# When 1+1 does not = 2

Discussion in 'Elementary Education' started by Tired Teacher, Aug 3, 2019.

1. ### Tired TeacherGroupie

Joined:
Jul 31, 2019
Messages:
1,432
722

Aug 3, 2019

Does anyone remember the days when we could be more creative? I used to love doing an activity like that with the kids. Once they got on a roll, they'd come up with a lot of answers! Nowadays, I think parents and admin might have a fit if I did it.
The kids who knew math would give answers like negative 1 + positive 1 does not equal 2.
1 fourth + 1 half = 3/4 and so on.....
The ones who leaned towards creativity came up with answers like: 1 hungry cat + 1 slow mouse = 1 full cat.
Can anyone think of some funny ones?

Joined:
Jul 27, 2015
Messages:
1,358
841

Aug 4, 2019

Woah! I thought I might be the only teacher who asked that question. Another answer might be 1 nickel + 1 dime = 15 cents.

I agree with you. Math is more than just copying down answers on a workbook page. Kids need to think. I'll always remember the workshop when the leader asked how many adults complete workbook pages in math. In real life, math is much more.

Gravity was in the news, again--testing Einstein's theory with a black hole. Without creativity, we'd have no gravitation theories, and we wouldn't be wondering if further research on black holes will alter that theory. We wouldn't even have Newtonian ideas. Another workshop, a highly respected school psychologist expressed concern about the suppression of creativity in the classroom.

I like using imagination in the elementary classroom, too. One of my favorite lessons is to have the students take care of invisible rabbits on their desks. We use these rabbits as manipulatives in learning multiplication. Especially fun is when a rabbit or two hop off of a desk and the student has to get up and retrieve it. Of course, a couple of invisible carrots help keep them on their desks.

Backroads and Tired Teacher like this.
4. ### MrsCMultitudinous

Joined:
Aug 8, 2005
Messages:
14,055
1,878

Aug 4, 2019

Thinking about Obadiah's rabbits: 1 male rabbit +1 female rabbit = many rabbits!

On the same lines, one question I've used is, "Show how 1/3 is greater than 1/2."

Obadiah and Tired Teacher like this.
5. ### Tired TeacherGroupie

Joined:
Jul 31, 2019
Messages:
1,432
722

Aug 4, 2019

Obadiah, I love your 1male rabbit + 1 female rabbit =many rabbits!
Imaginary rabbits sound fun, but I am afraid I'd have to use real candy instead of pretend carrots to keep them all from hopping off and total chaos ensuing. (unique population here...)
I had never heard of Show how 1/3 is greater than 1/2. I could actually sneak that 1 in there and get away with it. Thanks for the idea!
I am not close to planning fractions yet. Fractions are Q3 on our pacing guide, but to be honest, I have not even planned week 1 yet. I like to rest up and enjoy summer, but the time is near for me to start back up.
The math workbook question is a good one. I use ours for skills practice sometimes. I'll rip the pages out. They come in very handy for when I have subs. Parents (especially here) like to see that the kids are doing the workbooks because that is the way they learned as kids.
At 1st, I didn't use it at all. I had learned to teach math another way in another state.
A nosey teacher down the hall spread a rumor that I did not teach math when she noticed my workbooks had not been used. I think most people know I do now because I have had a lot of teacher's kids.
That's when I learned to use them for practice, grade them, and send a few home each week.. lol Also, they are handy to look at and pull some ideas out.
Yep! The lack of imagination has sure decreased in our country over the yrs. Part of the cause , I feel is we have been pushed to rush kids through so much that we do not give them enough time to "play with the ideas." Just a guess, but I think it was about 6 years ago that all of our standards got pushed up 1 grade level. 3rd grade standards now include the old 4th grade standards.
Kids in Kindergarten are expected to know how to read now. I know many kids can and do learn without a problem. Some little boys mature slower and need that extra year to learn. The funny part is there are so many studies out there that say kids who learn to read young and kids who wait a year are usually at the same place by 3rd- 4th grade. ( With the exception of gifted kids who would have been ahead of the ballgame to start!)

6. ### Tired TeacherGroupie

Joined:
Jul 31, 2019
Messages:
1,432
722

Aug 4, 2019

Mrs. C, Sorry! I read both comments before replying and got them mixed up. My edit button does not work either. Show how 1/3 is greater than 1/2 will be a fun 1 for my higher kids and I know it will not draw as much attention. lol I am going to definitely pull that 1 out on my higher kids. Thanks for the idea!

7. ### futuremathsprofPhenom

Joined:
Jun 27, 2014
Messages:
4,398
1,300

Aug 4, 2019

This activity only works when numbers are provided without context. If I said, “Which is greater: 1/2 or 1/3?,” then the only correct answer is 1/2. If, however, I said, “Which is greater: 1/2 of 50 British Pound sterling or 1/3 of 75 euros?,” then the 1/3 *amount* is greater, not the numeric value of 1/3 itself.

Likewise, with the rabbit scenario, 1 fertile male rabbit + 1 fertile female rabbit = 2 fertile rabbits until they reproduce. Now, let’s say I put one infertile male rabbit with one fertile female rabbit, then there will only ever be 2 rabbits (until death). The mathematics still holds.

1 + 1 = 2 always without context.

Last edited: Aug 4, 2019
a2z and Tired Teacher like this.
8. ### Tired TeacherGroupie

Joined:
Jul 31, 2019
Messages:
1,432
722

Aug 4, 2019

Very true! I had thought of the word fertile too!
With younger kids, you don't want to "go there." lol
They'll ask you what fertile means and kids often get things like that mixed up when they go home and tell their parents!
Parents of younger children are more likely to believe "their kid" doesn't lie. I was seriously shocked yrs ago when a parent told me, " My son has never lied to me." It was a situation where I had seen with my own 2 eyes what the child had done.
As the mother heard the same story, year after year from many about her kid, I think she eventually "got it."

futuremathsprof likes this.
9. ### futuremathsprofPhenom

Joined:
Jun 27, 2014
Messages:
4,398
1,300

Aug 4, 2019

Haha, love it! And that is crazy that the parent thought her son never lied to her. Talk about naive! I’m glad that the mother finally got it.

Tired Teacher likes this.
10. ### Tired TeacherGroupie

Joined:
Jul 31, 2019
Messages:
1,432
722

Aug 4, 2019

Yeah, I taught K/1 my 1st yr teaching and being the 1st 1 to have to tell a parent something about 1 of their little darlings was tough!
I am now glad to at least have had a few teachers before me tell the parent the same issue. I think your average parent is able to see that their child might not be perfect by the time they reach 4th grade.
Then you get some that never "get it." I have had times though where some parents have told me how horrible their kid can be and the kid turns out saintly in class. You never know!

Joined:
Jul 27, 2015
Messages:
1,358
841

Aug 6, 2019

Something I've done each year, I have the students cooperatively play with a fraction manipulative of their choice and create equations and/or inequalities. These are written on paper, but they also choose one equation to write on construction paper and display with their manipulative as an example on a table. The papers are a nightmare to check as the students are quite creative, but the exercise is well worth the time. I actually don't recall ever having an incorrect equation or inequality on a paper.

That's for sure! I've taught in 3rd grade stuff I never learned until high school.
I question, what's the rush? I do agree with enriching the curricula as time allows, but if and only if the students have mastered the basics. The only other exception, sometimes a little extra can help the students master a basic concept. In third grade, I found the science standards were much easier to teach after I added some "experiments" concerning gravitational theory.

Tired Teacher likes this.
12. ### Tired TeacherGroupie

Joined:
Jul 31, 2019
Messages:
1,432
722

Aug 6, 2019

Obadiah, I don't remember doing Algebra/ Geometry before 7th grade. There were certain things I don't think I ever learned (lol) or at least remembered until I taught 3rd grade. ( When you have to teach it, you learn it quickly so as not to look like a moron. )
Yes, I wish we would go back and make sure the kids knew the basics inside and out before pushing the students to learn things we learned later in life. For sure, we need enrichment. Then sometimes, we'll get kids who are brilliant and need to move on at a different pace or they'd get bored.
It is funny because I know a group of successful, smart people ( Most with PhD's in their field of studies) who haven't used anything other than basic math in their careers. They breezed through classes like Advanced Statistics in school. ( I had to study very hard to do well in those type of classes. They did not come easy to me.) I had fun learning, but I was not as quick as them. ( Maybe because I skipped High School. lol)
A group of us were together last night and out of curiosity, I showed them the "highly disputed viral math problem". I assumed all except 1 would come up with the answer as 1 and defend it to the end. It absolutely shocked me, but none of them even remembered the order of operations with the exception of 2 who only remembered to do the parenthesis first. What we teach in school is not always relevant to real life.
I am curious about your experiments in gravitational theory. If you have time, can you share an example? It is not in our standards here, but I am always up for fun experiments. Have you ever done 1 with a Pepsi, Diet Pepsi, Caffeine free- Pepsi, and Diet Caffeine- free Pepsi? It is a fun one.
Oh, I know what you mean about the papers being a hot mess to read after doing fraction equality and inequality that way. I do it too. Fraction museums are fun and definitely make them easier to read. ( We could easily teach on the same team, I think.) Unfortunately, I HAVE had a few who come up with the wrong inequalities. haha Usually, the kids do ones they feel safe with, but some will try to go for the gold or just truly don't "have a clue" yet!

Last edited: Aug 6, 2019
13. ### futuremathsprofPhenom

Joined:
Jun 27, 2014
Messages:
4,398
1,300

Aug 6, 2019

I think it is because students oftentimes get contrived examples from teachers that don’t have the subject-matter knowledge to provide math problems one would encounter in the real world. From day 1, I embed concrete examples throughout my courses so that my students can see how mathematics is used to solve every-day problems. For example, when I taught geometry, I explained to students how they can find the length of a tunnel that civil engineers plan to build through the base of a circular mountain using the diameter of a semicircle (the rough shape of the mountain). I then gave them the dimensions of the width of the tunnel (in square feet) in the form of a blueprint and had them find the area of the rectangular base in the tunnel. After which, I directed them to use the given square footage to find the cost of building the roadway by providing them the cost of concrete and/or asphalt per square foot.

In another example, I had them construct a rudimentary clinometer to find the angle of inclination from where they are standing to the height of various trees outside on campus. After they did that, I directed them to use trigonometry to figure out how far said trees would fall if a forester were to fell them to see if they would be clear of the crushing hazard.

Here’s one more: I had them construct bridges using popsicle sticks with various geometric shapes (triangles, quadrilaterals, etc.) in different designs and then we tested them all out by attaching heavier and heavier weights until each bridge collapsed so that they could see that triangles are the strongest shapes found in nature. The objective is for them to realize why suspension cables in suspension bridges are fastened in triangular patterns.

Students need to encounter real-world examples and not ridiculous scenarios like, “Sally went to the store and bought 500 watermelons.”

Also, people use math in the real world more than they think. Excel sheets anyone? Writing computer code? Stock-market simulation software? Aviation? Building circuits? Actuarial science? I could go on and on.

Last edited: Aug 6, 2019
Obadiah and Tired Teacher like this.
14. ### Tired TeacherGroupie

Joined:
Jul 31, 2019
Messages:
1,432
722

Aug 6, 2019

Exactly!!!!! One of the most important things about math with kids is how it ties to the real world. I taught my kids so much in the grocery store. I'd have them weigh produce, look at the price per pound, and estimate the cost. I taught them how to figure out how much tax they were paying on their purchases. Also, this is a basic skill a lot of kids do not know nowadays: Counting back change. Money is still a math standard, but you'd be amazed at all of the kids who do not know a quarter from a nickel in 3rd grade.
I suppose it is because almost everyone uses credit or debit cards now. Change does not buy you much nowadays either. I think kids are less likely to save up their money to buy something too. More and more parents are just charging what their kids want when they want it.

futuremathsprof likes this.
15. ### Tired TeacherGroupie

Joined:
Jul 31, 2019
Messages:
1,432
722

Aug 6, 2019

Yes, it totally depends on their career what types of math each person will use as an adult though. I think math skills are needed in every job and for life planning. 1 of my friends is an author that has done very well in life. She uses math still in a lot of ways, but was 1 who had totally forgotten PEMDAS... ( other than parenthesis first) lol because that is not the type of math she uses and she's been out of school a long time. Another couple are psychologists who use more business math for private practice. Also, they are very good at investing. Another is an English professor who had forgotten. I think you tend to remember what you use after being out of school for a long time. It makes me sick things I have forgotten how to do because I have not had a reason to use it for so long. It does not make me sick enough though to switch to teaching older kids. lol I have way more patience for younger ones.

Joined:
Jul 27, 2015
Messages:
1,358
841

Aug 7, 2019

My "experiments" are actually demonstrations. First of all, we jump off of a safe platform and discuss how gravity causes us to go down to the floor.

We view some NASA videos the astronauts made just for classrooms (available from NASA. I got mine at NASA in Greenbelt when I was working a summer job in the area. The astronauts explain how gravity actually is experienced in space, but because the ship is falling around the earth, they experience micro-gravity.

I had to play around to find just the right large piece of cloth, but because I had several homemade tablecloths in my room, it wasn't that difficult. I'd put a large ball in the middle of the cloth that the students were holding. Then I'd drop a smaller ball from the edge of the cloth. (See Brian Green's first book on string theory, which is where I got the example).

I'll write more later. I'm out of time. The Internet on both my dial up desktop and my cell phone was acting weird this morning and slowed me down.

Tired Teacher likes this.
17. ### futuremathsprofPhenom

Joined:
Jun 27, 2014
Messages:
4,398
1,300

Aug 7, 2019

Wait a minute, dial up still exists?! Why not upgrade? There are now much faster internet connections.

18. ### a2zVirtuoso

Joined:
Sep 16, 2010
Messages:
6,185
2,115

Aug 7, 2019

Yeah. Obadiah must just be too stupid to not know there is much faster internet available to her. Thank goodness you came through with that suggestion. /s

https://www.cnet.com/news/life-in-the-slow-lane-welcome-to-the-internet-in-rural-america/

Sometimes it is lack of access. Sometimes it is lack of access and cost if you can get access.

Last edited: Aug 7, 2019
Tired Teacher likes this.

Joined:
Jul 31, 2019
Messages:
1,432
722

Aug 7, 2019

20. ### Tired TeacherGroupie

Joined:
Jul 31, 2019
Messages:
1,432
722

Aug 7, 2019

Obadiah, Oh! My kids would be "all in " when it comes to jumping off platforms! " I will look up the NASA site to get some ideas. I will look up Brian Green to get the example on the cloth and balls. It sounds fun! Thank you! We have a replica of the Challenger close enough for a field trip. The kids love going on missions. I understand 100% about running out of time. I am just not back at work yet. The time is creeping up on me though!

21. ### Tired TeacherGroupie

Joined:
Jul 31, 2019
Messages:
1,432
722

Aug 7, 2019

a2z, When I first built my place ( far from civilization), there were only 7 internet connections available in this area. There are only 6 log cabins in between a couple of miles. You'd think , no problem! There was a big problem. 1 guy in a big cabin down the road used 2. I had to plead with him to let go of 1. ( Baked cookies for him even)
When he did, I ended up with dial up too. Right after that, I got to know a young, computer techie guy who worked for the internet provider. He used to die laughing at my questions because they were simple answers to him. I find humor in myself, so I was never offended. We actually developed an unusual friendship.
He called me 1x and told me to drive to a place about a 40 miles away to pick up something he had left for me and to call him back. I still do not know how he did it, but he hooked me up to the speediest internet. It is faster than what we even have at work.
My bro in law used to be sooooo jealous because he had had internet way before me out here and he always checked my speed every time he came over. He wasn't jealous in a mean way....just frustrated that he could not get his sped up too.
I know a guy who owns a computer shop here who told me that we were getting some federal grant soon ( that was a couple of months ago) that would make internet available to a lot more people in rural areas.

a2z likes this.
22. ### futuremathsprofPhenom

Joined:
Jun 27, 2014
Messages:
4,398
1,300

Aug 7, 2019

Oh calm down, SJW. I was legitimately surprised that dial up was still a thing. I meant nothing by it.

Joined:
Jul 27, 2015
Messages:
1,358
841

Aug 8, 2019

(Smile) We thought about switching over to a higher speed service, but we're satisfied with dial up on our desktops and high speed on our cell phones. I found a superb cell phone service with Cricket that's adequate for my usage at only \$35 monthly and no contract. Cost was the major factor; we've chosen to use our money in other projects. My only complaint is with atozteacherstuff forums; it's too easy to bump a button unintentionally on a cell phone and sometimes too slow on dial up.

Back to my earlier reply, (and yipes! I'm running short on time again this morning, but not due to the Internet this time--just busy this morning), the book I referred to was The Elegant Universe by Brian Greene, if my memory serves me correctly, loaded with all kinds of illustrations on many difficult to comprehend scientific concepts. I tried to locate it on my Hoopla e-books, but it wasn't available, and I tried to find the specific illustration about the ball on the cloth on Google books, but couldn't during my search. But it should be available in most libraries. An excellent book--highly recommended.

Other demonstrations I've used:

The students tie a plastic throwing disk to a string. As they spin it around, the disk orbits their body similar to earth's orbit around the sun. The draw back to this illustration is that it's closer to Newtonian physics than Einstein's current theory of gravity, but with explanation, my students seemed able to comprehend the simulation. See spaceplace.nasa.gov : Why do the planets go around the Sun?

For micro gravity, this demonstration, in my opinion, was so cool!!! We had a large platform with a safe railing on the playground. The students, a couple at a time, would drop a plastic coffee can off of the platform, to represent a spaceship falling. (Spaceships fall around the earth). Prior to dropping the can, however, they held a toy astronaut (I used any action figure) in the middle of the can. They dropped both at the same time. The can kept the action figure from experiencing air resistance, so they both fell at the same time and of course, it seemed that the action figure was floating as in micro-gravity. See curious.astro.cornell.edu : Ask an Astronomer for an excellent story illustration using Superman to further describe orbiting and free fall.

futuremathsprof likes this.

Joined:
Jul 20, 2012
Messages:
3,931
1,914

Aug 8, 2019

Dial up is the only internet available in some rural areas.

25. ### futuremathsprofPhenom

Joined:
Jun 27, 2014
Messages:
4,398
1,300

Aug 8, 2019

Obadiah just said that they were thinking about switching to the higher-speed service. I’m confused.

26. ### Tired TeacherGroupie

Joined:
Jul 31, 2019
Messages:
1,432
722

Aug 8, 2019

Obadiah, I am hoping/ thinking you are joking when you say it has many DIFFICULT to comprehend scientific concepts. I haven't ever taught anything higher than 6th grade! I looked yesterday for Brian Greene and science experiments + you tube with no luck. Sometimes you tube has good ones, but he was not there. It makes sense, they want you to buy the book.
I don't use CC's or shop online ( friend's joke- Dave would not approve) anymore, but will see if a friend will order it for me on Amazon.
We have a library about 40 minutes from where I live, but it has not been updated in probably 25 yrs. The astronaut and coffee can is definitely 1 I would do with the kids. It sounds fun! Thanks for the demonstration suggestions and resources. I will definitely use them.

27. ### TeacherGroupieModerator

Joined:
May 13, 2005
Messages:
29,807
1,165

Aug 8, 2019

I think the young people are using "jelly", as in "You just got a new instant cooker? I'm so jelly!" for that kind of envy-without-malice. The usage makes my teeth hurt, however. The phrase I myself use, especially in print where tone of voice and body language can't be depended on to convey the lack of corrosiveness for me, is "cheerfully jealous". I'm cheerfully jealous of Obadiah's consistent sweetness of spirit (which is, of course, precisely the characteristic in him that makes it easy for my jealousy of him to be cheerful).

Tired Teacher likes this.
28. ### a2zVirtuoso

Joined:
Sep 16, 2010
Messages:
6,185
2,115

Aug 8, 2019

One of the requirements when moving was that the area had to be technologically up-to-date at the time. Even so, we were at the end of a cable line where they company didn't provide enough high powered hookups for the houses that were far from the boxes. We would call the company, they would come and move the line from one port to another. The neighbor would call a week later, get a different tech who would move the line to a different port. On and on this happened for a year or more. None of us knew what was really going on. Since no tech ever came twice, no one knew the problem. All we knew is that a tech would come and it would be fixed for a while.

I saw where my relatives lived and they even had trouble getting any type of cable where they were. Also, being in a valley made antenna TV near impossible also. They were thrilled when satellite TV came around. Remember those 5 foot dishes? LOL

Also, for many people, even in areas with high-speed internet, cost is an issue. Then to have cell phones and home internet is half a month's rent for the service in non-high-cost-of-living areas.

Tired Teacher likes this.
29. ### TeacherGroupieModerator

Joined:
May 13, 2005
Messages:
29,807
1,165

Aug 8, 2019

One of the formative experiences of my young life was the last five minutes of Jonathan Winters's weekly broadcast comedy show: someone would hand him an object, and he would improvise with it. He usually started with the thing itself and a joke or two, and then he'd start riffing on attributes: a fairly obvious attribute, like overall shape (golf putter as cane, then pool cue); subtler elements of shape (a golf putter tapers: mariner's telescope!) and combine that with another attribute (golf club has a head and a handle: canoe oar! ladle!), and so on, all delivered with patter that played by turns with current events, Hollywood gossip, social mores, history, and much more. It was punning in three dimensions, and it made me think consciously about the usefulness of not only knowing what a thing IS, but what it IS LIKE and how, and the many ways in which that information can be made use of. It is, in short, a mental exercise with a family resemblance to "When does 1+1 not equal 2?"

And I've gotten a fair bit of use out of pointing out that units of measure work exactly like variables, in the sense that, just as 3a•3a•3a = 27(a squared) (and please forgive the workaround: as far as I know, A to Z lacks superscript and subscript), so also 3 in • 3 in • 3 in = 27 (inches squared).

(a2z and futuremathsprof, I'm issuing moderator's demerits and I'll see each of you after class.)

Tired Teacher likes this.
30. ### Tired TeacherGroupie

Joined:
Jul 31, 2019
Messages:
1,432
722

Aug 8, 2019

"Hip phrases like "jelly" make it to AK, usually 10 yrs after they are used in the lower 48. lol
I will be on the lookout for it though. That is so smart of you to add cheerfully to jelly when it is going to be seen without voice tone.
Some people read into things in a negative way. I even catch myself having to reread 2 people's emails at work several times to take the hostility spin out of it and try to figure out what they are really saying.
A friend could send me the exact same email and I would understand it asap and read it in a joking or friendly way. Our minds can work in strange ways!

31. ### Tired TeacherGroupie

Joined:
Jul 31, 2019
Messages:
1,432
722

Aug 8, 2019

When I moved out here, I never realized it could be a problem even. It probably would not have changed my mind though! It is the most peaceful place I've lived in my life. That is hilarious that you and your neighbors were kind of taking turns without knowing it. ( I'm guessing it was not funny at the time though.) I could not get cable where I live and people still have those big satellite dishes in this area. ( About 15 minutes away is the 1st one.) Then they are all over. I only get 3 channels on TV. I am not home enough once work starts to even justify paying for TV.

32. ### futuremathsprofPhenom

Joined:
Jun 27, 2014
Messages:
4,398
1,300

Aug 8, 2019

Tired Teacher likes this.
33. ### Tired TeacherGroupie

Joined:
Jul 31, 2019
Messages:
1,432
722

Aug 8, 2019

OK Your demerits cracked me up. The 1st time I saw demerits used was my son's 1st yr in TX. In my mind, you had to do something terribly obnoxious to get a demerit. He'd get them for different things and I'd get mad at him.
Finally, his teacher called me in and explained to me that no one was perfect and that it was perfectly normal to get demerits. When she told me the average number of demerits for the students in her class and my son had fewer than anyone else, I realized that had I misunderstood how you got demerits. ( My son told his teachers a few things I wish he had not shared over the years.)
Once his male teacher was at my house when I got home fixing something my son had broken after I told him not to mess with it. He messed with it right before we left for school. I was not as patient as people are nowadays. It had to do w/ home security. I was so embarrassed because I could only imagine how unreasonable I must have seemed.

So my new 1 for this thread would be 1 demerit + 1 demerit = 1 really irked mom!

Last edited: Aug 8, 2019

Joined:
Jul 27, 2015
Messages:
1,358
841

Aug 9, 2019

Tired Teacher likes this.
35. ### Tired TeacherGroupie

Joined:
Jul 31, 2019
Messages:
1,432
722

Aug 9, 2019

Thanks! That was interesting to read. Unfortunately, my 3rd graders would not understand most of it. I wish I could send you links because I found a you tube video that goes with what you are teaching.
Unfortunately, my computer weirded out on me before finishing this message, I had to restart the computer, and lost the site.
I have always had Dell computers, but was persuaded to get a Lenovo recently. It has a quirk that I finally figured out how to fix.

Last edited: Aug 9, 2019