I asked over on my Facebook page if anyone would try this method with their students, and the responses were very interesting. I've included some of the comments below. I would love to hear what you think, leave a comment on this post, let us know what you think.
Tim Koschmann My concern with this is that I've seen younger students get different ideas mixed up together and make more mistakes if you try to teach multiple ways of doing the math.
This could be elaborated on when the kids are more mature like middle school grades, but in elementary schools I'd veer away from this.
Karen Bocock I teach different ways in elementary school. and i let the students choose which works best for them....they are very capable of doing that. I think this would be great to use in elementary grades
Tricia Anne This would be extension for those students who have consolidated original skill
Brigette Parsons My son is autistic, and despite years of practice, he cannot subtract accurately because he always forgets to borrow when the number on top is smaller than the ones on the bottom. This is a method I can actually teach him and he can finally succeed.
Blaire Richter I made up a technique that is very close to this for my son when he was younger. He also has ASD. It was like magic! He went from being frustrated and in meltdown range to happily "getting it".
Keri Casler Actually elementary grades ARE learning multiple ways to learn how to solve problems in math now. It's not like we were in school. They learn multiple strategies and then can use which works best for their brain. Much better in my opinion.
Alice Laybourne I wish I could agree. I am teaching students in high school who can learn the upper level concepts but still don't have foundational skills. I don't think recent methods are working.
Deanna Mann Alice Laybourne recent methods are working. We can't help,that standards changed and left a ton of gaps that we can't fill in the time we are given. You should see a huge difference in a few years when these methods reach your level.
Miracle Marchette I'd think this requires some understanding of integer rules, which we don't teach until middle school in VA.
Keri Casler (integers are learned in 6th grade not elementary ) elementary grades learn multiple ways to solve problems so kids who learn differently have various ways to solve problems. As a former teacher (credentialed), private homeschool teacher, tutor and now after school teacher I see the benefit to kids having learned various strategies so they can then choose the way that works for them ...And so they can understand math at a deeper level. Kids that struggle with math are now having options for solving problems . If you aren't ok with that good luck- it's happening everywhere in public and private schools. I've had to learn all new ways in order to help my students because it's expected in schools and because my after school students come to me to double check a problem is right and I can now look at their math done in various methods and know it's right. Because they aren't stuck doing it one way- they choose which way works for their preference- and much of it is visually laid out better than how we learned.
Michelle Bjorklund I am a big supporter of teaching multiple algorithms for math, but this one doesn't have the educational value that other have because the age it could be helpful doesn't have the understanding of integers and the age that understands integers would already know and be used to using the standard algorithm. However, I love to find little tricks like this and would teach it as a fun little trick.
Shawna Follett Bulger I was thinking the same thing... the kids learning three digit subtraction don't know integers... however if they had a number line beside them, then maybe...
Scott Workman I agree but I would definitely use it with older kids to drive home the point that math has multiple ways of finding answers.
Allayne Pearson I think kids could understand -50. They have familiarity w game shows of -50 so why not? This helps with the middle school idea of say 7 1/8 - 3 5/8 = 4 and -4/8 which is 3 4/8. Before anyone jumps on me I taught middle school math for 10 years yes they can do this, they come up with this on their own.
Stacey Pergunas I'm confused as to why they need to understand integers? I see it as place value (hundreds, tens, ones)?
John T. Duffin Stacey Pergunas If you imagine that the equation was 536 minus 484, the values would be +1 -5 +2 instead (100 - 50 + 2 = 52). From that POV, you've implied the integer concept.
Miracle Marchette I agree that it may not be helpful for younger kids. However, the assumption that the older kids already have a firm enough grasp on the concepts and skills that they wouldn't find this beneficial is laughable. I WISH my 6-7th graders all came with this basic understanding.
Kristen Frankie I wouldn't teach it, but if a student came up with this on their own and could show me how it worked I would let their work and answer stand.
Dorrie Smith Young I teach MS kids who struggle with math. This past week, I worked with them on regrouping and they have a hard time. Since they have learned integers, this would be a great way to help them be successful.
Marissa Day I've done this with my fifth graders, but only when I knew they had a solid grasp of place value and number sense in general.
Kristin Peterson Huh... So really you're saying... What's the difference between these numbers... And yes! Yes! Yes! I most certainly would teach it that way...
Sue Lowden Nope! Most find decomposition confusing as it is! I would consider it as a fun extension activity for pupils who were really secure though.
Pattie LeSueur It would be beneficial to some kids I'm sure. Certainly wouldn't discount it. Knowing place value is necessary to do this but there's always more than one way to solve a problem.
Thaddeus Dobracki I'm not too much of a fan of this one - except perhaps as a parlor trick for smarter kids, who might have the capability of understanding double (or dare I say triple) negative signs and numbers. But it's not going to help any youngsters who are learning about place values and how to subtract with borrowing - it will only confuse them.
Here's one that is infinitely more powerful - you work from left to right and the carryover/borrowing is a simple correction to the bottom line answer and should be able to be explained and executed even more simply than the conventional algorithm! The basic idea works for addition, too.
Donna Trafford Funny! This makes far more sense to me than what I was taught( first way). Wish I were a math student all over again, now that math has become more thinking and less rote.\
Marlene Gundlach Nope....just a memorized trick and shows no real understanding of the concept. I think I would show it to my high kids because they think these types of things are fun. Would confuse most!
Katie Horst Crisman In Texas they don't learn negative numbers until middle school anyway, so no, this wouldn't be helpful at all for my students.
Sue Colegrove The old way is the best way.. Why are they trying to do something that is so simple and make it harder... This make no sense..
Melissa Appolonia-Babcock As a teacher of 5th grade many students still struggle with the old way and forget to regroup.
Sera Anh I love new and different techniques, but it may be confusing for them. Maybe I would show them if they know their place value and numberso really well first.
Tina Cain Mutschall Yes, after they mastered the right hand side & were at the level to understand negative integers. I'm a Math teacher for 23 years in 2 different countries.
Debbie Thomas Donohoo Gifted, or any student that understood Integers, yes ~ I teach 6th grade
Lindsay Nicole I totally see and understand the thinking behind this but my student's parents would freak out!
Carolyn Garland This is how we teach math, but we stack the numbers differently. The kids understand it much better. They are not afraid of negative numbers and we send out letters to educate the parents.
Patricia Murrell They would have to understand place value and expanded form first. But, that is how I see it in my head.
Joe Roicki In addition to challenging them to justify why it works.
Tim Ogul If I were going to do that, I'd just round the 486 up to 500, 534-500 = 34, 34+ 14 = 48.
Angela Mackey I like this idea, especially for those that have concept of integers, but sometimes make regrouping mistakes.
Deborah Shalibo Skroch No, at least not at the point that they're learning subtraction the first time around. They haven't got a solid sense of integers at that point. On top of that, it's like turning one problem into two. I would teach a left to right approach before I'd do this.
Tara Lynn O'Brien This is a great way for kids to know about and understand integers from a young age.
Tracy Alcon Oh very cool. But they'd really have to understand positive and negative numbers. Awesome though!
Katie King No, because parents would complain because it isn't what they are familiar with...
Susan Howard One of my math student in 3rd grade showed me this method!
Larry Wiandt Wow, that's sure a hard way to do simple subtraction.
Simon Very It would help to write the 100s,10s and 1s on separate lines and put placeholder 0s in.
Valerie Korte Murray They better have place value down pat and understand borrowing.
Tina Hollenbeck No. I prefer the traditional algorithm and showing my kids that other way would confuse them.
Gloria Neel Wow!! What a neat idea for students who already know the basic operation!!!
Chris Watson It would only make sense for older students to help demonstrate algebra fundamentals.
Dawn Geraci Campbell Yes, i have with certain kids but it is carefully taught with an emphasis on the place values
Erum Ahmer Can't be for 2nd grader but excellent technique for high grades
Joan Franke No, not until they had a good grasp of place value.
John Brunning Been using borrow and pay back for nearly 70 years and it still works fine.
Kim Rhodes Middle schoolers that understand integers yes.
Jodi Price Staggers Understanding is key. Integers have been a struggle for some.... Not as bad as slope....
Angie Wright I like it!! I love showing more ways to solve.
Katie Wanderscheid No because students nowadays can't even make change
Dawn Henderson Dean I teach lots of ways to see what works for them
Confusing for lots of others numbers though
MorningStar Leon That's how I do fast arithmetic in my head, self-taught.
Kathy Kozlowski I teach 2nd grade, and I would NEVER do this. Kids who don't understand will try to subtract going up and just write the 152 without the negative marks.
Ana Vieira Not really. I used this method with kiddos with special needs very successfully. They actually grasp this much more naturally. Our brains are programmed to naturally deconstruct problems in order to solve them. 😊
Diane Christenson Thanks. I was wondering about special needs. They don't always understand regrouping so I was wondering if they wouldn't get this easier.
Pattie LeSueur Differentiate!!
Jennifer Hopton-Villalobos This does not teach number sense. Absolutely not.
Rebekah Johnston Campbell True, it doesn't teach number sense. Students would have to already have very good number sense to use and understand this strategy.
Blaire Richter I feel like with proper teaching, it does promote number sense.
Michael Brown What do you mean it doesn't teach number sense? This is decomposing, positive negative and laying some great groundwork for Algebra.
Nicole Miller I love this!! It's a great jumping point to get kids to talk about the meaning of the numbers... that 1 is really 100 and so on. That flexibility with numbers is so important to get going in the younger grades.
Karen R. Dunn Very interesting! As a 7th grade math teacher who teaches integers it would be a fun way to teach it. I do feel having the understanding of place value is so important first though!
Phyllis Kannady I don't understand what is wrong with old school math? It was easier to learn without all the extra confusion that we try to add to "make it easier". Kids are graduating school with less education because we are trying to sugar coat too much, make it too entertaining. I was in school in the 80's, I LOVED school, we were entertained in music class and at recess, the classroom was mostly work and we learned a lot more. We are also requiring our little ones to learn more than their brains are developed to retain. Kindergarten, when I was a kid, we learned socialization, colors, alphabet, how to write our name, learned to follow directions, and how to color inside the lines. Now we require them to be able to read and do math problems. Let them be little!
Miracle Marchette No it wasn't. It was easier to remember math facts and algorithms. Those that could, did well. Those that couldn't, or needed more concrete understandings...failed miserably. Now, students can be taught the number sense pieces in depth, which in turn allows them to really explore and grasp the other concepts.
I do however, agree with you as far as the push for more and more in younger grades. It is exhausting.
Tracy Meyers Grosick No. I'd rather have them model the traditional algorithm with concrete manipulatives and extend into real-world applications. Plus, I think "new math" methods undermine the triangulation of parent-teacher-child support. If parents don't understand it, support at home diminishes.
Cindy Wolf No way, but it's cool!
Robin Pineo Wow cool with the right understanding
Bonnie Wood Personally I believe that finding the answer with traditional regrouping is the best way. Doing all this stuff with 100 and 10 is confusing the lower achievers and frustrates them to no end. They actually get the borrow from your neighbor concept much better. Just my opinion.
Ana Vieira They don't really get borrowing; they just memorize the steps. This method they actually get. I have used it very successfully, especially with my kiddos with special needs/learning disabilities. 😊
Blaire Richter I absolutely agree with you, Ana. I see a number of students who can go through the steps because they have memorized them but have no idea what it means. When i explain it further with the place value logic, a light bulb goes off and it almost seems like they feel like they have been told some secret to the universe or something. Haha! Honestly, I have even worked with high schoolers who are genuinely shocked when I tell them what's really happening in these types of problems that they rotely memorized without logic. It's exciting to see actual thinking and connection going on.
Miracle Marchette Nope. If a kid has a firm grasp of number sense, base TEN, and place values...it translates into success in later grades with things like powers of ten, scientific notation, percents, etc...
Erica Humphrey Does it always work
Blaire Richter Yes. It's pretty easy to prove that it works.
Courtney Melbourne Wow! - have you ever seen this "trick"? I was never taught this and it's mind blowing! Pretty neat! I wouldn't teach it to our babies necessarily but WHOS!
Lydia Thompson I have been experimenting with this. I noticed that when i added the thousands period you must look at the difference as a whole in that period. Our students struggle so much with regrouping in subtraction that i am willing to see if this helps them. I worked 24,263 - 12,987. I could break apart the ones, tens, and hundreds and find the difference between the numbers but I had to find the difference between 24,000 and 12,000 for the answer to be right. Hope this makes sense.
Jen Fritz have you seen this before? Mind. Blown. I think if kids have a strong sense of numbers and place values they will totally get this.
Rachael Hackett-Cornaggia I showed this to my kids and they love it! Now we do mental math with it. You should have seen the kids faces who were absent the day we did this! Everyone else was ready with an answer while they were still trying to mentally do the other method.
Beth Spindler Neat! I love the way the numbers just beautifully connect like that. Math is just the amazing spider web of paths to the solution with simple, yet intricate relationships. So beautiful.
Jennifer Goodin I don't think I would use it as a standard method, but I love to see how the numbers go together. I would definitely teach it as a method as I think it would help students make sense of integers.
Marla Enderson This is great when teaching integers! I teach negative numbers then when we do the basic subtraction algorithm they say, "Well, we actually CAN take 9 away from 3. Why regroup?!" Found my answer! Thanks!
Gina Meehan Kilday Even better when it comes from the kids rather than the teacher "trying it". I had a 3rd grader teach me true partial differences like this years ago. Such great thinking and math communication.
Karen Ratliff Heatherly I don't see it as a trick at all, if you teach it the right way. It just replaces the borrowing. You're actually saving steps and making the subtracting easier on the end. Plus, the borrowing in the standard algorithm leads to misunderstanding when not taught correctly. Kids still say "take 9 away from 12" when it's really taking 90 away from 120.
Michelle Engelstad I didn't see this as a trick. I know one day we were reviewing subtraction and the students asked why it can't be negative. This lead to this method. Several of my students who had not understood subtracting by borrowing understood this method much easier. I would agree that for most it is confusing, but for some that haven't understood it by middle school and understand integers, this works.
Erin Ramsey Hoffman Honestly this TOTALLY (imo) uses number sense and place values understanding. I only teach middle and high, so I am not sure of the developmental place it could go, but I really do love it. Kids can have a concept of negative numbers and this process may make way more sense than the concept of borrowing!! I really like it!
Colleen Nash Ulbrich Well we actually would say and do "700-500 is 200, 20-90 is neg 70, 3-9 is neg 6" so we use proper place value language all along!
Colleen Nash Ulbrich Yep! I do this with my students in elementary school! It makes much more sense than regrouping does!! They can actually choose the strategy that works best for them, and this is one that works very well.
Ashley Collins Yes! This is how I was taught to subtract after I didn't understand borrowing. I understood place value just fine, but borrowing confused me so much. This made it far less confusing to subtract.
Penny Greenler what age group? many kids already subtract top number from bottom number ... are you going to explain negative numbers?? and why is the hundreds not a negative number?? tricks are useless to understanding math.
Sharon Bailey Because 7-2 is positive 5, or more accurately there 700-200 is positive 500.
I see this as requiring and using number sense and understanding of place value.
I like it!
Emma Thompson I've used this for youngsters that get in a middle with the carrying. They find it very logical and the place value makes sense. And complete it very quickly.
Glenn Petty I didn't read the whole article but if I ever had to subtract 599 like in the thumbnail, I would subtract 600 and then add 1. 👌
LeighAnn Delabre Even very young children can understand "less than 1." The greater understanding a child has of place value the more successful they are in in later years of algebra. Children need mathematical flexibility far more than they need mastery of 1 standard algorithm.
Lucy Johnston Decomposition why on earth wouldn't you?? It teaches students how to break up place value properties correctly and it's fun for them??
Allayne Pearson This helps with understand of fraction subtraction. 4 1/4 - 2 3/4 = 2 - 2/4 = 1 2/4. this would eliminate the borrowing from whole which many students don't get.
Donna Foster Students are most successful in math when they are given multiple strategies and allowed to use the ones that work and make sense for them.
Charlene Barbieri-Luigi I love this! Problem is many teachers don't even like or understand math and have to teach it at the elementary level. If someome who doesn't understand math is teaching math, what can we expect? This is the reason why I stronly believe in departmentalization!
Kat Brady I have done this with my fifth graders and even other adults and they are amazed!
Alma Morales Potter This is cool! I wouldn't necessarily use it to teach the concept INITIALLY, but it would be neat to show to older students and have them explain WHY it works.
Anne Hesse This method emphasizes place value and is a more natural method of subtracting. The "traditional" method is a pencil and paper method.
I use something similar to teach subtraction of mixed numerals when borrowing is required. My students actually understand it.
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