I am afterschooling my 2nd grader in math using RS level C. I did B with him as well. He needed more challenge in math and the school wasn't providing it for him. He now thinks math is fun again!

ANyhow, in RS, you see an array as 7 taken 5 times. That would be 5 rows of 7 beads or 7x5. our district uses Everyday math. THere an array of 2x4 would be drawn as 2 rows of 4 rather than 2 taken 4 times as in RS ie 2+2+2+2. Now I fully understand the commutative property and so does DS. But I'm wondering if I should switch him to thinking of it the PS way (actually the way I think of it since I naturally think of 7x5 as 7 sets of 5 or 5+5+5+5+5+5+5). I ask this b/c I've seen numerous times on the web where students have been marked wrong in PS for drawing the array the wrong way or for stating the multiplication equation in the reverse order.

Should I continue as we have been doing and he'll have to switch his thinking when he gets to multiplication in PS?

thanks,
captuhura

Dear Captuhura,
I commend you for being proactive in your child's education and not leaving it to others to make this choice for you. My recommendation would be to introduce him early to the commutative property by showing him on the abacus and & math balance that three taken four times and four taken three times is equivalent. You are demonstrating a principle of mathematics in several ways so he can then prove his work if he is questioned about its accuracy. On the abacus all you need to do is enter the quantity and then turn the abacus on its side to show it is the same, but represents a different array. I would also recommend that you go to your state site for your standards to see how he will be tested there. They have sample questions that have been released which should help you see which way your son will be held accountable to in the final annalysis. However, Joan's way is the mathematically correct way of stating it.
Nancy

Nancy,

Thank you for responding to my question. DS understands the commutative property for quite some time. He figured it out on his own. I have seen where parents report on the internet that their children were marked wrong for writing the equation for an array *backwards* even though the children tried to explain the commutative property to the teachers.

When I do multiplication, I actually think the PS way as in 3x7 would be 3 sets of 7 ie 7+7+7. My understanding w/ RS is that 3x7 is 3+3+3+3+3+3+3. I believe Singapore math also does the PS method. Now that I'm doing the RS method, that one makes perfect sense to me as well. Can you point me to some literature explaining that the RS way is the mathematically correct way in case DS's teacher questions it? She is very open to new ideas so I'm not worried so much about this but I thought I'd see what other afterschoolers might have done in this situation.

Sybil

Dear Sybil,

Here are a few more explanations from Dr. Cotter for you to consider as well as share with your child's teacher.

"In adding, subtracting, and dividing, we start with a number and then do something with it. For example, 7 + 5 is 7 with 5 added to it. So, multiplication should be 7 and then duplicate it. The Japanese and Montessori also do it as 7 x 5 meaning 7 five times.

There is another reason. On a coordinate system, we always go horizontal first and then vertical. So, for 7 x 5, it is across 7 and then down (or up) 5."

I hope this helps explain the RS way of "seeing" and processing math and why it makes sense to do it this way. However, as Nancy said, you might want to check what your state tests are looking for, even though in the end it's not what the test says, it's how much math our children understand, along with their ability to reason and problem solve.

Thank you for your post.

Sincerely, Rosine

Rosine,

Thank you so much for responding. I've decided to keep moving w/ RS method and deal with any problems as they come up!

Regarding Japanese method for teaching multiplication. I have Singapore Primary Math 1B. In it, , for ex: 4x3 is illustrated as 3 flowers in each of 4 pots (3+3+3+3). The RS method would be 4 taken 3 times ie 4+4+4.

Anyhow, I'm not obsessing over this lol. I just have a keen interest in teaching math!