Long multiplication and division

[Anonymous]

Anonymous wrote:

Anonymous wrote:

Anonymous wrote:None of this matters as much as memorizing the multiplication tables.

I find it beyond absurd that Montessori would teach this in first grade. If I were that pp, I would be embarrassed to have posted that.

You need to take a look in a Montessori classroom. No child would be doing this type of work without a solid understanding of the decimal system and the ability to instantly multiply numbers under 12 (not necessarily through chanting tables as you imply.) But Montessori is great at teaching and reinforcing that.

First and second graders in Montessori classrooms regularly solve problems like that using manipulatives like the checker board. My own 7 year old Montessori child can now do problems like those above in a matter of minutes without manipulatives or other materials, just paper. She does have a particular interest in math and may be ahead of most other kids her age in her class, but it's Montessori, so I have no idea about where most of the other kids are.

Very interesting that this is not taught for several more years in trad schools.

yes, they can use the manipulatables to work it out, but it's not like many understand what they are doing. You can hand them the problem OP posted and have them get the answer without using the racks and tubes or whatever (your child is different I understand). I think it is fine, but it's not really what OP asked. My child is 1st grade in an AMI Montessori classroom and basically is just following steps with the materials with a general sense that he is "dividing it up." And he has no understanding of decimals and can't multiply numbers under twelve at all.

that should be "can't" hand them . . .

[Anonymous]

DD did both in third grade. She is in private school.

[Anonymous]

Anonymous wrote:

Anonymous wrote:

Anonymous wrote:None of this matters as much as memorizing the multiplication tables.

I find it beyond absurd that Montessori would teach this in first grade. If I were that pp, I would be embarrassed to have posted that.

You need to take a look in a Montessori classroom. No child would be doing this type of work without a solid understanding of the decimal system and the ability to instantly multiply numbers under 12 (not necessarily through chanting tables as you imply.) But Montessori is great at teaching and reinforcing that.

First and second graders in Montessori classrooms regularly solve problems like that using manipulatives like the checker board. My own 7 year old Montessori child can now do problems like those above in a matter of minutes without manipulatives or other materials, just paper. She does have a particular interest in math and may be ahead of most other kids her age in her class, but it's Montessori, so I have no idea about where most of the other kids are.

Very interesting that this is not taught for several more years in trad schools.

yes, they can use the manipulatables to work it out, but it's not like many understand what they are doing. You can hand them the problem OP posted and have them get the answer without using the racks and tubes or whatever (your child is different I understand). I think it is fine, but it's not really what OP asked. My child is 1st grade in an AMI Montessori classroom and basically is just following steps with the materials with a general sense that he is "dividing it up." And he has no understanding of decimals and can't multiply numbers under twelve at all.

Does your child understand units, tens, hundreds, thousands and their relative places? That's the decimal system. When other kids at my child's school have demonstrated checkerboard and racks and tubes to me I was convinced they understood what they were doing. But every kid works at his or her own pace.

[Anonymous]

Anonymous wrote:

Anonymous wrote:

Anonymous wrote:

Anonymous wrote:None of this matters as much as memorizing the multiplication tables.

I find it beyond absurd that Montessori would teach this in first grade. If I were that pp, I would be embarrassed to have posted that.

You need to take a look in a Montessori classroom. No child would be doing this type of work without a solid understanding of the decimal system and the ability to instantly multiply numbers under 12 (not necessarily through chanting tables as you imply.) But Montessori is great at teaching and reinforcing that.

First and second graders in Montessori classrooms regularly solve problems like that using manipulatives like the checker board. My own 7 year old Montessori child can now do problems like those above in a matter of minutes without manipulatives or other materials, just paper. She does have a particular interest in math and may be ahead of most other kids her age in her class, but it's Montessori, so I have no idea about where most of the other kids are.

Very interesting that this is not taught for several more years in trad schools.

yes, they can use the manipulatables to work it out, but it's not like many understand what they are doing. You can hand them the problem OP posted and have them get the answer without using the racks and tubes or whatever (your child is different I understand). I think it is fine, but it's not really what OP asked. My child is 1st grade in an AMI Montessori classroom and basically is just following steps with the materials with a general sense that he is "dividing it up." And he has no understanding of decimals and can't multiply numbers under twelve at all.

Does your child understand units, tens, hundreds, thousands and their relative places? That's the decimal system. When other kids at my child's school have demonstrated checkerboard and racks and tubes to me I was convinced they understood what they were doing. But every kid works at his or her own pace.

no. I am basing what I wrote on what my child is doing (racks and tubes and multiplication checkerboard with little understanding though getting the calculations correct in his notebook) and what the teacher told me (don't worry, in montssopri they don't "abstract" the mathematical concepts they work on till 2nd or third grade). My child can't even add simple numbers (4 + 6) reliable on his own.

[Anonymous]

Ok, my kid's primary work in Montessori was to get very comfortable with adding and subtracting numbers up to ten. Again and again. Your kid will get there soon, PP!

[Anonymous]

Also, he or she should still be working on the number rods, not checker board and racks and tubes if he or she can't add and subtract reliably and instantly under ten.

[Anonymous]

Anonymous wrote:Also, he or she should still be working on the number rods, not checker board and racks and tubes if he or she can't add and subtract reliably and instantly under ten.

how do you know this stuff? Been at Montssori for three years and know nothing

[Anonymous]

Granted we are no longer in Virginia, but my third grader is doing this in math now. My children attend a public Waldorf charter school on the central coast of California.

[Anonymous]

Common Core Math Standards for 4th grade introduce multiplying 4 digits by one digit or 2 digits by 2 digits. Long division for 4th grade is four digits divided by one digit. It does not specify that students need to use the standard algorithm.

5th Grade Common Core Math standards indicate students should use standard algorithm to multiply and divide multi-digit numbers. The actual standard says:

Find whole-number quotients of whole numbers with up to four-digit dividends and two-digit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models.

So the long division given in the example isn't even taught in 5th grade because only 2 digit divisors are required.

This is expanded in 6th grade. So the answer if your child is going to school in a state that uses Common Core is 5th to 6th grade. Really though those problems are tedious not hard. If you can do 2 digit by 2 digit multiplication you can solve those problems by using different methods. In some schools the

Here is the 4th grade Common Core Math standard:
4th grade standard Use place value understanding and properties of operations to perform multi-digit arithmetic.

CCSS.MATH.CONTENT.4.NBT.B.5
Multiply a whole number of up to four digits by a one-digit whole number, and multiply two two-digit numbers, using strategies based on place value and the properties of operations. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models.
CCSS.MATH.CONTENT.4.NBT.B.6
Find whole-number quotients and remainders with up to four-digit dividends and one-digit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models

[Anonymous]

Anonymous wrote:

Anonymous wrote:Also, he or she should still be working on the number rods, not checker board and racks and tubes if he or she can't add and subtract reliably and instantly under ten.

how do you know this stuff? Been at Montssori for three years and know nothing

I'm not an expert by any means, but materials are only introduced when the child has mastered the previous step. My understanding is that there are multiple ways of working with numbers under ten and skip counting that are essential to master before there is any point moving on to racks and tubes. All the math material build on from one another. Does your school have parents events where the kids present to the parents?

[Anonymous]

Anonymous wrote:

Anonymous wrote:My son learned slightly shorter problems, like

328
x 7

in 3rd grade using the lattice method.

He's learning several algorithms this year in 4th grade.

He's in a private school, using the Everyday Math curriculum, which has a lot of critics. But for him, so far, it's been good. He is solidly learning the material. I "don't" know if it's in line with what other 4th graders are doing, though.

Come back and post when your child is in middle school and has big gaps in his math education. Everyday Math is a weak math program.

I understand your concern. It was mine, too. Apparently it is not a weak math program substantively. But it doesn't work well if teachers aren't trained well in it. And that happens often in many public school systems. However, my school does annual training for teachers. And the middle school part of the private school has a much higher-than-average placement of students in the SMAC magnets in high school. So I'm not overly concerned at this point.

[Anonymous]

my DCPS is teaching long division now (so mid 4th grade).

[Anonymous]

Anonymous wrote:

Anonymous wrote:

Anonymous wrote:

Anonymous wrote:None of this matters as much as memorizing the multiplication tables.

I find it beyond absurd that Montessori would teach this in first grade. If I were that pp, I would be embarrassed to have posted that.

You need to take a look in a Montessori classroom. No child would be doing this type of work without a solid understanding of the decimal system and the ability to instantly multiply numbers under 12 (not necessarily through chanting tables as you imply.) But Montessori is great at teaching and reinforcing that.

First and second graders in Montessori classrooms regularly solve problems like that using manipulatives like the checker board. My own 7 year old Montessori child can now do problems like those above in a matter of minutes without manipulatives or other materials, just paper. She does have a particular interest in math and may be ahead of most other kids her age in her class, but it's Montessori, so I have no idea about where most of the other kids are.

Very interesting that this is not taught for several more years in trad schools.

Umm, did you go to school? Long division and multiplication are not usually taught in first grade.

Probably somewhere that taught me better comprehension skills than yours. Please read the bolded sentence again. If you are still having trouble let me know and I'll put it into shorter, simpler words for you.

You mean your incomplete sentence with misspellings? Yes, perhaps you should translate that for all of us.

[Anonymous]

K12:

3rd: multiply 3-4 digits by 1 digit, place value through thousand and hundredths
Divide 3-4 digits by 1 digit, no decimals

4th: Multiply 3-6 digits by 1-3 digits, place value through ten - thousands and thousandths
Divide 3-5 digits by 1 digit, dividend must already have a decimal or be money if quotient has a decimal, place value through ten - thousands and hundredths

4th grader is starting 5th grade Math and ela next week, no idea what that holds yet

I can tell you that kindergartens can understand the process if they grow up hearing older children discussing it. I have a k who knows how to do 0-5 for multiplying and can separate into as many groups as need be, if he has enough time to think. Kids who are pressured or encouraged too strongly shy away, but if it's just something they hear, they want totry.

[Anonymous]

Homeschooler using Singapore Math materials here.

4th grade for the multiplication problem. I don't think Singapore explicitly teaches beyond 3 digit by 3 digit multiplication.

The triple digit divisor (ugh) is in either 4th grade, 2nd semester, or the 5th grade books. I can't recall for sure.