Hi Nancy,

Thanks for your reply.

My first question (problems 15 & 16) had to do with surface area, not volume. Area is two dimensional (A = w x h) so the answers should be in cm squared.

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Regarding my second question, can you point me to the lesson(s) where order of operations was covered so I may review them.

I understand what you are saying about multiplying each of the numbers by pi before adding them together and we did do it this way. You can also simplify the equation first by combining like terms (400 pi and 200 pi) to get 600 pi and then multiply that number (600) by pi. I showed him that he can solve it that way too.

I am now thinking that he's not grasping that pi is a variable here because he knows it has a number value too. That is what I don't know how to remedy.

Thanks for your help.

Julia

Dear Julia,

You are right; the areas should be cm squared. I'll change it. Thanks.

Regarding the second question, refer to Worksheet 78-2, Problem 6. Pi is not really a variable because it always has a definite value. You might ask him to think about substituting 3 for pi.

Joan Cotter

Dear Joan,

Thanks for clarifying our question about cm squared.

Also, regarding pi, I think Liam could see the similarity to the problem in Lesson 78.

It helped ME to know that pi is NOT really a variable. He substituted 3 for pi and then I had him show me how to solve it. When he said he still didn't understand why you couldn't do 600(6), I was then able to discuss order of operation as Nancy suggested. I told him that was a Math rule.

But we also looked at it visually. I had him demonstrate 2 x 3 + 4 x 3 with cubes. He could see that 6 cubes + 12 cubes = 18 cubes. Then I had him demonstrate how 6 cubes x 3 cubes also equals 18 cubes. Then I had him demonstrate his thinking: 6 cubes x (6 cubes) which does not work, of course, because he didn't have enough cubes!

I think he finally gets it.

Thanks for your help on this sticking point.
Julia



Thanks, Liam

Dear Julia,
Thanks so much for that great visual demonstration. I am sure it will help other reader too.
Nancy & Joan