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# How Can You Use Your Hands as Multiplication Manipulatives?

Another math coach related to me today the story of how a student she taught had named fingers sections as something that comes in groups of threes.  She took this concept and helped students use this to develop multiplication strategies to learn their threes multiplication tables.  Fours multiplication tables can be learned as well if students include counting the top part of their palm.  See the pictures below for more clarification.

Update September 2017:  Due to one of the comments below, I made a video describing how this works with the 3s multiplication facts.  Click here for the video.

#### 53 Responses to How Can You Use Your Hands as Multiplication Manipulatives?

• youjiang says:

hi, can you explain further how this work? do i have to write all the numbers on the different sections of the fingers? is the maximum range 3*5=15? only up to 5? hope you can help. thank you.

• Ms. K says:

Well, I wouldn’t recommend actually writing the numbers on the fingers (although I guess you could). I just did that for the picture so that it would be easier to explain. Students naturally count on their fingers, so making them aware that there are three sections on their fingers would help them count each section of their fingers to figure out a multiplication fact. Eventually. students could count by 3’s as they touch each finger and would no longer have to count each section by 1’s as they get more comfortable with the multiples of three. You could do up to 3×10=30 on your hands. I was just holding the camera with my other hand and so my other hand isn’t in the picture. Let me know if you still have questions.

• Carrie says:

Oh my goodness! Stop crossing your zeros! I have to get my upper level math kids out of this habit. A crossed zero means no solution, not zero. These are very different things.

• Kw says:

It also means zero so not to confuse it with an O

• Shannon Venable says:

This is confusing. Can you explain how it works?

• Ms. K says:

Did the above comments section help you understand how students can use their finger sections to learn their 3’s multiplication facts? If not, what exactly is it that you don’t understand, so that I will better know how to answer your question.

• chell says:

This is TOTALLY confusing……..someone please explain and yes I’m human>>>>>>

• Ms. K says:

If you look at the back of your hand, your fingers are divided into 3 sections where they bend. If you train children to touch each part of their finger then they will have fifteen sections on each hand …or 3 sections per finger. So if a student was trying to solve let\’s say 3 x 4, then they could hold up 4 fingers and count the sections by ones. For the first finger they would count 1, 2, 3…the second finger 4, 5, 6, the third finger 7, 8, 9, and the fourth finger 10, 11, 12. So there are four fingers with 3 sections on each leading to the answer 12. Eventually students would hopefully stop counting each section by ones and realize that each finger could be counted by 3. At that point, then the child could count on four fingers saying 3 as he touches the first finger, 6 as he touches the second finger, 9 as he touches the third finger, and 12 as he touches the fourth finger.

• lucia lang says:

I get the numbering of the fingers but I do not know how you come up with the answers. Must you count every digit to get to the answer or is there a short cut to the answer?

• Ms. K says:

There is no shortcut. Students would have to count each finger section by ones if they are fledgling learners of multiplication. Eventually they will hopefully count just the whole finger skip counting. Using your finger sections is a very concrete direct modeling strategy according to CGI (Cognitively Guided Instruction) in which each item is counted. When students gain some understanding of multiplication as equal groups, then they can use a skip counting strategy.

• Mary Scheckman says:

It looks to me that the purpose of the numbering is just to help kids skip count. I would introduce the 3 section concepts but perhaps have them write only the 3,6,9,12,15 on the bottom section of each finger for the first lesson. I taught my kids skip counting songs. They could partner up both strategies.

• J Sicat says:

Wow! This is cool. It makes sense and you can even expand it to your second hand if you’re really desperate to figure something out without a calculator on hand. I’m sharing this. 🙂

• Tiffany says:

This is great!

• Shon says:

MS. K, This is brilliant! Thank you so much for sharing your multiplication tip. I cannot wait to show it to my nephew.

• Ms. K says:

Great! I’m so glad I could help!

• Tara says:

Please oh please stop teaching students hand tricks to teach multiplication Facts! Please Have your students memoriZe their facts! I am a middle school math teacher and it is difficult to teach algEbra when theY don’t have the facts memorized. Students take timed tests in middle school and do not have the time to Perform these tedious triCks when they are required to solve multi stEp math word problEms. Thank you so much!

• Ms. K says:

I understand your concern. I work with older students, as well as ones with fledgling understanding. I do emphasize memorization after students have developed a foundation for understanding of multiplication. The multiplication hand trick is merely a step in foundational understanding.

• lynn says:

Sounds like Tara teaches to the test. Enough said

• Jill says:

Middle school kids should have already mastered their facts long before.
This math trick is useful for younger children who need to understand that 5×3 means 5 sets of 3. Once they understand the concept, then they should go on to start memorizing a few facts.

• Ms. K says:

Thanks for your comment! I agree… I think that the you tube video trick would be somewhat confusing because it took me a while to figure it out after watching it…however, I still think it’s cool and I want to figure out what makes it work :)!

• thisisme says:

Except 5×3 would be 5, 3 times so 3 sets of 5 and 3×5 would be 3 five times so five sets of three.

• Teachermom says:

Teaching to the test….it’s what all great teachers do!!

• joellen claypool says:

Memorization Is very important. However I struggled for years with my older boy with that method. We would repeat them and practice over and over again and the next day he would forge them. I learned that he had dyscalculia and could not learn that way. Once I was introduced to the hand tricks and lattice math our lives became much easier and in turn he was able to remember some of them because he could picture the method in his mind. People have to learn the way that is best for them.

• Ms. K says:

Great comment! That reminds me of a story the math common core trainer for our state told about her son with a VERY high IQ who couldn’t learn his math facts. She said she worked and worked with him every night, and he would never learn them. She had him tested 6 times to make sure they hadn’t made a mistake with his IQ testing! She said that it wasn’t until he got to 9th grade and had to use a calculator that he learned them. He could remember them by visualizing them on the calculator screen!

• Rebecca Burton says:

joellen – well done for your comment – I was quite disgusted to read some of the other comments saying children SHOULD memorise all theses facts. My daughter also has dyscalculia and it doesn’t matter how many times she is forced to try and memorise the numbers – she just doesn’t see it. All I can say is that I am glad that some of these blinkered teachers on here don’t teach my daughter. Everyone has different learning styles and as teachers they should be aware of this – or do they just label these kids a thick (as I was labelled, as I now know I also have the same problem as my daughter and at the age of 41 I still cant real off my times table!)

• Melba says:

For heaven’s sake lady. By the time the child reaches middle school and doing algebra he or she should have the tables memorized. This is just a tool to help young people learn their tables. I really doubt that when the student is older he or she would not be counting on their fingers unless they have learning disabilities. A math teacher and you can’t use common sense to figure out this fact! Really!! Ye gads we are in trouble with you teaching our children.

• Fi says:

It is not just about memorisation. I was a bright kid at school – I finished with the highest grades overall in the year at my school, however although I UNDERSTAND maths, it has never come easily to me. I can work things out, I understand why they work, but I don’t do it quickly and I haven’t got things memorised. Surely the fact that students can earn marks in maths exams (even if they get the answer wrong) by writing down their workings out if they have got the process right, shows that having a memory isn’t as important as understanding how to get to the answer. You can only memorise a finite number of combinations, but teach someone HOW to get to the conclusion and they can work it out.

• Mrs Guerra says:

I agree!!!!

• Ms. K says:

oh my gosh! This is the coolest thing ever. This video shows the multiplication facts from 6’s to 10’s on your fiingers. i don’t know if this would help or confuse kids, but i just found it….see what you think.

• Jill says:

I think the trick in the video would only work for older kids (it can be pretty confusing) who have pretty much already learned their times tables, and maybe have a couple they occasionally forget. But then I still think it still would be faster to add them up.
The trick you showed in your post is helpful for younger children — they *need* to actually *SEE* that 5×3 is 5 sets of 3 each. Eventually they will start learning a few multiplication facts now and then, and will gradually not need to count anymore.
Counting should only be used to teach the concept of multiplication; not relied on in place of memorization.

• Bahni says:

I lOve this! I home scHool my girls and Am always looking for tricks to make math easier and fun. Thank You!

• Ms. K says:

I appreciate your comment! Thank you for reading my blog…come back and visit soon ;)!

• Rita says:

The hand trick for 6’s and higher works! I had a fourth grader this year who couldn’t get her facts memorized. Once I showed her the video and we practiced the strategy she soon had the facts down. She just needed something tactile to help her remember.

• Ms. K says:

Thank you so much! That is good to know!

• Tonja says:

Wow, what a fascinating concept. I am looping with my class and this a perfect trick for the 3s and 4s. Thanks for sharing!

• sam says:

Does this strategy only go with the number 6? if not may you please state. thx

• Smith says:

I never memorized my multiplication facts (not for lack of trying) and to this day don’t know them. I couldn’t pass a spelling test either. I came up with a method similar to this in middle school (perfected it in college by applying counting in sign language). However, I use the back of my hand and count nuckles. I came up with it so I could count on my fingers discreetly because I didn’t want to be made fun of for still needing to count on my fingers. (Teachers obsessed with memorizing made me an easy target. Teachers, also sometimes need to think before speaking) I got VERY fast at it and still use it. It looks like I’m just rubbing my hands together but I’m really doing math. lol

• Ms. K says:

Please do tell more!!! Could you explain further about how your method works. I am sure others would benefit from your method as well.

• Susan says:

Thank you. Thank you. Thank you. My daughter says thank you, too!

• Ms. K says:

You’re welcome!!

• Monique says:

Thank you from all the moms who have struggled with trying to get their kid to memorize their multiplication facts for years, and the child has not memorized them yet despite what teachers say.

• Brandi says:

Thank you for sharing this! My 16yr old daughter still doesn’t know her times tables despite years of tutoring, being diagnosed with a learning “differentiation” in math and being in team-taught math classes. I’m going to see if this sticks with her!

• Mel says:

This is amazing!!!! 🙂 got it right away!!!

• than you for the sharing its useful

• Fiona says:

I found this method fabulous to teach the kids. It is so visual it makes sense to them. Thanks

• Ms. K says:

I’m so glad it helped your kids! Thank you for letting me know!

• Shelly says:

Memorizing teaches nothing! They have to be able to see why 3 × 4= 12 or all math concepts later in life will not truly be understood! Excellent visual! 🙂

• Kait says:

Not sure I would use when beginning to teach multiplication but could be used as a great way to help students who might be struggling.

• Diann Roberts says:

This may save my grandson’s 3rd grade life! THANKS!

• Ms. K says:

You are most welcome!

• Lisa lopez says:

A video demonstration would be great.

• Ms. K says:

I will consider making one. Thanks for the suggestion.