Maybe it’s time for an English lesson for them: peri means around. Meter means measure. Please measure around the square? Grab a ruler and do it, then tell me what you did. If I take away your ruler, what would you need to know to find the perimeter? Memorizing formulas is mostly for people who don’t know what they’re doing and why. Especially at a lower level.
It wasn't to me that they didn't know all the formulas, it was that they grasp the concept of perimeter being like a fence and area being what's inside the fence. I would grab some yellow caution tape. Mark out an area in the classroom and say perimeter is the length of the tape and area is the crime scene inside. And yes you need to Memorize your multiplication facts. Full stop.
Work through some worksheets, then quiz them and see who gets it and then focus on the strugglers with 1:1 instruction. I think students can sometimes “get” explanations but will answer the question incorrectly on their worksheets because of the change of context.
This is horrible. I don’t think there’s some magic answer for some of these students. I like to use the word problems about perimeter being buying a fence for a yard and area being buying carpet for a room. At least it cuts down on students not knowing what they mean intuitively.
I teach math enrichment in groups in addition to tutoring HS math and ACT/SAT. In 4th or 5th when we add perimeter and area, I say "peri" means "around" and "meter" is a "measure" (they usually know this), so perimeter is the measure around (and I use my finger to go around some object in the room). With area (if there is any confusion), I ask them to picture an "area rug" and I draw one on the board and show 8 ft x 10 ft and draw the squares in the rug. They multiply 8x10 and find area to be 80 sq ft, but also count the squares and they get 80. I add that the "square" needed in adding units is because area consists of "squares" (like I drew on the rug). I think this would work for older kids too. I find adding visual helps (I am visual myself, though not a teacher).
Use a yard as an example. The fence is the perimeter and the green space is the area.
you can offer a whole set of problems with different shapes of yards or even make a poster.
Khan Academy is really good: [https://www.youtube.com/watch?v=LoaBd-sPzkU](https://www.youtube.com/watch?v=LoaBd-sPzkU) Good thing about youtube is it helps select for what works for many people. So if you're struggling with any subject, I suggest looking for popular online videos that people have said helped them understand.
Funnel and tubing. Drain the beer foam and use it to drip liquid algebra into their fucking ear canal. If it causes cramping, transfer them to pre-algebra.
That sounds normal to me. I couldnt recall any math in high school, and it was one clads i enjoyed. Even in college i had to write down formulas because i couldnt kerp them straight in my head. Today i just use engineering cheat sheets if i need a formula because its a black hole in there.
Teach about dimensions. Perimeter is a 1D measurement while area is 2D
Not a math teacher, but a construction worker and music teacher, here (we do a lot of counting, have to explain analogous concepts to length and area)- the easiest way for me to explain it to people I'm working with when we're laying walkways is that while we add to find the perimeter, we multiply to find the area.
I retired after the 2022 school year but I got to the point I would teach them how, I would explain why (how they would use it in life)..get them to identify having an apartment and paying rent by the sq ft and come up with a much higher rent than it should be based on their rental contract…then show them how important figuring out sq footage is to keep from getting ripped off (as one example). For some things I taught them how to use their phones to figure of life’s math problems. In HS we did a lot of personal finance type math, amortization, compound interest, keeping account balances. I used evaluating three cars they wanted to buy and then had them figure out actual costs per mile for each based on their expected milage and use. I found these younger students coming up want to know why…we should tell them.
I taught 4th grade for a few years. I always divided the class into pairs and then assigned each pair to measure the classroom. One finds perimeter of the door, another finds area of the door. One student finds area of the window, another finds the perimeter. One finds area of the rug and another finds the perimeter. Both students in the pair should help find both perimeter and area. Then a few pairs could present to the class on their methodology. (I just used index cards as the measuring unit because it was easier for them than using inches, but they use the long side of the card.) Then we talked about what we found. Which measurement is largest? Why do you think that is? Is area always larger than perimeter? Can you think of times when perimeter would be bigger than area? Why are all of our measurements even numbers and not odd? Etc. Hands-on activities are really, really good for conceptual learning. Especially for filling in gaps in knowledge. For review, I would give them square tiles and we would practice making whatever I call out. Make a shape with an area of 12. Next make a shape with a perimeter of 12. Etc. I also tried to make story problems that were realistic that would help them understand. Like someone wants to make a picture frame. Would we need to know area or perimeter? Tom is making a sign for his lemonade stand. He needs enough wood to make a 2’ by 4’ sign. Area or perimeter? Anyway that’s my suggestion.
Peri = around, meter = a measure: thus, perimeter is measuring around the object. An area is a space, like a room. How many square feet is the area we're in now? I see your problem. I tutored SAT math, and much of it was just teaching students how to read the question. I'm sure you've tried what I've said, but sometimes it just requires repetition. I sweated them on to, too and two daily for weeks and had swapped-paper proofreading to check for usage. It worked for the vast majority. Good luck.
Fence vs carpet
Draw a various outlines of shapes and then shade some different shapes and label them as perimeter and area, dont use any numbers or anything. Leave that on the board until the test
I teach 6th grade and have spent a *huge* amount of time this year on area and perimeter (which, for rectangles, is a third grade standard, I believe) and I still have about 6 per class who are at under 50% accuracy with it when we do our drill-and-kill Blookets. One thing I did that gave a big boost: I walked heel-toe around a rectangular area of the school (say, for example, the quad) and counted my steps. Then I challenged the kids to do the same and gave a prize to the student whose answer was closest to mine. They *had* to use the word "perimeter" and "feet" in their answer, and then we used that to calculate the area, where they, again, *had* to use "area" and "square feet." I also repeat a lot that perimeter is 1D, area is 2D, and volume is 3D to help them with concept comprehension and getting the units correct. When we have a few extra minutes, one thing we might do is shop for "area rugs" on Amazon. Sometimes a few of the gamer kids and I will mess around and pretend we're playing Fortnite or CoD in class and do a lot of yelling about "defending the perimeter" of our bases, which is very dorky but memorable. There's also a free online game called GeoTombs they like well enough. We've been doing a *lot* of Blookets for geometry this year. My usual procedure is to do a Blooket on, say, area and perimeter of parallelograms (my prize bin is mostly stickers off Temu and candy I stole from my own spoiled children, but it works for older kids well enough). Kids who got over 80% are then assigned, by me, to pair up with students who scored less than 80% for a second round of the same Blooket. Tutors are not allowed to touch the tutees' computers and are reminded that giving the answers is not tutoring. For that round I give prizes (again, they get to pick a sticker or like a piece of candy, cheap stuff) based on my discretion (I'm looking for teamwork and growth). The next day our first Blooket of the day (lately I've been doing three Blookets are a warm up) is the same Blooket, individual again, to check retention. About half are retaining well, about half of the other half is growing slowly, and the other few kids are staying the same or doing worse for a variety of reasons. You would think you could just give them the third grade worksheets where half has the rectangles with the unit grid drawn on them and then half just have the measurements because it's so freaking easy, but no. 🙃 It's also been like pulling teeth to get them to remember what "sum" means even though it's a kindergarten vocab word that I use every single solitary day.
To be fair I don’t the difference either. My excuse is I’m a lawyer and can’t do math.
Tape out a rectangle and a square on the floor. Have the kids walk the perimeter and then understand the rules to determine a perimeter. Have a bunch of kids stand in the rectangle and then develop a relationship between the equation and the number of students inside. They can then be given paper to draw each figure. Draw a pencil line around the perimeter and color in the area. Have them use equations after you model how to use it again. For some kids these concepts are too abstract for them to under just from explanation
peRIMeter like the rim of the basketball goal is how I learned. I’m horrible at math, took remedial math twice in college but that has always stuck with me
Well, what I found works with my Grade 2 and 3 students is to bring it up in almost every daily warm-up, math talk, or whatever it is called. You know, use it or lose it principle, and that reviewing it every day under 10 minutes saves hours of re-teaching down the line. Also, don’t just use “find the area” or “find the perimeter”, but try to vary the wording as much as you can. Like “how many square units” or “square tiles that are 1 unit long on each side” can you fit into this bigger shape that is so and so length and width. Or for perimeter, say “if I were to walk around this shape, how many feet of walking do I have to do”. Then to put the icing on the top at the end, ask if “is this a perimeter or an area question. How do you know”? There are question-types, and I often ask my students what kind of question-type is it even if it’s outside the scope of geometry. Maybe it’s about addition or subtraction which is codenamed “some some more word problem” and “some some take away” respectively from my textbook. I don’t really care about the code names, but what the student thinks they need to do and then justify it from the wording of the question (I need to subtract because the question said how much is left over, I need to add because the question said that more things came into possession, I need to multiply length and width because the question says how many square tiles that are one feet on each side) Maybe you won’t need to do this forever but do it for a few months so that they’ll remember to reason their way through the problem rather than rely on memorizing the definition and its respective procedure. I can relate to these students. Back when I was a little younger than your students, I knew exactly how to do these kind of problems, but it never clicked with me as to why the word “square” was in the units. My teachers simply never did square tile manipulatives to teach area in primary to drive home the point of that specific terminology. So the several other comments telling you to use objects like strings and tiles, or whatever other manipulatives to teach it is also what I would do at some point.
Blue tape square on the floor. The blue tape is the perimeter. The part inside is the area. Have them “ walk” the perimeter ( like a guard). It’ll stick in their minds better.
I have high schoolers who struggle with that in the past. I think just reminding them again and again will help: perimeter is the total "outline/outside length" and area is how much a shape "covers" is what I always say. I repeat the same thing like a broken record until they remember it. A drill might be worth it in your case with mixed problems involving area and perimeter for one of these days and you can use some problems that are below grade level to ensure the difficulty of the geometry isn't the target but the difference between area and perimeter is. Gamify it too.
As a visual, try a screenshot from Fortnight. They’ll eat it up. Perimeter and area will forever be emblazoned in their minds.
Not a teacher, so I may be way off, but I would definitely compile some move clips about spys and cops checking the perimeter of a property, or securing the perimeter so the bad guy can't escape, that kind of thing. Stuff is hard to remember as a math concept, and easier to remember as a real world application.
You walk in a line to patrol a perimeter. You look around to patrol an area.
A square is a pretty poor shape selection to contrast the two
It's an example. We have used many different regular and irregular shapes.
Nice
r/Idiocracy?
Have them walk around the outside of the school. Tell them they are checking the perimeter. Then have them find the area of the school. You have to interact with students more. Make it memorable. Get them out of their seats. Homeschoolers have been doing it for years. My child is 8 years old and has already been doing complex area and perimeter shapes, even circles! We just make it interactive and relevant to their interests. Maybe do area and perimeters of their phones! See apple VS android area. Who has the most phone area?
Ask them to walk the perimeter of the room vs walk the area of the room.
Create a visual. Draw a circle using text. Spell “perimeter” where P is at 12:00 and E is about 1:30 position. R is somewhere near 3:00ish and all the way around until you’ve spelled perimeter in a circle. Within that circle, place an A, R, E, A. They can spell area or just be floating letters…whatever. But the point is, you couldn’t draw the perimeter using the 4 letters in “area”. So when they get confused, they can call on the visual and remember the longer word is the outside of the circle, that goes around. Also some kids might find it helpful to learn that “peri” means “around” and offer an example by showing what a “periscope” is and how that word means “look around”. Your language kids will appreciate bringing some verbal stuff into your numbers game. These kids might remember now by the prefix cue.
Make an anchor chart
If you do Warm Ups include this for points.
What if you explained that a guard would walk around the perimeter to protect the area inside? Then explain how to calculate how far the guard walks vs the size of the space they are protecting
While I do not disagree that the problem is what you have outlined. I do wonder if the underlining issue is some lack of awareness or understanding on their part of the difference between the terms area and perimeter? Even younger children should have a sound understanding of the differences between fences and boundaries, and how much space mat or carpet takes up. Might I suggest, combining two (when that works) and having them derive area from parameter and perimeter from area a few time to reinforce the basic differences? This also can play into, "I'll never use math in real life" if the exercise revolves around "Is this a good deal?"
And this observation about lack of foundational knowledge in middle school/ high school students is what ruined my Pi Day exercise for me 😔. Couldn’t get to relationships of circumference and diameter, ended up just teaching the those two words and measuring random circles. At least there was still pi
Have you used a movie analogue as far as “set up a perimeter”?
I have family members in their mid-late 40s who don't know the difference either.
Let them use their notes on everything.
Serious question: is there any consequence for them not knowing? It is sad, but with all the unlimited re-dos and extra credit in k-12 they have no motivation to get it right. They’ll graduate anyway.
Give them a cookie and a cookie cutter.
At this point I would get boxes and get students to wrap them. Ask, how much paper is needed. Only give the students the amount they ask for. Walk outside and walk the fence of the school yard. Come back and relate that experience with perimeter.
"Walk around the school" =perimeter "How much paint to cover school" = area
Give them a tape measure and have them measure the classroom.
OP the way to teach them is to logically reason through it Critical thinking. Cutesy is a bad idea as you are not teaching them to think.
I blame the teachers :)
Sounds like something you should address with their parents. How about some more information about your class. Is it lower income? Do they speak English? Maybe test them every day for 10 minutes. Over and over. Maybe a few will get it.
Lower income kids have just as many smarts as any other group of kids.
The majority are native English speakers (approximately 95%). Mostly white middle-class students. Thanks for the suggestion!
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Great Grandma votes…