Hi,

We think there is an error on the Solution Page 152-2. We didn't see an errata sheet for it.

The answers for both the Area of a cylinder and the Area of a sphere are given in cm cubed. Shouldn't that be in cm squared?

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Also, my son had trouble understanding the following equation from the area of a cylinder. I was hoping you could help me to explain it better:

200 pi cm squared + 400 pi cm squared = 600 pi cm sq.

His problem was with pi. He didn't know what to do with pi in these problems. He wanted to solve it as:

600 (2 pi) cm squared.

He said if you were adding the numbers that you should add the pi also. He said that pi + pi = 2 pi or 6.28. I told him if it was 200x + 400x the answer would be 600x. I think he has trouble with pi because he knows it can be a number.

I had him work out 200 times pi + 400 times pi (1,885)and showed him how it was the same as 600 times pi (1,885), but he just doesn't understand why it works. I tried explaining that pi was just a variable like x or people or boxes.

I was trying to remember if there was a previous lesson that dealt with this because sometimes it helps in these situations to review something learned earlier and then apply it to the current lesson.

Can you point me to an earlier lesson that might help explain this, or can you think of a better way to explain it? Maybe this is just too abstract for him right now.

Dear Julia,
The answer in the score key is correct. It is cubed not squared. Think about what squared means. It is two dimensions (width times length). Cubed is three dimensional. Visualize a square verses a cube. The volume has to be three dimensions, not just two, or it would be flat.

The question about pi is a good one. I would recommend you go back over order of operations. [Parenthesis, exponents, multiplication & division before addition & subtraction] You have to multiply the 200 and 400 by pi first before you add the answers together. Does that help?
Nancy

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