I'm 53 years old. I don't think I was ever taught this in school. In school, I always lined up numbers vertically and did calculations. To me, mathematics was never understandable beyond knowning when to use a formula or a format to get the right answer. Only in the past couple of years have I learned a bit about what you are talking about here. On quiet days now, I sometimes try to add or subtract numbers in my head. I try to find relationships between numbers, borrowing from one number to add to another. With this video, I learned that you can add or subtract totally unrelated numbers to an equation to make it easier to calculate. Well, of course you can. I can see that now. Why couldn't I see that before? I think my 53 years is proof that I never would have thought of it on my own. My own fear of math blinded me and kept me from even trying to understand. I enjoyed this video. Thank you.
OMG, my daughter is 8 years old and she has so many troubles learning the timetables because she is still developing basic mental maths. I’m thinking that she has a learning disability… and she is getting behind her classmates. Thank you for teaching us these strategies. I love them. 😊
Just as a parent, I am trying to find the joy and appreciation in the math to hopefully inspire my daughter to become fluent in math. I realized the only way to do that was to relearn algebra, geometry, and I never realized how much CONCEPTS MATTER to both kids and adults to retain information. Math was my worse subject in school and I fully believed it hard for myself but me, the kid left behind in school with undiagnosed ADHD can do the math now and I work physics equations for fun/hobby. It’s weird how accepting not being good at math is.
I have a kindergartener who does a lot of mental math. This gives me more ideas on how to talk it out with him. We are learning place value and multiplication. Started money work as well.
the way sums are written is completely different to 20+ years ago. Im homeschooling and I find this very interesting. I want to teach my daughter to be able to understand and break down numbers, so thank you.
Thank you for explaining this, at school we were taught not to do mental maths and to write everything down instead so I just realised now that I’ve been over complicating it by using a mix of the two techniques in my head when I could have just gone for one
I recently found your site and love it. You are a great explainer, Susan. I just wanted to point out that the Compensation and Constant Difference "adjustments" for addition and subtraction can all be streamlined to be simpler to understand while also being mathematically correct and matching the language students will learn in middle school. They all follow the same "zero it out" rule you mentioned. For your part 2 Compensation problem of 37 + 58, you correctly added a 3 and subtracted a 3 (+ 3 and - 3 combine to make zero, as you noted) keeping the same sum as the original problem. When you solve 64 - 28, you can follow the same rule: introduce two amounts that combine to make zero. The trick is to realize that in a subtraction problem, the second number (the subtrahend) is a negative number (less than zero) and must be treated that way, even in primary grades. Since you wanted to make the negative 28 a negative 30 (getting more negative) you have to combine it with a negative 2 (- 28 - 2 = - 30). Because you use a negative 2 with the - 28 (to make it smaller), use a positive 2 (add 2) with the 64 to get 66. 66 - 30 = 36. Understanding this distinction actually makes the rules for these problems easier to remember, because there is only one rule! It is always the same. During the Constant Difference problem of 61 - 27, you are really subtracting 3 from the - 27 to get - 30. Then when you add 3 to the 61, you are repeating the same language as in the earlier two problems: whatever you do to one part of the expression, do the opposite thing (same number, other sign) to the other part. Here is where this difference becomes clear. Starting at 14:40, you explain that you want to add 3 to make the 27 a 30. Then, you write out 61 + 3 - 27 + 3. Plugging this into a calculator gives 40, which is 6 larger than the correct answer of 34. Why? When you calculated - 27 + 3 = - 30, it should have been - 27 + 3 = - 24. A difference of 6. Showing the negative numbers on an open number line on the floor makes this easier for students to understand. To go from - 27 to - 30, they have to continue walking to the left, farther away from zero, getting more negative (in the direction of "Negativeville"), thus - 27 - 3 = - 30. It's the same idea as in addition: to add 61 + 3, they start on + 61 and walk right, farther from zero, getting more positive (we usually say "larger"), in the direction of "Positive Town", to get to + 64. To combine + 64 and - 30, (a/k/a "subtracting" 64 - 30), they start on + 64 and go left, in the negative direction, 30 steps to reach + 34. Plus, they think it is very cool to learn about negative numbers!
OMG. NO WAY I CAN TEACH THIS TO MY JUST 6 YR OLD GRANDDAUGHTER. After watching this, guess I'll give up so I don't confuse her. I'm learning disabled a d I could just cry. Blessings, julie
I feel the same way. The old method seemed to be working fine. Seems like they’ve made it complicated for no reason. My son wasn’t getting it at school so I made a string of wood beads numbered them 1-20 and then just practiced with him after school everyday. He’s improved so much. Different things work differently for different people
Thank you!!! I'm doing envision math with my children and this really helped me understand. The math I am accustomed to uses much different strategies. Now I can try and help them solidify their understanding. I also have a child going into third grade and I see you only teach til second, Can you recommend a channel or resource to help this home school mom manuever through the next grade please🙏🏽
Thanks for explaining this. As a parent my child comes home with homework that lacks examples for the problems. Thanks for explain going this, it was very clear; this gives me confidence in helping him with his work now. Also, I’ve always done subtraction by adding, so it was great to learn what that processed is called. Take care, Anna.
I’m so happy you found it useful for your work in this subreddit I really enjoy the work and love your videos on the art side but the fact is you can get the most of your own stuff from a shop that ❤ ❤😂😊
How would these strategies be introduced/taught? Each one a few days before introducing the next? Also, is “old school” borrowing and carrying not taught ? Thank you in advance for responding. Love your videos. You have provided me (everyone) a wealth of information and ideas.
Our public school (Missouri, but I think it depends on your school district) doesn’t focus on borrowing & carrying. They use these mental math strategies - rounding up/down to arrive at the same answer. Google math strategies vs alogarithms. The thought seems to be that strategies, once mastered can be faster, easier and used with fewer errors. In kindergarten the kids focused on 10 frames and at the end of K into first grade the they introduced multiple digit numbers (expanded forms, sums and differences). Games, videos, manipulatives, worksheets, songs and movement help reinforce the math concepts. Teachers are your best resource - ask your school’s math specialist (almost all schools have one) what apps and resources they recommend for your child.
My school in UT teaches strategies like these which then lead into the standard algorithm (borrowing and carrying--which are also now called ungrouping and regrouping). I'm an older 1st year teacher, so a lot of this was a surprise to me. I do not remember learning anything other than the standard algorithm. I would introduce one strategy at a time and practice it for a few days before teaching a new strategy.
Currently my daughter in grade 3 is learning this and she is struggling with this and I have never learned something like this way. I need to go over this video a few times to understand so that I can help her. I love the way you explain things. Sometimes i do understand and other times I do not. Is there another easier way to understand it. thanks
Hi Susan Any videos or recommendations in regards to teaching 4 year old's? I have a very witty playful and happy daughter, who likes learning. She can do additions through counting fingers, but I want to teach her super simple strategies in a fun playful way.
Did you try moonpreneurs - great mental math for 7 to 15 year olds. For third graders it could be a perfect start. They offer free trial program for their trial class.
I was taught completely different. Gen x here. The schools expect us to teach our kids at home but it isnt the same so all this does is cause confusion. And when its time to divide, this isnt going to work. 44 is 4 10's + 4 one's. Not 3 tens plus 14 ones. You still have 4 tens no matter what.
Awesome video. There are four different ways, but which one should I teach? Should I show all four ways and let my child choose whichever option he likes and finds easy and fast to solve? I feel that if I make him learn all of them, it might confuse him, and he may just get lost and not know which strategy to use and get stuck. ?? Thoughts...thx
I really love this but my biggest issue with my kids school is there are pretty rigid on how kids show work. They want THEIR way to be shown in the work. Even deducting points if they find the same answer a different way.
This method is great, but we need to allow different learning styles. mental math has additional steps for young learners and they can feel overwhelmed.
This seems like they trying to make kids feels "dumber" what in earth isa friendly #?my daughter does fine adding the numbers and these strategies are so confusing and she will never be used .So infuriating as a parent seeng her struggle because she knows addition/ subtraction without these strategies and getting low grades.
I have to disagree. This is a great explanation of mental math strategies, most of which I’ve used my whole life. I’m not sure if a teacher taught it to me or I just figured it out because it was easier. I think math teachers should teach this a few times each year all the way through school to help students and even if they don’t catch on immediately, they will later and be so glad. I’m a math tutor and I took notes and I’m going to teach all my students I’m tutoring this summer.
I say research Chinese math instruction strategies. My young Chinese students could quickly solve addition and subtraction problems in their heads. I was in awe.
I never got taught how to solve two digit addition or subtraction in Kindergarten. Some method in this video looked very time consuming for calcultion. You literally needed to know more rules before adding numbers in creative ways. Even I'm here to learn teaching skills, it made me headache halfway. Nice teaching concept though. I only knew the traditional vertical calcultion way.
This was unhelpful as it mostly focuses on double digit addition and subtraction. The first math problem had single digits, but it's more complex than, for example, 5+4-type of single digit math, which is what I'm trying to figure out to help my kid better understand the basics.
That subtraction problem at 12:28.🤦🏾♂️🤦🏾♂️🤦🏾♂️ Could've been done SO much simpler easier and faster by stacking them on top of each other the traditional way. This is ridiculous and complicating math for no reason. And it doesn't look like it's going anywhere any time soon.
I really hate this common core way they are teaching kids now. Something that was so simple and easy to do has become so complicated. Math used to be easy and would take a few seconds to add or subtract. Now these poor kids are having to break everything apart and it takes a few minutes per problem.
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I am 74 and this the first time that I have ever seen such a clear understandable explanation on how to do mental arithmetic.Thank You.
I'm 53 years old. I don't think I was ever taught this in school. In school, I always lined up numbers vertically and did calculations. To me, mathematics was never understandable beyond knowning when to use a formula or a format to get the right answer. Only in the past couple of years have I learned a bit about what you are talking about here. On quiet days now, I sometimes try to add or subtract numbers in my head. I try to find relationships between numbers, borrowing from one number to add to another. With this video, I learned that you can add or subtract totally unrelated numbers to an equation to make it easier to calculate. Well, of course you can. I can see that now. Why couldn't I see that before? I think my 53 years is proof that I never would have thought of it on my own. My own fear of math blinded me and kept me from even trying to understand. I enjoyed this video. Thank you.
31 here and completely agree
I'm in my 30's and I agree as well. It's the same thing when it comes to the sound of letters in the alphabet now.
😂
OMG, my daughter is 8 years old and she has so many troubles learning the timetables because she is still developing basic mental maths. I’m thinking that she has a learning disability… and she is getting behind her classmates. Thank you for teaching us these strategies. I love them. 😊
Just as a parent, I am trying to find the joy and appreciation in the math to hopefully inspire my daughter to become fluent in math. I realized the only way to do that was to relearn algebra, geometry, and I never realized how much CONCEPTS MATTER to both kids and adults to retain information.
Math was my worse subject in school and I fully believed it hard for myself but me, the kid left behind in school with undiagnosed ADHD can do the math now and I work physics equations for fun/hobby. It’s weird how accepting not being good at math is.
I have a kindergartener who does a lot of mental math. This gives me more ideas on how to talk it out with him. We are learning place value and multiplication. Started money work as well.
Is he a gifted student? Sounds very advanced from when I was in kindergarten
Awesome for math phobics and adults who didn’t get a full education or who have been away from math for a one time
the way sums are written is completely different to 20+ years ago. Im homeschooling and I find this very interesting. I want to teach my daughter to be able to understand and break down numbers, so thank you.
Thank you for explaining this, at school we were taught not to do mental maths and to write everything down instead so I just realised now that I’ve been over complicating it by using a mix of the two techniques in my head when I could have just gone for one
I recently found your site and love it. You are a great explainer, Susan.
I just wanted to point out that the Compensation and Constant Difference "adjustments" for addition and subtraction can all be streamlined to be simpler to understand while also being mathematically correct and matching the language students will learn in middle school. They all follow the same "zero it out" rule you mentioned.
For your part 2 Compensation problem of 37 + 58, you correctly added a 3 and subtracted a 3 (+ 3 and - 3 combine to make zero, as you noted) keeping the same sum as the original problem. When you solve 64 - 28, you can follow the same rule: introduce two amounts that combine to make zero. The trick is to realize that in a subtraction problem, the second number (the subtrahend) is a negative number (less than zero) and must be treated that way, even in primary grades. Since you wanted to make the negative 28 a negative 30 (getting more negative) you have to combine it with a negative 2 (- 28 - 2 = - 30). Because you use a negative 2 with the - 28 (to make it smaller), use a positive 2 (add 2) with the 64 to get 66. 66 - 30 = 36. Understanding this distinction actually makes the rules for these problems easier to remember, because there is only one rule! It is always the same.
During the Constant Difference problem of 61 - 27, you are really subtracting 3 from the - 27 to get - 30. Then when you add 3 to the 61, you are repeating the same language as in the earlier two problems: whatever you do to one part of the expression, do the opposite thing (same number, other sign) to the other part.
Here is where this difference becomes clear. Starting at 14:40, you explain that you want to add 3 to make the 27 a 30. Then, you write out 61 + 3 - 27 + 3. Plugging this into a calculator gives 40, which is 6 larger than the correct answer of 34. Why? When you calculated - 27 + 3 = - 30, it should have been - 27 + 3 = - 24. A difference of 6.
Showing the negative numbers on an open number line on the floor makes this easier for students to understand. To go from - 27 to - 30, they have to continue walking to the left, farther away from zero, getting more negative (in the direction of "Negativeville"), thus - 27 - 3 = - 30. It's the same idea as in addition: to add 61 + 3, they start on + 61 and walk right, farther from zero, getting more positive (we usually say "larger"), in the direction of "Positive Town", to get to + 64. To combine + 64 and - 30, (a/k/a "subtracting" 64 - 30), they start on + 64 and go left, in the negative direction, 30 steps to reach + 34. Plus, they think it is very cool to learn about negative numbers!
This was great, I've solved math like this since I can remember and I never knew it had a name/terms other than mental math. Thanks ❤
OMG. NO WAY I CAN TEACH THIS TO MY JUST 6 YR OLD GRANDDAUGHTER. After watching this, guess I'll give up so I don't confuse her. I'm learning disabled a d I could just cry.
Blessings, julie
I feel the same way. The old method seemed to be working fine. Seems like they’ve made it complicated for no reason. My son wasn’t getting it at school so I made a string of wood beads numbered them 1-20 and then just practiced with him after school everyday. He’s improved so much. Different things work differently for different people
I’m so happy to see this happening in my country
😂❤
This is helping me doing math more fast in grade 2. Thanks alot
Thank you! I love how you make these strategies explicit. I’m going to include this in my number talks with my first graders!
🥰🥰🥰
Thank you!!! I'm doing envision math with my children and this really helped me understand. The math I am accustomed to uses much different strategies. Now I can try and help them solidify their understanding. I also have a child going into third grade and I see you only teach til second, Can you recommend a channel or resource to help this home school mom manuever through the next grade please🙏🏽
Thank u 4 this gonna help me and my wife out with our child
Thank you Susan for making learning easy..
One of your best videos! Thank you for showing us the mental math strategies!
I’m grade two and I do three digit addition
Thanks for explaining this. As a parent my child comes home with homework that lacks examples for the problems. Thanks for explain going this, it was very clear; this gives me confidence in helping him with his work now. Also, I’ve always done subtraction by adding, so it was great to learn what that processed is called. Take care, Anna.
Great Video. I love the way you boke down the stratagies.
I’m so happy you found it useful for your work in this subreddit I really enjoy the work and love your videos on the art side but the fact is you can get the most of your own stuff from a shop that ❤
❤😂😊
I'm I my 2nd year education program and whe I were taught this I lost my mind , wasnver taught that so im so I'm so excited to teach it to my leaders
How would these strategies be introduced/taught? Each one a few days before introducing the next? Also, is “old school” borrowing and carrying not taught ? Thank you in advance for responding. Love your videos. You have provided me (everyone) a wealth of information and ideas.
Our public school (Missouri, but I think it depends on your school district) doesn’t focus on borrowing & carrying. They use these mental math strategies - rounding up/down to arrive at the same answer. Google math strategies vs alogarithms. The thought seems to be that strategies, once mastered can be faster, easier and used with fewer errors. In kindergarten the kids focused on 10 frames and at the end of K into first grade the they introduced multiple digit numbers (expanded forms, sums and differences). Games, videos, manipulatives, worksheets, songs and movement help reinforce the math concepts. Teachers are your best resource - ask your school’s math specialist (almost all schools have one) what apps and resources they recommend for your child.
My school in UT teaches strategies like these which then lead into the standard algorithm (borrowing and carrying--which are also now called ungrouping and regrouping). I'm an older 1st year teacher, so a lot of this was a surprise to me. I do not remember learning anything other than the standard algorithm. I would introduce one strategy at a time and practice it for a few days before teaching a new strategy.
This is such brilliant information and example. Thank you!
This is so helpful! Thank you! I love all these ideas.
Really a great video I remember when I was a kid
I have developed a compensation method as described
Many thanks
Currently my daughter in grade 3 is learning this and she is struggling with this and I have never learned something like this way. I need to go over this video a few times to understand so that I can help her. I love the way you explain things. Sometimes i do understand and other times I do not. Is there another easier way to understand it. thanks
I am goin g to watch it again before I try to teach this strategies. Thanks Susan!
I'm glad this was helpful for you, Hattie! 😊
Pin me
Hi Susan
Any videos or recommendations in regards to teaching 4 year old's?
I have a very witty playful and happy daughter, who likes learning. She can do additions through counting fingers, but I want to teach her super simple strategies in a fun playful way.
Did you try moonpreneurs - great mental math for 7 to 15 year olds. For third graders it could be a perfect start. They offer free trial program for their trial class.
I was taught completely different. Gen x here. The schools expect us to teach our kids at home but it isnt the same so all this does is cause confusion. And when its time to divide, this isnt going to work. 44 is 4 10's + 4 one's. Not 3 tens plus 14 ones. You still have 4 tens no matter what.
Awesome video. There are four different ways, but which one should I teach? Should I show all four ways and let my child choose whichever option he likes and finds easy and fast to solve? I feel that if I make him learn all of them, it might confuse him, and he may just get lost and not know which strategy to use and get stuck. ?? Thoughts...thx
We have taught the old way at home, let the schools teach the new way. The theory is, it doesn't matter how u do it as long as u get the answer right.
How quickly do you introduce each strategy?
From Egypt thank you
I teach fifth grade and I can't tell you how important this is. I have had students who can't accurately add single digit numbers. 😢
What a wonderful video! Thank you!
The last one was so much easier for me to understand and I think it’s also easier for my kids lol
I really love this but my biggest issue with my kids school is there are pretty rigid on how kids show work. They want THEIR way to be shown in the work. Even deducting points if they find the same answer a different way.
Thank you so much for this video!
How long do you exercise each strategy before moving to the next one?
How do you explain in simple terms to a 5 year old on why they need to compensate?
Great thanks ❤❤❤❤❤
Excellent
I don’t remember being taught this but I do it. lol. Never knew it had a name.
This method is great, but we need to allow different learning styles. mental math has additional steps for young learners and they can feel overwhelmed.
Very helpful!!
I ,am 73 years old sory.I, am teacher of grade 5.
Mental Math Strategies Video cut-out besfore the end. You were talking about Constant Difference - and the video cut out.
thank you so much
Good info
This seems like they trying to make kids feels "dumber" what in earth isa friendly #?my daughter does fine adding the numbers and these strategies are so confusing and she will never be used .So infuriating as a parent seeng her struggle because she knows addition/ subtraction without these strategies and getting low grades.
👍 Awesome way of teaching numbers.. glad that I saw the video
Thank you Susan. Very well explained😀
Very helpful
This is an awful mental strategy for first and second grade. Sorry to say, extremely overcomplicating it.
I have to disagree. This is a great explanation of mental math strategies, most of which I’ve used my whole life. I’m not sure if a teacher taught it to me or I just figured it out because it was easier. I think math teachers should teach this a few times each year all the way through school to help students and even if they don’t catch on immediately, they will later and be so glad. I’m a math tutor and I took notes and I’m going to teach all my students I’m tutoring this summer.
I say research Chinese math instruction strategies. My young Chinese students could quickly solve addition and subtraction problems in their heads. I was in awe.
I never got taught how to solve two digit addition or subtraction in Kindergarten. Some method in this video looked very time consuming for calcultion. You literally needed to know more rules before adding numbers in creative ways. Even I'm here to learn teaching skills, it made me headache halfway. Nice teaching concept though. I only knew the traditional vertical calcultion way.
I want to hire you for my 2nd grade daughter im not good in math too
Good
36+78.
36+4=40
78-4=74
11 4
Your very smart 😮
Hi I'm rama devi😊
This is confusing me
Is it me or this is confusing basic math?
This was unhelpful as it mostly focuses on double digit addition and subtraction. The first math problem had single digits, but it's more complex than, for example, 5+4-type of single digit math, which is what I'm trying to figure out to help my kid better understand the basics.
That subtraction problem at 12:28.🤦🏾♂️🤦🏾♂️🤦🏾♂️ Could've been done SO much simpler easier and faster by stacking them on top of each other the traditional way. This is ridiculous and complicating math for no reason. And it doesn't look like it's going anywhere any time soon.
What
Am okay now
I really hate this common core way they are teaching kids now. Something that was so simple and easy to do has become so complicated. Math used to be easy and would take a few seconds to add or subtract. Now these poor kids are having to break everything apart and it takes a few minutes per problem.
I'm grade two
Im cute😊
No ur not..
am cute
I like the vid but all of others i hate it
Poor kids this is ridiculous confusing for kids coming from kinder garden 🤦🏻♂️
Try to think about if you be kid is it clear for understanding 🤯🤯🤯 no really not a good tips 👎👎
Way too much talking. Cut to the chase
YOUR EYES LOOK CRAZY AF
Good