This looks right to me but teacher marked him wrong? (number properties)

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Tdsj81

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Ok I don't know much on this kind of problem even though it's only for 3rd grade math. I never paid much attention in school. But now my son is in it. Simple question is he really wrong here?

Seems like all associative problems use parentheses. And commutative problems don't use them. So I think he's correct? 20191003_094719.jpg
 
Associative is definitely correct, but not quite for the reason you state.

The associative property involves only moving parentheses (that is, changing the grouping). The commutative property involves only changing the order of addends; there may be parentheses, but they won't move (relative to their content).

For example, (1 + 2) + 3 = 3 + (1 + 2) illustrates the commutative property, because things have only been moved around, without changing grouping.

In your example, only the parentheses moved, so it is the associative property that was applied.
 
Dr.Peterson said:
Associative is definitely correct, but not quite for the reason you state.

The associative property involves only moving parentheses (that is, changing the grouping). The commutative property involves only changing the order of addends; there may be parentheses, but they won't move (relative to their content).

For example, (1 + 2) + 3 = 3 + (1 + 2) illustrates the commutative property, because things have only been moved around, without changing grouping.

In your example, only the parentheses moved, so it is the associative property that was applied.
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Wow. Ok thanks. They expect a 9 year old to get this? I'm 38 I'm either really dumb or ok I'm really dumb ... But still I can hardly wrap my head around what you just said. I get the idea. But to apply it literally is beyond my grasp
 
Ok, I understand "find each sum". But to identify the property don't we need to see the right side of an equality?
4 + (6 + 2) = what? If it's (4 + 6) + 2, then it's associative. If it's (6 + 2) + 4, then it's commutative.
What should I do with the second expression? Is it equal to the first?
 
It is definitely poorly stated, though possibly if we saw the whole set it would be a little clearer. I'm assuming the intent is to verify that both expressions have the same value, and then state which property explains that.
 
Tdsj81 said:
Wow. Ok thanks. They expect a 9 year old to get this? I'm 38 I'm either really dumb or ok I'm really dumb ... But still I can hardly wrap my head around what you just said. I get the idea. But to apply it literally is beyond my grasp
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You are not dumb. The curriculum is.

In learning arithmetic, what is important to understand is that the order in which you add or multiply two numbers makes no difference.

[MATH]7 + 2 = 9 = 2 + 7 \text { and } 7 * 2 = 14 = 2 * 7.[/MATH]
That is not true for subtraction and division.

[MATH]7 - 2 = 5 \text { but } 2 - 7 \text { does not equal } 5.[/MATH]
The purpose of parentheses is to specify the order in which things are done. You do what is in parentheses first. But if all you are doing is adding or multiplying, order does not matter, and so parentheses do not matter.

[MATH]7 + (2 + 11) = 7 + 13 = 20 \text { and } (7 + 2) + 11 = 9 + 11 = 20.[/MATH]
In addition and multiplication, order does not matter (commutative law).

In addition and multiplication, parentheses do not matter (associative law).

In subtraction and division, order does matter, and so parentheses matter. They are not commutative and not associative.

When does order matter and when does it not matter. That is what 9 year olds need to know, not the technical names used to specify those facts.
 
I fully agree. The names of the properties are useful in algebra, where you need to talk about such things by name; they are not helpful in arithmetic.

The Common Core standards say that students show be able to apply these properties:
​
Apply properties of operations as strategies to multiply and divide.​

But there is a footnote:

Students need not use formal terms for these properties.​

There is no mention of identifying the properties by name. But I get the impression that many curriculum writers miss the footnote and think they need to test students on this.

The same issue shows up even in first grade!
 
lev888 said:
Ok, I understand "find each sum". But to identify the property don't we need to see the right side of an equality?
4 + (6 + 2) = what? If it's (4 + 6) + 2, then it's associative. If it's (6 + 2) + 4, then it's commutative.
What should I do with the second expression? Is it equal to the first?
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Here is the full paper. This all started because it looked like #7 had also been marked wrong when I think it's correct.
 

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Dr.Peterson said:
I fully agree. The names of the properties are useful in algebra, where you need to talk about such things by name; they are not helpful in arithmetic.

The Common Core standards say that students show be able to apply these properties:
​
Apply properties of operations as strategies to multiply and divide.​

But there is a footnote:

Students need not use formal terms for these properties.​

There is no mention of identifying the properties by name. But I get the impression that many curriculum writers miss the footnote and think they need to test students on this.

The same issue shows up even in first grade!
Click to expand...

I finally got around to taking a picture of the entire paper. As stated above this all started when I thought #7 was also marked wrong when I thought it to be correct. Hopefully this helps. I agree in math I understand 7-2=5 but 2-7 cannot = 5
 
I see your son needs to learn to read directions; it says to write the letter for the correct (multiple-choice) answer in the blank, not to write the numerical answer and circle the choice!

I don't know whether that sort of detail is involved in the incorrect grading. #7 has the right answer, but is lacking the dollar sign and looks like a decimal point rather than a comma -- but that shouldn't be relevant when the answer isn't supposed to be written in the first place ...

But the answer to #2 is definitely correct, if circling the answer is acceptable.

Of course, #1 should be C.
 
I am going to try not to be too technical.

What they wanted done in the first two problems was for your son to determine the numeric value of the expression and the name of the formal property of addition involved in finding . Like Dr. Peterson, I am not enamoured of the wording. And both of us agree that the name of the property is not important at this stage of your son's education, but understanding the property is important.

Of course, if a school is going to test your child on the names, then he needs to memorize the stuff, however useless it may be immediately.

Additive identity is 0: a + 0 = a.
Commutativity of Addition: a + b = b + a
Associativity of Addition: a + (b + c) = (a + b) + c = a + b + c.
Multiplicative identity is 1: a * 1 = a.
Commutativity of Multiplication: a * b = b * a
Associativity of Multiplication: a * (b * c) = (a * b) * c = a * b * c.
Distributive Property of Multiplication over Addition: a * (b + c) = (a * b) + (a * c) = a * b + a * c.

I am not convinced that knowing the names of these properties is important even in elementary algebra as taught in high school.
 
Knowing how to use the properties is important, knowing their names is almost meaningless. I have thought that for years and am happy to see that the other helpers agree with me.
 
JeffM said:
Additive identity is 0: a + 0 = a.
Commutativity of Addition: a + b = b + a
Associativity of Addition: a + (b + c) = (a + b) + c = a + b + c.
Multiplicative identity is 1: a * 1 = a.
Commutativity of Multiplication: a * b = b * a
Associativity of Multiplication: a * (b * c) = (a * b) * c = a * b * c.
Distributive Property of Multiplication over Addition: a * (b + c) = (a * b) + (a * c) = a * b + a * c.

I am not convinced that knowing the names of these properties is important even in elementary algebra as taught in high school.
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What, no order properties and no mention of the linear continuum? :devilish: In for a penny, in for a pound.

-Dan
 
JeffM said:
In third grade, I doubt that they are discussing real numbers.
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But why not? If you can teach it to them while they are young then you don't have to re-teach it later! ?

Honesly, it seems like the curriculums are now built that way. (Not that I think they actually work like they're supposed to.)

But I suppose this conversation belongs in a different thread.

-Dan
 
The saddess part of all this is that the student received a grade of D when the paper is not bad at all. I would have been proud of my daughter if she got those results. It really looks like an A paper to me. Dr Peterson does have a point about following directions but to go from an A paper to a D is rediculous!
 
Jomo said:
The saddess part of all this is that the student received a grade of D when the paper is not bad at all. I would have been proud of my daughter if she got those results. It really looks like an A paper to me. Dr Peterson does have a point about following directions but to go from an A paper to a D is rediculous!
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I noticed that as well, but I am not sure that we saw the complete test.
 
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