The Power of the Visual: Seeing Long Division

Here's a little video explaining the pure visual power of place value applied, here, to the arithmetic of long division. [For the full story, see Exploding Dots at www.globalmathproject.org.]

[@mabarbhuiya131]

At last, my confusion has been cleared watching your video.Thanks.....

[@stephenhenneberry5201]

Fantastic work! When maths is explained visually it becomes so much more inclusive for both kids and adults. It's like putting skis on the feet of someone trudging through deep snow. A chore becomes an art form.

[@pragyatewari1022]

I loved it so much. I am really thankful to you James for emphasizing on the visual thinking and learning. AHA moment

[@IKostman]

Brilliant, and wonderfully visual 😊 I am homeschooling my son for third grade this year, and this video will provide tremendous benefit

[@christopherburgos966]

He has so much swag!

[@Tcdancer0001]

Love your work and enthusiasm!! Sharing this with all the math teachers I know!!

[@christopherburgos966]

This guy has so much swag!

[@magicjim1]

Fantastic as always, Jim!!

[@TheSpottedArtist]

Thank you!!! I’m homeschooling to catch up my kinesthetic 9th grader with a 4th grade math education. We’ve made great progress in just a month, but I’ve been searching everywhere for a way to help him visualize long division. I have base-ten blocks, but with my granddaughter around, I don’t want to use the choke-able pieces. This is a fantastic solution!! Again, thank you SO much!! 🤩

[@KittyGangsta]

I'm 33 years old! Where was this explanation when I was young!!!!!!! I demand to see the Manager!!!!!!!

[@christopherburgos966]

just say you did not pay attention in class.

[@rezakhadem79]

James, this is a great method for people to understand arithmetic operations! I think once they practice with enough dots and anti-dots, they should just use base-10 numbers in the places and work with them keeping in mind that the places can have the ones place and the rest of the digits in the number in a place has to be moved to the left and be literally added to the number in the previous place on the left. To move digits to the right the digits keep their place value and are added to the place to the right as a digit in their own place value. For example, To divide 4473 by 21, we start with 1000s and see that there are no groups of 21 in 4, so we add the 4 to the number in the place to the right, keeping its place value and make 4 a 44. Then there are 2 groups of 21 in 44 with remainder 2, so we erase the 44 and write 2 in 100s place. Then move the 2 to 10s place and add it to 7, again keeping its place value of 10s, and get 27. And there is 1 group of 21 in 27 with remainder 6. So, we erase 27 and write 6 in 10s place. We move the remainder to ones place and make it 63. There are 3 groups of 21 in 63 with remainder zero. So, the answer is 213. Of course, I would use this after they work with some simple examples with dots.

[@LoriBothwell]

Brilliant mate! Just frickin Brilliant!! 🎉Finally a game to explain what kids struggle with the most! Thanks 🙏 A 1000, 000

[@christopherburgos966]

Bruhhh, why you need to curse? kids read the comments...smh

[@caitygart]

Amazing video. I love the idea of making long division visual.

[@anjollabanton230]

Just subscribe and finished skimming the viedo. Actually feel with you in my corner I might be able to tackle A level maths 👍👍👍 You are a dyscalculia Genie. Thank you 👍 👍 9th

[@oreoooreo7968]

Amazing! That makes sense, really!

[@timedclutch7780]

Love this video, I’m almost a adult (17)but I still think this is the best way to teach kids division, hopefully this video gets more recognition! Also is this some kind of aero board or something?

[@DakshChaudhary-i3u]

I love this ❤❤❤❤❤❤❤❤❤❤❤❤. This is best

[@MolioVaikai]

This is just amazing!!!

[@huyentran80]

Great teacher👍👍👍.

[@christopherburgos966]

Lmaoo. Not going to lie chat; this man right here got swag!

[@NyuuSkullz]

Im so confused... my kid has 3rd grade homework for 48 ÷ 8 ...and none of these things are making sense to me. Please give me a dummy down method. I used to be AP honor roll and after 9 yrs of being a SAHM... im realizing i forgot entirely HOW to divide but i refuse to not grow so i can help her

[@siddappasonakanal8483]

How to divide with decimal number

[@kimberlymatsuda6596]

I'm stuck on the first practice problem

[@maryj7423]

I love this. My fear of math just exploded! Thank you

[@davidliz315]

Amazing

[@kimberlymatsuda6596]

I actually figured it out by decomposing the extra 100.

[@renerenatorivera9062]

4745 divided by 213=21 with a remainder of 2.

[@takiahansley8193]

Please show 475/25. I'm not getting my dots expressed right

[@JamesTantonMath]

Yep .... this is an awkward one (for dots and for regular long division). 4|7|5 = 2+2 | 5+2 | 5 that gives me one 25 at the tens level and one at the ones level and leaves behind the dots 2|0|0 still to contend with. Unexplode and unexplode to then see eight 25s at the ones level.

[@jadduvenkataswami7399]

Sir how can we divide 676 with 24 using dots method explain

[@JamesTantonMath]

Have a look at Exploration 5 here: globalmathproject.org/exploding-dots/ You can always "unexplode" dots to see more groups of what you are looking for.

[@carlossousaoficial599]

How i do resolv square roots with dots?

[@carultch]

As an example, consider the square root of 10. First, we recognize that the nearest perfect square is 3*3 = 9. So construct 9 of our dots into a perfect square, and we have one remaining. For that one remaining, explode it into 10 pieces, each representing 1 tenth. Look for groups of 6, that we can use for adding to our existing square. We like groups of 6, because this means adding 3 to the width, and 3 to the height, and building an almost perfect square. There's only one group of six tenths that do this, so we get a 3x3 square, with two rectangles of 3 * 0.1 added to it. For the remaining four tenths, explode these into 40 hundredths. We still have a tiny square to complete, which has dimensions of 0.1 by 0.1. This is only a single hundredth, so subtract a single hundredth, to complete the square we have so far. We now have a complete 3.1 by 3.1 square, with 39 hundredths left over. Now, we're looking for groups of 6 hundredths to continue adding to this square. We have 39 of them to work with, so this is 6 groups of 6 hundredths, and 3 hundredths remaining. This now allows us to form an almost-complete square, of dimensions of 3.16 by 3.16, but what's missing? We're still missing a square of 0.06^2, and two rectangles of 0.1*0.06. This adds up to a total area of 0.0156 square units Take this away from the three hundredths remaining, and we're left with 1.44 hundredths. Thus far, we can conclude that 3.16 is approximately the square root of 10. We can continue expanding the hundredths into thousandths, and into ten thousandths, and continue adding decimals. However, for any number that doesn't start as a perfect square of an integer or ending decimal, we'll be in an infinite loop, adding non-repeating digits to the result.

[@jhilmilvarshney6793]

Hello sir can we solve division upto decimal point by this method or not

[@JamesTantonMath]

Check out Exploration 8 here: globalmathproject.org/exploding-dots/

[@jadduvenkataswami7399]

Sir how can we divide 676 with 24 using dots method

[@JamesTantonMath]

How about ... 6|7|6 = 4|27|6 = 4|8+19|6 =4|8+16|32+4 from which I see 28 groups of 24 with 4 left over.

[@justhere7947]

so u just cured my learning disability ok cool thanks

[@seanlopez1051]

You sound like Stewie giving math lessons 😅

[@krulerm]

2566/15=?

[@loandinh8019]

How’s about 1781 : 60?

[@carultch]

Given: 1781 divided by 60. Start off by multiplying by 1 in a fancy way, so that we're really dividing by 6: 1781/60 * (1/10) / (1/10) = 178.1/6 Form four boxes, for hundreds, tens, ones, and tenths. In the hundreds box, put 1 dot In the tens box, put 7 dots In the ones box, put 8 dots In the tenths box, put 1 dot We can't divide the one dot in the hundreds box by six, so move it to the tens box and explode it. Now we have 17 dots in the tens box. Gather as many groups of 6 as you can. I count 2 groups of 6, with 5 remaining. So put a 2 in the ten's place of the solution. Move the 5 tens over to the one's place, and explode them into 50 dots. This gives us 58 dots. Count groups of 6, and we see 9 groups of 6, with 4 remaining. So now our solution becomes 29, thus far. Move the 4 remaining ones, to the tenths box, for a total of 41 dots in the tenth's place. Among the 41 dots, there are 6 groups of 6, and 5 remaining. So thus far, our solution is 29.6. Add a new box for the hundredths. Move the 5 tenths remaining, here, so we now have 50 dots in the hundredth's box. Among them, 8 groups of 6, with two remaining. So thus far, our solution is 29.68. Continue moving the dots to the thousandth's box, and you'll find we're in an infinite loop of always dividing 20 by 3, getting 3 and a remainder of 2. So the result has a repeating decimal of 3's, which is thus 29.683333333....

[@kimberlymatsuda6596]

402/3

[@denitam2063]

do this 9216÷72

[@JamesTantonMath]

9|2|1|6=7|22|1|6 = 7 | 2+14 | 61 | 6 =7 | 2 +14 | 4 + 56 | 16 = 0|1|2|8 x 72