switching to a calculator for multiplication and division

[Shellydon]

My 6th grade DD struggles with multi-digit multiplication and long division and it is causing issues with moving forward in math.  Right now she is doing decimals and fractions.  She is needing to multiply  things like 79.97 x .37 then subtract that answer to get a percentage off of sale.  This problem took her more than an hour because she kept making mistakes in the multiplying.  She understands how to do it, and given a LONG time she can get it right.  However, we are two hours into our school day and she had done 2 problems.  Do you feel like letting her use a calculator now is going to cause problems in when she starts high school math?  If we don't, she will not complete more than 10 lessons in her math book this year because she is so very slow and constantly makes small mistakes and has to redo each problem at least 5 times.  Up until now, I have not allowed her to use a calculator, but school is now taking 8 or more hours each day because math takes 2-4 hours.  She absolutely has trouble focusing, but there isn't any fixing that piece.

[vonfirmath]

30 minutes ago, Shellydon said:

My 6th grade DD struggles with multi-digit multiplication and long division and it is causing issues with moving forward in math.  Right now she is doing decimals and fractions.  She is needing to multiply  things like 79.97 x .37 then subtract that answer to get a percentage off of sale.  This problem took her more than an hour because she kept making mistakes in the multiplying.  She understands how to do it, and given a LONG time she can get it right.  However, we are two hours into our school day and she had done 2 problems.  Do you feel like letting her use a calculator now is going to cause problems in when she starts high school math?  If we don't, she will not complete more than 10 lessons in her math book this year because she is so very slow and constantly makes small mistakes and has to redo each problem at least 5 times.  Up until now, I have not allowed her to use a calculator, but school is now taking 8 or more hours each day because math takes 2-4 hours.  She absolutely has trouble focusing, but there isn't any fixing that piece.

 

If it helps, my 6th grader is in a brick and mortar where they allow them to use calculators for the arithmetic so they can focus on learning the other skills...

 

I'm not thrilled about it. But my own kiddo is one that makes sloppy mistakes in simple arithmetic so using a calculator he's actually doing much better because he can show he understands the skill they are actually trying to teach.  At home, we have talked about how to estimate what size of answer you are expecting so you make sure you've entered the number correctly in the calculator and notice when it gives you something obviously wrong.  (And we still have him do some problems by hand here and there so he doesn't forget how to do it)

I know in my job, math problems like that get done on the calculator (or in Excel) I'm not doing them by hand.

[RenaInTexas]

I am in the anti-calculator group before Algebra. My reasoning is number sense. In my job, everyone used calculators too, but I know of situations where erroneous numbers were presented because of a lack of number sense. It didn't occur to them that the answer made no sense; they just put the numbers in (the computer/calculator) and that was the answer they got back.

Later graphing calculators (if all features are used heavily) will definitely inhibit the development of algebraic thinking. The math department I worked in saw this first hand and we actually discussed banning graphing calculators in algebra, department-wide. Several teachers banned them in their classes all the way through Calculus. This was a college campus, so if a student had become too dependent on a (graphing) calculator before arriving at this college, they were is for a huge struggle. 

I think I would try to uncover why she is struggling and try to address that. Maybe you could address that on the side, while using a calculator (or working the problems with you) to keep things going. Or step back for a week or two to address the issue.

As for the constant small mistakes, IMO, that is a fairly important skill as well. Yes, understanding the math is important, but the ability to do it accurately is just as important. After 15 years in Corporate America, a calculator or computer will not ensure accuracy for a person who is mistake prone. Use math to teach the importance of working carefully, neatly, and reviewing your work because no computer or calculator will overcome those flaws. 

If it helps, math always seems to slow down at the 'decimals and fractions' chapter. It speeds back up later in the book.

[Tanaqui]

If she's working on learning arithmetic then I'm not sure a calculator is a good idea. How about giving her a table that she can refer to? It can just go from 1 - 9, and you can have her fill it in before she starts her lesson every day if you like. Then when she's doing her problems and she gets stuck on "What's 7 x 3" she can look it up rather than having to laboriously calculate it. This is actually what my dyslexic kiddo does.

With that said, the particular combination of "trouble focusing" and "trouble with times tables" makes me wonder about the possibility of a learning disability. A NT sixth grader who has spent a reasonable amount of time on practice and drill should not have excessive problems with her times tables. (I assume that before posting here you have tried tricks such as playing endless games of multiplication war and the like, right?) I'm not saying she does have one, but it's definitely something you might want to look into.

[lewelma]

I tutor math. Calculators are fine for what you are describing. She needs to do fractions by hand though or she will struggle in algebra.

 

[alisoncooks]

My DD uses a math table for situations like long division. I make her do fact practice separately. 

[Jean in Newcastle]

I am another who would use a multiplication table (and have with my kids in the past) instead of a calculator.  I allow calculators once we get to Algebra. 

Edited January 9, 2019 by Jean in Newcastle
spelling

[prairiewindmomma]

One of mine uses a calculator. He has had evaluations, known issues, and years of intervention. He has his basic addition, subtraction and multiplication facts memorized and needs the calculator for multi digit stuff. It’s been fine—but the paperwork trail has been necessary for when it comes time to do standardized testing. 

Don’t forget to spend time learning factors. That’s a huge mental help when doing fractions and percents. It’s a huge time suck if you have to use a calculator to reduce numbers in fractions or convert percents. 

 

[daijobu]

The example you give is pretty nasty, and not the sort of problem you would see in AoPS for example.  I only cite AoPS because it's one of the more challenging math curricula.  Why are the easier math curricula so much harder than AoPS?  (end of vent)

Would it help if you scribed for her?  Be sure to have her tell you where each digit goes and is able to explain why.  

[mamamoose]

15 hours ago, RenaInTexas said:

I am in the anti-calculator group before Algebra. My reasoning is number sense. In my job, everyone used calculators too, but I know of situations where erroneous numbers were presented because of a lack of number sense. It didn't occur to them that the answer made no sense; they just put the numbers in (the computer/calculator) and that was the answer they got back.

Later graphing calculators (if all features are used heavily) will definitely inhibit the development of algebraic thinking. The math department I worked in saw this first hand and we actually discussed banning graphing calculators in algebra, department-wide. Several teachers banned them in their classes all the way through Calculus. This was a college campus, so if a student had become too dependent on a (graphing) calculator before arriving at this college, they were is for a huge struggle. 

I think I would try to uncover why she is struggling and try to address that. Maybe you could address that on the side, while using a calculator (or working the problems with you) to keep things going. Or step back for a week or two to address the issue.

As for the constant small mistakes, IMO, that is a fairly important skill as well. Yes, understanding the math is important, but the ability to do it accurately is just as important. After 15 years in Corporate America, a calculator or computer will not ensure accuracy for a person who is mistake prone. Use math to teach the importance of working carefully, neatly, and reviewing your work because no computer or calculator will overcome those flaws. 

If it helps, math always seems to slow down at the 'decimals and fractions' chapter. It speeds back up later in the book.

You can have excellent number sense and be terrible at memorizing math facts. I think this is a memorization problem. 

[SeaConquest]

20 hours ago, daijobu said:

The example you give is pretty nasty, and not the sort of problem you would see in AoPS for example.  I only cite AoPS because it's one of the more challenging math curricula.  Why are the easier math curricula so much harder than AoPS?  (end of vent)

Would it help if you scribed for her?  Be sure to have her tell you where each digit goes and is able to explain why.  

This is my reaction too. I always know that my son and I have the answer wrong if we are having to do heavy calculations to arrive at the solution (he is working in AoPS Pre-A). Could you, perhaps, move her to a math curriculum that is more conceptual in nature, so that she is not having to grind through these heavy calculations? I always remind my son that the curriculum is called the Art of Problem Solving vs the Art of Calculating for a reason.

[Gil]

On ‎1‎/‎9‎/‎2019 at 11:59 AM, Shellydon said:

My 6th grade DD struggles with multi-digit multiplication and long division and it is causing issues with moving forward in math.  Right now she is doing decimals and fractions.  She is needing to multiply  things like 79.97 x .37 then subtract that answer to get a percentage off of sale.  This problem took her more than an hour because she kept making mistakes in the multiplying.  She understands how to do it, and given a LONG time she can get it right.  However, we are two hours into our school day and she had done 2 problems.  Do you feel like letting her use a calculator now is going to cause problems in when she starts high school math?  If we don't, she will not complete more than 10 lessons in her math book this year because she is so very slow and constantly makes small mistakes and has to redo each problem at least 5 times.  Up until now, I have not allowed her to use a calculator, but school is now taking 8 or more hours each day because math takes 2-4 hours.  She absolutely has trouble focusing, but there isn't any fixing that piece.

I'm really sorry OP, but this whole thing leads me to think she's been allowed to be sloppy and moved along because she "gets the idea" when she should've been made to master the idea, pay attention to detail, scaffolded and supported as she showed her steps, mastered simple techniques to keep her work neat, and been practicing for accuracy as well. It also kind of sounds like she's doing math unsupervised...is she?

To me, the central question isn't whether she should use a calculator. The question is whether she

a- understands what task she's asked to perform AND
b-knows any method to accurately perform that task.

There are a number of ways to break that problem down and solve it but if it's taking her 1 hour to solve 1 problem of this caliber, then it seems like she doesn't know any single method to accurately solve that problem on her own. Which is a slightly bigger worry than whether or not she knows her times tables well. 

Multiplying by double-digits shouldn't take a kid in the 6th grade an hour, it just shouldn't.

[8filltheheart]

I also wonder I feel she really understands what she is doing. How easily can she multiply 79.97 x 7?  79.97x3? Those are basic 3rd grad math problems. Does she understand that the answer to x37 is simply x3x10 + x7? 

I would see if she can do the problems of x7 and x 3 (using different number so it doesn't look like the same problem and I would remove all decimals and simply have her 4 digit by 1 digit problems. If she can, then, no, I wouldn't let her use a calculator bc the concepts are the problem, not the recall. If she can't do those, I would try those with a multiplication table and see how easily she completes them.  I would take this approach to actually narrow in on what it is she is really struggling with.

[Bambam]

I think you stick with pencil and paper. Provide multiplication tables to make it easier. Use graph paper so her numbers all line up. I did not allow my kids to use calculators until Algebra -and then only on a few problems (marked in their book). Although this is basic math, you need to understand it, and you should be able to do it competently and with some speed (although not lightning speed) proves that you do understand it.  I *might* be tempted to do fewer problems every day, but she still does them. 

[City Mouse]

Can you find and/or create similar problems for her to do that cover the same concept but with easier nun era to multiply. For my kids (who attended public school) staring in about 7th grade thee would be both kinds of problems those designed to be solved using a calculator and those designed to be solved by hand or mentally.

[kiwik]

On 1/10/2019 at 12:32 PM, daijobu said:

The example you give is pretty nasty, and not the sort of problem you would see in AoPS for example.  I only cite AoPS because it's one of the more challenging math curricula.  Why are the easier math curricula so much harder than AoPS?  (end of vent)

Would it help if you scribed for her?  Be sure to have her tell you where each digit goes and is able to explain why.  

With a problem like that I suspect they are assuming calculator use.  Can she estimate it mentally?

[73349]

We use the box method for problems like that--it'll come in handy when multiplying polynomials anyway. It's an easier way to see how things are distributed than the usual algorithm IMO. Using graph paper, make four columns and two rows (one for each digit):

            70             9            .9            .07

.3

 

.07

 

And then find the product for each box, and add them all together. (For that many, it's best to stack them; many simpler problems can be finished in one's head.)

Edited January 16, 2019 by whitehawk

[vonfirmath]

An example of a calculator problem.  Working on finding the length of the diagonal in a rectangular prism given height, length, and width.  He did all the math on paper and got the square root of 285 for the length of that diagonal.  Worked the factors -- and there is no repeated factor 3 x 5 x 19.  So he ended up finding the answer to the nearest tenth (as requested) using the calculator.

[Coco_Clark]

I'm another "no calculator until algebra" person.  It's a hill I'll die on, and yes, several of my 5th graders have learning disorders that make math harder than average. They still do it on paper.

I see three possibilities on why your daughter is having issues.  One- She doesn't have her facts memorized.  This is absolutely essential.  It's hard. Almost all kids can do it though.  Sing them, chant them, use visuals.  

Two- Sloppiness. Long division and multiplication take neatness.  So does algebra, so learn it now.  Some of my kids prefer graph paper.

Three- she doesn't know it as well as you think she does.

[Shellydon]

On 1/9/2019 at 5:32 PM, daijobu said:

The example you give is pretty nasty, and not the sort of problem you would see in AoPS for example.  I only cite AoPS because it's one of the more challenging math curricula.  Why are the easier math curricula so much harder than AoPS?  (end of vent)

Would it help if you scribed for her?  Be sure to have her tell you where each digit goes and is able to explain why.  

Yes, it does help if I scribe.  However with 4 kids to homeschool, it isn't practical. 

[Shellydon]

On 1/16/2019 at 9:53 PM, Coco_Clark said:

I'm another "no calculator until algebra" person.  It's a hill I'll die on, and yes, several of my 5th graders have learning disorders that make math harder than average. They still do it on paper.

I see three possibilities on why your daughter is having issues.  One- She doesn't have her facts memorized.  This is absolutely essential.  It's hard. Almost all kids can do it though.  Sing them, chant them, use visuals.  

Two- Sloppiness. Long division and multiplication take neatness.  So does algebra, so learn it now.  Some of my kids prefer graph paper.

Three- she doesn't know it as well as you think she does.

She has all of her math facts memorized completely. I have her use graph paper, which definitely helps, but doesn't completely solve the problem.  It would probably help some if she were neater, but it would help even more if she had a better attention span.

[Shellydon]

On 1/13/2019 at 2:26 PM, 8FillTheHeart said:

I also wonder I feel she really understands what she is doing. How easily can she multiply 79.97 x 7?  79.97x3? Those are basic 3rd grad math problems. Does she understand that the answer to x37 is simply x3x10 + x7? 

I would see if she can do the problems of x7 and x 3 (using different number so it doesn't look like the same problem and I would remove all decimals and simply have her 4 digit by 1 digit problems. If she can, then, no, I wouldn't let her use a calculator bc the concepts are the problem, not the recall. If she can't do those, I would try those with a multiplication table and see how easily she completes them.  I would take this approach to actually narrow in on what it is she is really struggling with.

She can do the 79.97 X 7 without too much difficulty and yes she understands that concepts behind the math. 

[Shellydon]

On 1/13/2019 at 2:10 PM, Gil said:

I'm really sorry OP, but this whole thing leads me to think she's been allowed to be sloppy and moved along because she "gets the idea" when she should've been made to master the idea, pay attention to detail, scaffolded and supported as she showed her steps, mastered simple techniques to keep her work neat, and been practicing for accuracy as well. It also kind of sounds like she's doing math unsupervised...is she?

To me, the central question isn't whether she should use a calculator. The question is whether she

a- understands what task she's asked to perform AND
b-knows any method to accurately perform that task.

There are a number of ways to break that problem down and solve it but if it's taking her 1 hour to solve 1 problem of this caliber, then it seems like she doesn't know any single method to accurately solve that problem on her own. Which is a slightly bigger worry than whether or not she knows her times tables well. 

Multiplying by double-digits shouldn't take a kid in the 6th grade an hour, it just shouldn't.

This is pretty judgmental...

[Shellydon]

Thanks for the ideas.  I'll print out multiplication tables and see if that helps.  Dad has a Ph.D in engineering, so math is a big topic in our house. I haven't allowed her to be sloppy nor am I a poor teacher. 

[8filltheheart]

1 hour ago, Shellydon said:

She can do the 79.97 X 7 without too much difficulty and yes she understands that concepts behind the math. 

If she can do that problem without difficulty, than the difficulty of the example problem does not make sense if she really understands the concepts.

[prairiewindmomma]

8 minutes ago, 8FillTheHeart said:

If she can do that problem without difficulty, than the difficulty of the example problem does not make sense if she really understands the concepts.

unless she has visual processing issues and/or dysgraphia.  79.97 x 7 is only one line of numbers in the answer.  Multiplying multi digit numbers together creates multiple lines of numbers in the answer which then also have to be dealt with.

Was there also an issue with multi digit addition and subtraction?

Things we tried:

*graph paper with every other column highlighted

* putting each value into different colors (ones were written in green ink, tens in  bright blue, hundreds in red, thousands in black---you want high contrast between the colors

Edited January 18, 2019 by prairiewindmomma

[Coco_Clark]

1 hour ago, prairiewindmomma said:

unless she has visual processing issues and/or dysgraphia.  79.97 x 7 is only one line of numbers in the answer.  Multiplying multi digit numbers together creates multiple lines of numbers in the answer which then also have to be dealt with.

Was there also an issue with multi digit addition and subtraction?

Things we tried:

*graph paper with every other column highlighted

* putting each value into different colors (ones were written in green ink, tens in  bright blue, hundreds in red, thousands in black---you want high contrast between the colors

 Yes, after the replies by OP I'm starting in this direction too.  My ADHD daughter would absolutely not be capable of long multiplication or division if unmedicated.  Heck, even on meds there are days.  

A learning disorder would definitely explain the struggle.  Because, I hate to say it, but I agree there is no reason why a problem like they should take an hour.  Now that math facts memorization, neatness, conceptual understanding, and plain willfullness has been discounted.  Not consistently.  

  

[vonfirmath]

24 minutes ago, Coco_Clark said:

 Yes, after the replies by OP I'm starting in this direction too.  My ADHD daughter would absolutely not be capable of long multiplication or division if unmedicated.  Heck, even on meds there are days.  

A learning disorder would definitely explain the struggle.  Because, I hate to say it, but I agree there is no reason why a problem like they should take an hour.  Now that math facts memorization, neatness, conceptual understanding, and plain willfullness has been discounted.  Not consistently.  

  

 

Woah. ADHD affects this? Becuase my son was just diagnosed at the beginning of the year but we are using strategies to combat, not medication.

[prairiewindmomma]

11 minutes ago, vonfirmath said:

 

Woah. ADHD affects this? Becuase my son was just diagnosed at the beginning of the year but we are using strategies to combat, not medication.

My severely ADD kid (different one) needs meds to do schoolwork. Pm me if you want details. I resisted meds for him for a long time.

[Coco_Clark]

3 hours ago, vonfirmath said:

 

Woah. ADHD affects this? Becuase my son was just diagnosed at the beginning of the year but we are using strategies to combat, not medication.

 

TBH, my daughter's ADHD is overlapped by ODD and fetal exposure to both alcohol and meth, which means it's unbelievable severe.  She's on two different ADHD medications in order to function.

My son, not born drug affected, has your more average ADHD.  He's not currently medicated, as we can compensate.  But the above girlie did teach me that yes, there's a place where the child can be served by medication.  And it probably won't be long for him too.

But yes, ADHD can, and very often does, affect executive functioning skills like staying organized.  It does in both my ADHD children.  Not to mention, the obvious ability to focus.  It can also affect emotional control in a huge way.  Our current neuro-phychistrist will talk your ear off about how many boys she gets with "violent rage" or an "anxiety disorder" when nope, they are ADHD.

It's easy to think of ADHD as just hyperactivity and attention issues, cuz that's the name.  But honestly their entire mind just works differently.

[8filltheheart]

7 hours ago, prairiewindmomma said:

unless she has visual processing issues and/or dysgraphia.  79.97 x 7 is only one line of numbers in the answer.  Multiplying multi digit numbers together creates multiple lines of numbers in the answer which then also have to be dealt with.

Was there also an issue with multi digit addition and subtraction?

Things we tried:

*graph paper with every other column highlighted

* putting each value into different colors (ones were written in green ink, tens in  bright blue, hundreds in red, thousands in black---you want high contrast between the colors

Would separating the problem into 3 separate steps help? 79.97 x .07=  ,  79.97 x .30= , and then adding them together as the next step? 

[Sk8ermaiden]

Yep.. DD has ADHD and she will understand the concept but make a million dumb mistakes in the execution when she is not medicated - exact same as me when I was younger.

Meds are life changing. 

My kid is super smart. Not Gifted, but really bright and curious. We'd use Brainpop at our small co-op. She loves BrainPop! She is engaged and listening! She's interested in the topic! We get to the quiz at the end and she would get EVERY QUESTION wrong. Every one. The first co op after she got on meds, she answered every question correctly, and was the first kid to come to each answer. She was able to take that information and file it in the correct places, and then recall it when needed. I could bang out examples of how it changed her life all day long and I have similar stories for myself. Her writing came up several grade levels up the week she went on meds. The ability to think about what you need to write, plan it in your head, and get it to the paper in a coherent fashion without getting overwhelmed in the process. The most insidious part of ADHD is that it makes smart kids feel that they are stupid; good kids feel like bad kids.

[Gil]

9 hours ago, Shellydon said:

This is pretty judgmental...

I'm sorry that I made you feel attacked. That wasn't my intention. 

9 hours ago, Shellydon said:

Thanks for the ideas.  I'll print out multiplication tables and see if that helps.  Dad has a Ph.D in engineering, so math is a big topic in our house. I haven't allowed her to be sloppy nor am I a poor teacher. 

I hope that you find the solutions that you need. All the best.

Edited January 19, 2019 by Gil

[Sk8ermaiden]

9 hours ago, Shellydon said:

Thanks for the ideas.  I'll print out multiplication tables and see if that helps.  Dad has a Ph.D in engineering, so math is a big topic in our house. I haven't allowed her to be sloppy nor am I a poor teacher. 

 Oh man, I posted up thread about ADHD, and I'm NOT saying your kid has it because it could be a million things, but for mine, it was. And she made mistakes all the time, could always find them when she had to re check, and so, so obviously understood the concepts. She's extremely mathy. If I had made her do the same concepts over and over until she had a high level of accuracy quickly, we would still be doing second grade math, at best. We used graph paper to keep things straight as well as a number of other strategies (many of the strategies people suggest for this are super hard for an ADHD brain to implement, so not that useful.) It also was not because she was allowed to be sloppy or that I was a poor teacher. Once we figured out what was wrong, her answers started coming quickly and with accuracy. She obviously fully understood everything and had not been harmed by being allowed to progress normally despite mistakes. 🙄

It's like suggesting that the teacher or child is at fault when a child with dyslexia struggles with writing. It's not. Some things are just not a simple fix.

[prairiewindmomma]

1 hour ago, 8FillTheHeart said:

Would separating the problem into 3 separate steps help? 79.97 x .07=  ,  79.97 x .30= , and then adding them together as the next step? 

 

For my kid working independently, no.

If I am scribing and working directly with him, yes.

 He has WAY more going on than just visual processing and dysgraphia....see my above post about lots of testing, known issues, and years of interventions with qualified specialists on board.