whoops sorry, step 1 should just say plus 7 more slices (nor slices of cheese).

1. What do we know?

Pepperoni + Cheese = 15 slices
and
The number of Pepperoni slices = A certain number of Cheese slices + 7 more slices of Cheese

So there are more pepperoni slices than cheese slices. Visualize more pepperoni slices than cheese slices.

2. Now:
Instead of using "P" we will now start using (C + 7), (which is another way of saying P). This way we can start using one letter, which is C.

So:

(C + 7) + C = 15 slices

3. Hmmm,, we know that the 2 C's are the same number.

So, lets start plugging some numbers in to what C could be.

Will (3 + 7) + 3 = 15 slices? No, it will only equal 13 slices.

Will (4 + 7) + 4 = 15 slices? Yes, it does.

So, P = 11 and C = 4 = 15 slices altogether

Admittedly, there is guess work, but I think that might be okay for 3/4 graders who are learning the concept.

OK, spacing was totally off there, sorry about that.

I'm a middle school special educator. f I was presenting this in my classroom, to kids with a 3rd or 4th grade math level here's how I'd do it.

I'd think of this as a 2 step process. First we need to figure out the different combinations that can meet the first rule (7 more pepperoni than cheese)

So, I'd set up a function table that looked like this:


Cheese Pepperoni
= Cheese + 7

1 8

2 9

3 10

4 11

Once the kids had created and filled out the table, I'd ask them to add another column for "total slices".

So, it would look like this:



Cheese Pepperoni Total
= Cheese + 7 = Cheese + Pepperoni

1 8 9

2 9 11



Then they'd just need to choose the one that equals 15.

When students are not undestanding, I try to break the process into smaller steps in translating:

"seven more slices of pepperoni pizza than cheese pizza"
So the number of cheese slices + 7 is the number of pepperoni slices
C + 7 = P

The total number of slices is 15
The number of cheese slices and pepperoni slices = total number of slices
C + P = 15

So combining those two equations above

C + P = 15
C + (C + 7) = 15

since + and - are all equal priority
(C + C) + 7 = 15
(C + C) + 7 - 7 = 15 - 7
(C + C) = 8
2C = 8
C = 4

So Cheese slices is 4 and Pepperoni slices = (C + 7) or 11

Anonymous wrote:

Anonymous wrote:P + C = 15
P= c+7
(C+7) + c = 15
2c +7 =15
2c = 8
C =4
P=11

Almost no third and fourth graders can do this.

Well, it is how the problem is solved, except I would spell it out more on paper.

Anonymous wrote:Isn't it
p-7 = c/2 or alternatively P= (c/2) + 7

cheese slices = 4
pepperoni slices = 11

No

Anonymous wrote:P + C = 15
P= c+7
(C+7) + c = 15
2c +7 =15
2c = 8
C =4
P=11

Almost no third and fourth graders can do this.

And to explain p = c + 7, I would say that as there are 7 more slices of pepperoni than cheese, whatever the number of cheese there are, you would add seven to that number to find out the number of pepperoni. So if there was 1 cheese, 8 pep, 2 cheese, 9 pep....

Isn't it
p-7 = c/2 or alternatively P= (c/2) + 7

cheese slices = 4
pepperoni slices = 11

The difficult concept is that you can represent an unknown with a symbol, on which you can then perform additional operations.

One exercise I found useful is to simplify down to something really easy, like

"You have c slices of cheese pizza. I give you one more. How many do you have?"

At some point the child will begin to see that if c can represent a number of slices, "c+1" is also a number of slices.

Then you say, now you have "c+1" and I gove you one more. Then you guide them in simplifying (c+1)+1 to c+2, since they know the associative property of addition.

P + C = 15
P= c+7
(C+7) + c = 15
2c +7 =15
2c = 8
C =4
P=11

(11:56 here) I should have said also that (7+c) = P

c+ (7+c) = 15

in short, the problem says: there're 15 slices of pizza total; there're seven more slices of pepperoni pizza than cheese pizza.

based on that, I wrote these two equations:

P + C = 15, which they (seem to) understand, and
P = 7 + C, which they had a really hard time with

so, how would you teach them to convert "seven more slices of pepperoni pizza than cheese pizza" into "P = 7 + C"? I ended up using a crappy example of 3 = 1 + 2 means 3 is one more than two. but I know they still didn't get it.

BTW, I know this is way beyond their grade levels but the problem is in a 3rd-gr math workbook I bought for my rising 4th grader (I'm OP of that workbook for C student thread) to review his math topics last year. I'm curious how teachers help make this 'transition' happen in their little heads, coz I found it almost impossible to use my languages to convey the idea/reasoning and grasp a new concept, even with my own kids. I really think math is the hardest to teach...

THANKS!