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Is mental math a necessity in the primarily years?


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#1 EngOZ

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Posted 01 March 2017 - 03:52 AM

I've never really done any mental math - not consistently anyway- with my kids at the primary level.
I don't see it as a necessity, but I see it's value i.e learning the times table. In the primary grades my kids don't use a calculator, they tend to work things out in their heads or with their fingers. There's also enough problems to tax their brains in a typical lesson. That's my justification.

Edited by EngOZ, 01 March 2017 - 04:02 AM.


#2 Monica_in_Switzerland

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Posted 01 March 2017 - 05:11 AM

I suppose it's a matter of opinion, but in my mind, mental math is possibly the MOST important part of elementary math.  

 

Ex.  If my kids can do 216 x 4 in their heads, I know for sure that they are understanding the math, rather than memorizing steps to an algorithm.  Fast mental calculation abilities eliminates the need for blind memorization of the tables.  Ex, my dd has not memorized her x6 tables yet because we don't really worry about memorizing them much.  So when she came to a problem 8 x 6, she did the following, in her mind, in about 2 seconds:  6 x 10 is 60, cut in half to get 6 x 5 is 30, add 18 which is 6 x 3, so 6 x 8 is 48.  Now, that might seem convoluted compared to a memorized table, but it shows me, beyond any shadow of a doubt, that she understands the properties of multiplication.  Similarly, if she needs to divide by 4, she often times divides by 8 then multiplies her answer by 2.  It's weird, but it shows she knows that she's doing.  

 

Mental math is also what allows a student to "guesstimate" an answer to a problem, and then compare it to the actual answer and see if there is any obvious errors.  

 

I could keep going on about all the advantages of mental math, but I'm sure others will chime in to agree and disagree with me, so I'll stop there!  

 

 


Edited by Monica_in_Switzerland, 01 March 2017 - 05:13 AM.

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#3 regentrude

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Posted 01 March 2017 - 08:13 AM

Definitely a necessity. Especially in the primary years. Addition facts - you want to get to the point where the kid knows 3+4=7 without using the fingers or manipulatives. Then more complex additions/ subtractions. You want to build a number sense and fast execution of problems mentally. 

 


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#4 EKS

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Posted 01 March 2017 - 08:54 AM

I did not learn how to do math mentally (and barely any other way either) in school.  I learned when I worked in a lab and had to do calculations all the time.  When we had gloves on, we weren't allowed to touch the calculators, so I figured out how to do it then.  

 

I think it is a critically important skill.  It builds number sense in an authentic way.


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#5 mathmarm

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Posted 01 March 2017 - 09:29 AM

I think a strong number-sense is critically important and that being able to perform arithmetic accurately and quickly in your mind, in context situations is vitally important. We even teach/use numbers in the expanded format. In the early grades, we mostly call multi-digit numbers by their "ACTUAL math names", instead of their "nick names".

 

"Ten, Eleven, twelve, thirteen" doesn't communicate much about the quantitles to people, but "1-ten, 1-ten 1, 1-ten 2, 1-ten 3,..." does.

 

Others may disagree, but like Monica and Regentrude, I consider it a necessity.


Edited by mathmarm, 01 March 2017 - 09:30 AM.

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#6 OneStepAtATime

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Posted 01 March 2017 - 09:58 AM

Can you live without mental math? Yes.  You can memorize or use a calculator.  That's how I got through school.  No one taught me mental math.  However, I felt I was never very good at math.  Why?  I wasn't taught the concepts underlying all those algorithms and addition/subtraction/multiplication/division at a very meaningful level.  Without the mental math side it was kind of like doing math with half my brain tied behind my back.  I was so used to doing it that way that I didn't even realize how crippled I actually was, though.  This was just normal.

 

Having to start over teaching my own kids I realized that taking the time to learn math at a deeper level is a huge asset.  Some kids pick it up quickly while others need a LOT more time for it to sink in but it really is a huge asset.  Is it absolutely necessary?  No, you can survive without it.  But why keep doing math with one part of your brain tied behind your back?

 

 


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#7 RenaInTexas

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Posted 01 March 2017 - 11:01 AM

Yes, as far as knowing multiplication facts and addition facts: 1-12. 

 

However, I don't think it is a necessity to be able to do multiple digits mentally (236x7 or 125+988) in primary school. It should be encouraged but over time many will begin to do this naturally. 

 

My kids do 2 mental math problems a day with morning work and that is all. So encourage -- yes, absolute necessary - no.


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#8 EngOZ

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Posted 01 March 2017 - 07:06 PM

Thanks everyone, in the primary years, what do you want your kids to know/master when it comes to mental math?



#9 mathmarm

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Posted 01 March 2017 - 07:28 PM

Thanks everyone, in the primary years, what do you want your kids to know/master when it comes to mental math?

End of Grade K: Number bonds for addition/subtraction all the way to 20-10-10.

End of Grade 1: Number bonds for multiplication/division all the way to 100-10-10

End of Grade 3: Able to perform common calculations (estimating grocery bills, calculating change, tips and tax) in real time.


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#10 MistyMountain

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Posted 01 March 2017 - 07:33 PM

To me it is very important and I pause when I need to like I had to recently with a certain type of Signapore problem to make sure they were doing it the mental math way being taught. If I could go back I would do it differently for my oldest child who is now behind in math because she just learned procedural math. I think being able to solve problems different ways and being able to visualize what is happening is important. I like emphasizing left to right methods and calling things by hundreds, tens and ones. I like the idea of starting with the concrete and showing the problem before working out the problems. I also like doing a lot of subitizing type stuff then extend it to addition and subtraction so they can think through and picture what is happening. For my youngest I have done subitizing, then addition and subtraction within 20 with Cuisenaire rods, ten frames and the abacus then two digit with one digit, then two digits within 100 then any two digit number. For multiplication I really like teaching it first with rods by them figuring out how to group them to solve it the easiest and to introduce division at the same time. I like the way they show multiplication in Educational Unboxed. I know you mentioned using Miquon. That is a good curriculum for conceptual or mental math.

Edited by MistyMountain, 01 March 2017 - 07:37 PM.

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#11 regentrude

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Posted 01 March 2017 - 08:32 PM

End of Grade K: Number bonds for addition/subtraction all the way to 20-10-10.

End of Grade 1: Number bonds for multiplication/division all the way to 100-10-10

End of Grade 3: Able to perform common calculations (estimating grocery bills, calculating change, tips and tax) in real time.

 

I agree with the first, but am confused about the bolded: how do you teach a 3rd grader to calculate percentages? That is not covered by 3rd grade


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#12 debi21

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Posted 02 March 2017 - 02:06 AM

I never did it as a child, and I am not following a particular program with my son, but we keep talking about different strategies. I am starting to see it pay off. He is starting to intuitively use the distributive property, and he is able to effectively use some different strategies for mental subtraction. We were working on the traditional multiplication algorithm and he was trying to work a lot of the 2 digit by 2 digit ones in his head. So then I gave him like 2,351 x 498, trying to show him he needed the algorithm as the numbers got bigger. He didn't do it all in his head and used his paper, but multiplied by 500 and subtracted two times the number, demonstrating how he still didn't need the algorithm. I was pleased with the number sense he demonstrated.


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#13 RenaInTexas

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Posted 02 March 2017 - 11:38 AM

We use Singapore Mental Math. They only do 2-3 problems per day because my goal is to expose them to mental math strategies. I do not require mastery of them.

 

As far as mastery, I only require mastery of: multiplication (1-12 x 1-12) and addition (1-12 + 1-12); and estimation (so instead of 125x47 -- estimate 100x50).

 

I do require mastery of number sense; which can be done without mastering mental math beyond the basics. 


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#14 wendyroo

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Posted 02 March 2017 - 11:53 AM

I agree with the first, but am confused about the bolded: how do you teach a 3rd grader to calculate percentages? That is not covered by 3rd grade

 

I teach it as a mixture of multiplication and fractions long before I introduce the word percent.

 

"In our state, we have to pay the government 6 cents for every dollar we spend.  You want to buy a lego set for $8.99; about how many dollars is that?  Okay, so if you have to pay 6 cents for each of those dollars, how many cents do you have to pay the government in tax?  Perfect, so if you have to pay the store $8.99 and the government 54 cents, how much will you have to pay in total?"

 

Eventually we discuss that 6 cents per dollar means 3 cents per half dollar or 2 cents per third of a dollar or one cent per sixth of a dollar.  That is close enough for practical purposes until they actually learn how to calculate percentages exactly.

 

I use the same process with tips.  "We are going to tip 15 cents for each dollar we spent."  I want to emphasize multiplying and dividing by 10, so we always figure out 10% (or, as I present it, 10 cents for every dollar we spent), and then we halve that and add them together...all well within the wheelhouse of 3rd grade math.

 

Wendy


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#15 vonfirmath

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Posted 02 March 2017 - 11:56 AM

I teach it as a mixture of multiplication and fractions long before I introduce the word percent.

 

"In our state, we have to pay the government 6 cents for every dollar we spend.  You want to buy a lego set for $8.99; about how many dollars is that?  Okay, so if you have to pay 6 cents for each of those dollars, how many cents do you have to pay the government in tax?  Perfect, so if you have to pay the store $8.99 and the government 54 cents, how much will you have to pay in total?"

 

Eventually we discuss that 6 cents per dollar means 3 cents per half dollar or 2 cents per third of a dollar or one cent per sixth of a dollar.  That is close enough for practical purposes until they actually learn how to calculate percentages exactly.

 

I use the same process with tips.  "We are going to tip 15 cents for each dollar we spent."  I want to emphasize multiplying and dividing by 10, so we always figure out 10% (or, as I present it, 10 cents for every dollar we spent), and then we halve that and add them together...all well within the wheelhouse of 3rd grade math.

 

Wendy

 

!! I hadn't even thought about it. But you are right. I learned how to tithe long before I learned about percentages formally.  Just this way "ten cents per dollar to the church, ten cents per dollar to missions" And rounding to whatever form of change I could get best.

 



#16 wendyroo

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Posted 02 March 2017 - 12:27 PM

End of Grade K: Number bonds for addition/subtraction all the way to 20-10-10.

End of Grade 1: Number bonds for multiplication/division all the way to 100-10-10

End of Grade 3: Able to perform common calculations (estimating grocery bills, calculating change, tips and tax) in real time.

 

That is not how I approach things.

 

In K, I put a huge emphasis on number bonds within 10.  "Making 10s" is is one of my main K-level goals.

 

After that, I switch almost all of the mental math focus onto manipulating numbers, not memorizing them.  I would much rather them practice and learn how to figure out that 9 + 6 = 15, rather than just memorizing it as so.  Strengthening the mental pathway that "sees" one move from the 6 to the 9 to make them into a 5 and a 10, that is a multi-tasker skill that will serve them well when dealing with all sorts of numbers.

 

I am a happy camper if my first graders can mentally add two or three 2/3/4 digit numbers...even if they haven't committed 7 + 5 to rote memory quite yet.

 

When we move on to multiplication, like Monica_in_Switzerland, I put very little emphasis on drilling the facts.  Eventually, they will figure out that knowing the multiplication table is faster than having to calculate each answer every time.  Until then, however, there is a lot of value in them "seeing" 7 * 8 as 7 * (10-2) = 70 - 14 = 56.  That is the distributive property, and really, truly understanding how that works is worth a lot more to me than being able to simply spit back that  7 * 8 = 56.  

 

To me, mental math is almost all about making numbers dance for you.  Can a kiddo mentally figure out 38 * 4?  Can they figure it out another way to confirm their first answer?  Just for fun, how many different paths can they find to the answer?  Are some faster?  Are some slower?  Which methods would be most helpful if the problem was 39 * 4?  What about 38 * 5?  Etc.

 

Wendy


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#17 mathnerd

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Posted 02 March 2017 - 12:46 PM

Mental math is the single most important thing to learn in the elementary grades. But, I like mental math to be an extension of a well developed and sophisticated number sense. So, if a child were to work on a long division problem or a 4 digit multiplication problem, the child should have a sense of what the correct answer should look like and a sense that things are not going right when there are mistakes. This step comes before "checking your work" and I call this "arithmetic intuition" and with enough practice this becomes second nature.

I work on this number sense a lot in the early years. I incorporate it in several different ways constantly - and they are all basic commonsense math facts - some examples:

1. any multiple of 5 will always end in a 0 or 5, anything multiplied by 2 or any other even number will be an even number

2. anything divided by a number approximately half its size should result in approximately 2 as the answer and other variations of this theme

3. the fractions get smaller the larger the denominator gets

4. jump from landmark to landmark along an imaginary number line when performing additions or subtractions mentally - e.g. 350-205 -> start at 350 on the number line, jump by 50 to reach 300, jump by 50 to reach 250 and then jump by 45 to get 205 => 3 jumps together led us to the answer on the number line.

5. If an answer you get after multiplying 2 numbers is less than one of the multiplicands (positive numbers), the child should already know that he either dropped some trailing zeros or made some other mistake

6. If the result of a division results in a number higher than the original number, the possibilities are that the divisor is a fraction or that the child made a mistake

7. I teach tax and tips similar to how wendy described. In my state, the salestax is almost 10% - so, I taught how to calculate 10% first and then when that concept solidified, I taught how to calculate the exact percentage as per state tax which is 9.35%.

8. I teach how to regroup to add and subtract rather than to work with the numbers that are given in the problem directly

9. Another strategy is to regroup and multiply mentally  e.g. 235 X 5 = 200 x 5 + 30 x 5 + 5 x 5

10. Adding and subtracting using the 10-key and the 5-key method -> 5 + 7 = 5 + (10-3), 2 + 4 = 2 + (5-4) etc.

I will come back and edit this if I remember more.

After doing this for a few years, my son is very advanced in mental math. He can handle 3 digit multiplication mentally and he does it in his free time to challenge himself.

 

BTW/ most of the above strategies that I gained are from haunting this forum for several years - many generous posters have shared their math teaching philosophies for early elementary years here for a long time.


Edited by mathnerd, 02 March 2017 - 05:34 PM.

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#18 Spy Car

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Posted 02 March 2017 - 02:53 PM

Thanks everyone, in the primary years, what do you want your kids to know/master when it comes to mental math?

 

Here I think one need to differentiate between the ability to manipulate numbers in a fashion that builds number sense, and simply memorizing math facts. With Singapore Math the initial emphasis is on the strategic manipulation of numbers as opposed to memorization. This is the right emphasis IMO as the mental math skills are scaleable to numbers that are far too large for memorization alone.

 

Plus early memorization can frustrate early re-grouping work that is the most basic foundation of mental math skills. As when a kid says "I know 8 plus 7 is 15, why do I need to explain my re-grouping strategies?"

 

Obviously one will hope for (expect) automaticity with basic math facts. But better those come organically as part of the process of learning mental math and re-grouping skills (with follow up work if necessary) than putting the cart before the horse by focus on memory work.

 

I'd say mental math skills are fundamental and essential components of an outstanding elementary math education.

 

Bill


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#19 SparklyUnicorn

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Posted 02 March 2017 - 03:56 PM

Although what is meant by mental math?  Is this cold memorization of the multiplication tables, for example?  I assume nobody is talking about that.  So what is the OP doing that isn't what others here are saying they are doing or have done?  Sounds to me like EngOZ does in fact work on mental math. 

 

Hopefully I'm wording that correctly.

 

 


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#20 Ausmumof3

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Posted 02 March 2017 - 04:24 PM

I think it's important to define what you mean by mental math. Knowing the facts by rote or knowing how numbers work and being able to move them around in your head. Singapore does a great job of the second one more so than the first. I think for one of my kids the method has been very successful with the other one less so. In part because now with longer more complicated problems he is still having to manipulate the numbers to get the easier solutions within the problems then put it all together and often forgets one of the numbers or changes it and comes up with the wrong answer. For the other kid it's worked much better as they've internalised the math facts over time. I actually think a mixed approach is best in the same way I use phonics for reading but I still find some words are best taught as sight words in the early years. They improve fluency.

In the same way, I think, once you have a really solid understanding of how to manipulate numbers and work with them in your head it's really worthwhile for some kids just to spend time on the maths facts to improve speed and accuracy.

I remember sitting in one of those games for a pantry tea and one of the games involved adding up a grocery list. All the oldies who had been drilled in the old style were a lot faster than the younger ones.

I guess also a lot of it gets back to what your philosophy on maths is. Is it mostly for adding up a quick grocery list, checking your bank statement or whatever. To some degree calculators have replaced humans in this regard. So then what humans need is deeper conceptual understanding to a) make sure the calculators are programmed correctly and b)make sure the answers make sense. However mental math can be a big part of b)
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#21 mathmarm

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Posted 02 March 2017 - 10:35 PM

I agree with the first, but am confused about the bolded: how do you teach a 3rd grader to calculate percentages? That is not covered by 3rd grade

 

If a person can divide and multiply, they can figure a percent.

 

We teach arithmetic as holistically/big picture as possible from Day 1. Arithmetic is an applied subject the way that we teach it in my family (I'm a 2nd generation math teacher. My mom taught all of her kids math at home well ahead of the PS and I'm teaching my kids the same way that I learned.)

 

 

The "application" for calculating percentages is we have to pay taxes on store purchases and we pay tips at restaurants  so we talk about it as an x-cents, per dollar type of thing. (And we eat out somewhat regularly :blush:

 

All of my moms kids and grand-kids (so far) have been able to calculate percentages (at least in an applied situation) very fluently by the end of 3rd grade.



#22 mathmarm

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Posted 02 March 2017 - 10:41 PM

I teach it as a mixture of multiplication and fractions long before I introduce the word percent.

 

"In our state, we have to pay the government 6 cents for every dollar we spend.  You want to buy a lego set for $8.99; about how many dollars is that?  Okay, so if you have to pay 6 cents for each of those dollars, how many cents do you have to pay the government in tax?  Perfect, so if you have to pay the store $8.99 and the government 54 cents, how much will you have to pay in total?"

 

Eventually we discuss that 6 cents per dollar means 3 cents per half dollar or 2 cents per third of a dollar or one cent per sixth of a dollar.  That is close enough for practical purposes until they actually learn how to calculate percentages exactly.

 

I use the same process with tips.  "We are going to tip 15 cents for each dollar we spent."  I want to emphasize multiplying and dividing by 10, so we always figure out 10% (or, as I present it, 10 cents for every dollar we spent), and then we halve that and add them together...all well within the wheelhouse of 3rd grade math.

 

Wendy

Yep! This is so much more clearly and articulately explained than what I said, but pretty much exactly what I meant. Thanks for saying that better than I could.

:wub:

 

 



#23 EngOZ

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Posted 02 March 2017 - 11:56 PM

Yes we do use CWP, but working without a calculator, my kids are forced to apply their mental math skills anyway during a typical math lesson. There is plenty of practice here. However I was just curious if people deliberately pick out problems to practice mental maths skills with their kids, i.e. have a set of problems or facts for their kids to solve/memorise. 

 

Although what is meant by mental math?  Is this cold memorization of the multiplication tables, for example?  I assume nobody is talking about that.  So what is the OP doing that isn't what others here are saying they are doing or have done?  Sounds to me like EngOZ does in fact work on mental math. 

 

Hopefully I'm wording that correctly.

 


Edited by EngOZ, 02 March 2017 - 11:58 PM.

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#24 mathmarm

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Posted 03 March 2017 - 12:17 AM

That is not how I approach things.

For the how of my approach (copied from another thread, excuse the crummy formatting if this comes out looking wonky.)

 

...We automated the 5 and 10 fact families for addition and subtraction and the others we learned through repeated use---but we'd been taught to think of and visualize the relationships at all times from the beginning. I think mama specifically designed/chose to teach us this way so that we could do it that way--but I highly doubt that it was a happy accident or anything. All of my siblings and I did it this way and mama taught her tutoring students who struggled to think of numbers this way too, but it wasn't always successful for older kids who had been 'imprinted upon' by the local school.

 

If we were looking at, say 3 + 4, we usually did something like this:

1) use commutative property to put the larger number first: 4 + 3 = ___?

2) This is obviously smaller than 10

3) How is this related to 5? 4+ 1 is 5, so 4 + 3 is bigger than 5 *light bulb moment*

4) How much bigger than 5 is it well...we can disassociate 3!

5) 4 + 3 = (4 + 1) + 2 = 5 + 2 = 7!

 

I know that seems long and drawn out, but we got it down pat and could do it quickly. We learned math from about 3-6....

In K, I put a huge emphasis on number bonds within 10.  "Making 10s" is is one of my main K-level goals.

We probably have similar approaches, but different time tables. In our family math begins at 2-3 yos, so that by the time we start K, the main goal is interpreting and solving story problems and building fluency with the number bonds/math facts using the strategy that I outlined above. We do a lot of applied math in our daily life with the child.

 

We spend the years prior to 1st grade playing, learning and exercising various math skills such as counting by place value, counting on/back, skip counting fwd & bwd, the units in the base-10 system, how/when to compose and decompose units, patterns, even/odd numbers, interpreting basic word problems and finding math scenarios in their day-to-day life. This type of exposure doesn't stop when the child starts grade K/1. It continues in the background--always going bigger and broader than whatever is happening in "math class"

 

After that, I switch almost all of the mental math focus onto manipulating numbers, not memorizing them.  I would much rather them practice and learn how to figure out that 9 + 6 = 15, rather than just memorizing it as so.  Strengthening the mental pathway that "sees" one move from the 6 to the 9 to make them into a 5 and a 10, that is a multi-tasker skill that will serve them well when dealing with all sorts of numbers.

 

Again, I think that we have similar approaches but different time tables.

I am a happy camper if my first graders can mentally add two or three 2/3/4 digit numbers...even if they haven't committed 7 + 5 to rote memory quite yet. In my experience, once I could instantly see that 7+5 = 12 (1ten-2/twelve), instead of having to think through 7+5= (5 + 5) + 2, the easier it was for me to add/subtract multiple 2-4 digit numbers in my head.

 

When we move on to multiplication, like Monica_in_Switzerland, I put very little emphasis on drilling the facts.  Eventually, they will figure out that knowing the multiplication table is faster than having to calculate each answer every time.  Until then, however, there is a lot of value in them "seeing" 7 * 8 as 7 * (10-2) = 70 - 14 = 56.  That is the distributive property, and really, truly understanding how that works is worth a lot more to me than being able to simply spit back that  7 * 8 = 56.  

Yep, we also use the distributive property and do our written calculations (once we get to that point) L-R. But we find it easier/smoother if the kids are learning their multiplication table. We always teach and acknowledge the properties of the real number system from early on though, so we don't have 100+ multiplication facts to memorize. Instead we have 36 and we do encourage/require them to memorize them and give them systematic exercises towards that end, with the goal of them having used and practiced them enough that by the end of

 

Because of the kids understanding of the concept of multiplication and the distributive property *0, *1, *10, *11 and *12 are never studied/practiced. We only do the tables 2-9. But since we do a lot of doubling/halving, tripling/thirding, quadrupling and quartering during our Pre-1st grade number play and all the skip counting that they have done/do regularly means that the student is familiar with the multiplication sequence already. So memorizing them is pretty easy.

 

To me, mental math is almost all about making numbers dance for you.  Can a kiddo mentally figure out 38 * 4?  Can they figure it out another way to confirm their first answer?  Just for fun, how many different paths can they find to the answer?  Are some faster?  Are some slower?  Which methods would be most helpful if the problem was 39 * 4?  What about 38 * 5?  Etc.

I think thats a great way to summarize it.

 

Wendy

--mathmarm

 

 



#25 mathmarm

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Posted 03 March 2017 - 12:30 AM

However I was just curious if people deliberately pick out problems to practice mental maths skills with their kids, i.e. have a set of problems or facts for their kids to solve/memorise. 

 

Yes, on my end, the ability to perform mental math is one of the big goals in elementary mathematics, and we teach to that end. We do use specifically designed problem-sets to help with the mental math skills. I just make up my own sets gradually, but I imagine that you can find a book/pre-made program with similar problems in it.

 

 

I


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#26 calbear

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Posted 03 March 2017 - 01:53 AM

EngOz, I use the exercises that are in the back of the Singapore Math Home Instructor Guides (Standards Edition). I also use the Fan Math Express Math books as well. The latter are better than the former since the Fan Math books actually lay out the mental math strategy better.


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#27 EngOZ

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Posted 03 March 2017 - 04:31 AM

Cool calbear, I've seen exercises in the HIG's but I've never heard of the Fan Math books before.

 

EngOz, I use the exercises that are in the back of the Singapore Math Home Instructor Guides (Standards Edition). I also use the Fan Math Express Math books as well. The latter are better than the former since the Fan Math books actually lay out the mental math strategy better.

 



#28 SparklyUnicorn

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Posted 03 March 2017 - 07:48 AM

Yes we do use CWP, but working without a calculator, my kids are forced to apply their mental math skills anyway during a typical math lesson. There is plenty of practice here. However I was just curious if people deliberately pick out problems to practice mental maths skills with their kids, i.e. have a set of problems or facts for their kids to solve/memorise. 

 

Only thing I've had my kids work on in terms of memorization was the multiplication table, but even that wasn't just cold memorization.  That was more talking through strategies for working them quickly in their head.  That just makes life easier if they don't have to think too hard about it. 

 

I never used stuff like flash cards.  Nor have I ever gotten into timed drills.  Not saying that's completely useless or bad, but I just never did it.


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#29 Heigh Ho

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Posted 03 March 2017 - 08:36 AM

SM plus real life was enough for us - real life includes games, cooking, and helping parent. playing monopoly means percents have to be figured. Cooking means knowing volumes, since we don't always start with a full gallon of milk and may need to get more before we begin. Swim club demands converting laps to distance. Hiking means knowing which way is north without a compass. Vacationing means knowing clock and converting distance to time. helping in the garage means knowing how to measure and estimate mentally. same for scout projects. Shopping, dining out, and school field trips mean being able to figure if you have enough left for lunch if you spend part of what you have. Piano or recorder means knowing whole,half, and quarter.

Edited by Heigh Ho, 03 March 2017 - 08:39 AM.

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#30 Bluegoat

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Posted 13 March 2017 - 01:15 PM

I think it's important, but probably some kids benefit more

 

My dh, for example, seems as a child to have come up with many of the mental math strategies on his own, just by doing other sorts of math. 

 

I, on the other hand, only learned a few, until I taught my kids from SM and MM when I was an adult.  The speed and ease of my calculations has improved so much it's hard for me to believe, I actually feel like I could pick up where I left off and relearn my math skills.

 

With my kids, my eldest is a lot like me - she really benefitted from having strategies taught explicitly, and some practice.  Now that she is a bit older, she does get the practice just doing other kinds of problems.


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#31 ananemone

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Posted 14 March 2017 - 04:22 AM

I have one who picked up mental math quite easily and has the facts memorized in her head, which helps when she needs  to spend her brain power on more difficult problems.

 

I have another who never wanted to go to the effort of memorizing facts - even subtraction ones! - because he had fancy ways to do them in his head, which actually demonstrated a greater understanding of math than the facts DD had memorized.  He  could do multi digit multiplication by some weird internal way he'd worked out that was in fact correct, but did not rely on the methods I thought I'd taught him.

 

So, in conclusion:

 

I have no idea.


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#32 Bluegoat

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Posted 06 April 2017 - 12:18 PM

TBH, since doing a lot of mental math with my kids, my math skills are so much better and quicker than they were even when I first finished high school.


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