Division

: Does anyone have any good methods to teach division for a Math LD
: student?What kind of division?I’d start with a pie - a real one. Or a piece of chocolate candy. Ask the student to divide it by four people. Go from there. Stay real as long as you can. Then explain the transition between the division problems you can actualize with a piece of candy and the bigger numbers you’re working with. Move from the candy to paper and pencil.

: Does anyone have any good methods to teach division for a Math LD
: student?Sara’s ideas on pies are good, usually used later for fractions.For whole number division, get counters — checkers or poker chips (nice to have pretty colours, and easy to handle) or just beans.Start with a medium-sized number of counters, say six for example, and divide them into two equal groups/piles/stacks. 6/2 = 3. The put the six all together again and divide them into three equal groups. 6/3 = 2. Then make a rectangular array of two rows of three, and show how this means 2 x 3 = 6, 3 x 2 = 6, 6/3 = 2, and 6/2 = 3; four facts for the price of one, just depends on how you look at it. Get a couple of sheets of poster board and divide them into ten rows of ten squares each, plus a row and column for labels.Label one board multiply and label 0 to 9 each direction in black or blue. Label one board divide and label ONLY the side 0 to 9. Patiently work through the whole darn boards from 1 x 1 to 9 x 9, then zero row last (easy but feels weird at first) and at the same time fill in the same facts on the division board. Use a different-coloured marker from the labels, say red. Be sure to write problem AND solution in the box (this is why large boards are best) for example write 4 X 5 = 20 and 20/5 = 4, NOT just the answer; answer alone is meaningless to the student. Have the student do each and every multiplication/division with the counters and give you the result, not the other way around. If you can do it neatly, use a fine marker or pencil and draw the array of four rows of five, etc. in each box. This will take several days (weeks or months, depending on the student) to build, but that’s OK; you are laying a foundation of understanding. Don’t worry about memorization yet, just get the pattern of divide = backwards multiply, and that *both* division and multiplication involve equal-sized groups.Once you have the facts outlined and labelled, you can work on memory: first recite the times tables, eg 3 times 1 is 3, 3 times 2 is 6, 3 times 3 is 9, etc. When really well-known, recite the times and division related facts: 3 times 1 is 3, so 3 divided by 3 is 1. 3 times 2 is 6, so 6 divided by 3 is 2. 3 times 3 is 9, so 9 divided by 3 is 3. 3 times 4 is 12, so 12 divided by 3 is 4. And so on. Take a few weeks (months, years if necessary) doing ten minutes of this every day. First read the charts and look at the multiplication arrays, then when the charts aren’t being referred to much, go by memory.*At the same time* as you are getting the facts under control, do lots and lots of real-world problem-solving — the sort of thing where you have twelve candies to share among four girls, so how many does each get? There are lots of books of practice problems of this sort.Don’t rush into long division. You need multiplication and carrying well-developed first. And that’s another chapter …

Victoria and Sara gave you some good information. When you get to long division however, I would recomend that you check out the Landmark Arithmetic Program from the Landmark School in Mass. (landmarkschool.org) It is simple, sensible, visual, and makes sense to kids. The book is pretty inexpensive too.Robin

When my son learned to multiply, he could get it by skip counting. Then when we got to easy division he could skip count up to the number to see how many would fit into it. The easiest for him was dividing by 7’s because he could look at a calendar and count the weeks. He still has trouble with long division. We are trying to learn it by using DMSB (Dad, Mom, Sister, Brother), which stands for the steps you use (Divide, Mult, Subtract then Bring down). Good luck. I think this is one of the hardest things to teach an LD child. Brenda

: When my son learned to multiply, he could get it by skip counting.
: Then when we got to easy division he could skip count up to the
: number to see how many would fit into it. The easiest for him was
: dividing by 7’s because he could look at a calendar and count the
: weeks. He still has trouble with long division. We are trying to
: learn it by using DMSB (Dad, Mom, Sister, Brother), which stands
: for the steps you use (Divide, Mult, Subtract then Bring down).
: Good luck. I think this is one of the hardest things to teach an
: LD child. BrendaThe algorithm for long division is a toughie! However, this has worked for some of the children I’ve worked with…. Start with getting the child to divide a sum of money (and do this is a concrete way, without the algorithm). E.g. give the child $24 and ask him to share it between you and him. He would therefore give each person a $10 bill, and then 2 $1 bills.When he’s able to do this, introduce a problem like $34 divided by 2. This time, he would share out 2 $10 dollar bills, and have a third bill at hand. Guide him towards exchanging that third bill for 10 $1 bills. Then combine all the $1 bills (10 + 4 = 14) before sharing it out. Practice this until mastery before you introduce the algorithm for long division.When the algorithm is introduced, it helps to get the child to go through the activity whilst working through the algorithm, i.e. distribute the 2 $10 bills, then record on paper that each person has 1 (written above the 3), and $20 was distributed (written below 34). This way, the child sees the algorithm as a meaningful process - 1 (ten) x 2 = 20Then exchange the $10 bill for 10 $1 bills, and add it to the existing 4 $1 bills. Therefore, there are 14 (written below 20)…. and so on.Sorry I wasn’t able to illustrate it better, but hope this helps!

Just a short thanks for a clear and practical and meaningful way to work this instead of yet more mysteries.