I’m teaching a high school matyh class to five EMD/ LD kids, and WHEW! I’m not sure how to explain multiplication and division in such a way that they get it. They can multiply using a multiplication chart, but division just knocks them out. Are there any hands-on ways I can teach division? They’re okay with dividing a pie into two, three or four pieces, but after that, they fall apart.
Re: math reversability
I did the arrays and then took a 100 number chart and had them highlight the step counting on each chart for each multiple.. ie 2,4,6,8,10,12… Then by that chart they can visually see 2+2+2 is the same as counting over 3 hightlight spaces
Re: math reversability
Division is easy. Find a lots of pennies, or counters,
or M&M’s . Say the problem is 12 divided by 4.
Take out 12 pennies, and say you want to divide fairly
the pile among four people. Now first give each fictional
person one, see that there is still some left and then
pass each person a second, see that there is still some
left and pass each person a third. Now all the pennies
are given out. Ask if this everyone has the same amount?
Yes. Then ask how many pennies does each one get? Three.
Conclude that 12 divided by 4 equals 3. This concrete
method of division works for any numbers. You can then
turn this around and say if each of four people get
three pennies each how many are there in all? Twelve.
Now that is the same as saying 4x3=12. Fair division
is something most kids will understand, and it also
has connection with multiplication.
You can go on to talk about division with remainders
as well, illustrating in some cases there is no fair
division of the coins, for example 11 coins and three
people. You end up giving out nine coins and two
will be left over.
Re: math reversability
Are you familiar with Cuisenaire rods? They are base 10 blocks that offer a variety of ways to use them. The rods range in size from 1-10. You can show that 3 X4 = 12 by taking three-4 rods and place them above twelve (a ten and two rod). Of course you have to start with a basic lesson to teach the value of the rods and how to use them for all operations. There are books to teach the basics that often come with the purchase of the rods. I am an elementary teacher and have show second graders how to multiply and divide large numbers using rods. You can also use them for fractions, area, perimeter.
Use arrays — example three rows of four dots, total twelve. This shows 3 x 4 = 12, turn sideways for 4 x 3 = 12; then 12/3 = 4 and 12/4 = 3. Show these physically with groups of poker chips or coins and re-grouping them into equal groups, then visually by drawing the array of dots and looping around equal groups. Take your time on this, but in the end it works.