kitchen table math, the sequel: The meaning of an expression?

Sunday, September 11, 2011

The meaning of an expression?

I have a question about an Integrated Algebra homework assignment:
In 3-10, state the meaning of each expression in part a and in part b, and simplify the expression in each part.
The first two problems:
3.  a.  20 + (6+1)    b.  20 + 6 + 1
4.  a.  18 - (4 + 3)   b.  18 - 4 + 3 
What does "state the meaning" mean?  I suspect it means to write the equation in words, as explained in this Yahoo Answers response offered by a teacher.

Also, I noticed that every homework exercise in the textbook has a "Writing About Mathematics" section.  I wonder if the teacher will correct all the writing assignments.

Lots of writing ahead.

The book is Amsco's Integrated Algebra for New York State.


Crimson Wife said...

We just did a section in Singapore 5A on order of operations. In #3, the meaning of each expression is the same (27) because addition is commutative. In #4, the meaning of a is 11 while the meaning of b is 17 because the parenthesis changes the number subtracted and subtraction is not commutative.

Grace said...

Thank you, Crimson Wife
So would the answers to "state the meaning" and "simplify" be the same? In the case of #3a, wouldn't it be 27 for both.

Crimson Wife said...

No, I would interpret "simplify the expression" as asking the student to write a simpler expression that is equivalent to the original, more complex one.

3a: 20 + 7
3b: 26 + 1
4a: 18 - 7
4b: 14 + 3

Anonymous said...

I, also, would assume that the focus is on order of operations and properties. Here is what I would guess they are looking for:
3a. Meaning: 20 plus the sum of 6 and 1. Simplifies to 27.
3b. Meaning: Start with 20, then add 6, then add 1. Simplifies to 27.
4a. Meaning: 18 minus the sum of 4 and 3. Simplifies to 11.
4b. Meaning: Start with 18, then subtract 4, then add 3. Simplifies to 17.
The follow-up question will probably be "Why did the answers match for some problems but not match for others?"

Grace said...

It seems very murky.

How "simple" do you go to simplify an expression? Is 3b "26 + 1" or is it "27"? If it's "26 + 1", why isn't it "20 + 7"? And if it's "27", then what the heck is the "meaning" of the expression?

Crimson Wife said...

3b doesn't simplify to 20 + 7 because in the order of operations, one works from left to right.

lgm said...

If you scroll back up in the text,to the beginning of the section before the exercises which is labeled "Expressions with Grouping Symbols", you'll see the author has given examples of both 'meaning' and 'simplify':

In mathematics, parenthesis () act as grouping symbols, giving diferent meanings to expressions. For example,
(4x6)+7 means "add 7 to the product of 4 and 6", while 4x(6+7) means "multiply the sum of 6 and 7 by 4".

When simplifying any numerical expressions, always perform the operation in parenthesis first.
4 x (6+7)=4x13=52

From this, it is hard for students to understand what simplify is; usually the teacher will elaborate if they don't remember from pre-algebra. At this point, the students know simplify to be 'combine all like terms' but if it's just a numerical expression they know that a numerical expression is a name for a number and the simplest form is that number. So 27 is the simplest form of 26+1.

ChemProf said...

It is murky. There isn't some general definition for "the meaning of the expression." You need to ask the instructor what he/she is looking for, or if you are the instructor decide what you want.

"Simplify" can similarly be murky -- knowing when to stop isn't clear.

Grace said...

Thank you lgm, I found that section in the text.

It strikes me as excessive writing to have students write out "add 7 to the product of 4 and 6" or something similar for each equation after they've done the actual calculation. But I guess this is typical, and necessary for adherence to state standards.

lgm said...

I doubt it is necessary as it is part of the pre-algebra review, however with the number of ELL and remedial transfer students, it is probably a good idea for some classes to have that assignment. Neither of my children's algebra teachers covered that chapter.