Math help--order or operations/left to right?

[lindsey]

Nevermind. I need to figure out what I'm asking, unfortunately can't delete. LOL!

 

 

6 - 2 + 5 = ( )

 

I don't understand what order to use. Add first? Left to right? 

 

4 - 2 + 7 = ( )

 

Same here. I feel super dumb so be gentle. ::shuffle:: My husband says left to right. My kid wants to add first. I'm just super confused. :p

 

5 + 7 - 5 + ( ) = 0

 

Implying parentheses? Or do you have to add first? Because then this one contradicts it: 

 

2 - 3 + ( ) = 0 Adding first, it's...-1? 
 

Same page, 9 - 8 + 8 - ( ) = 0. Left to right it's 9 in the blank. But are we supposed to add first and then subtract? 

 

Helppp. The more I think about it the more confused I get. 

 

 

Edited September 9, 2016 by lindsey

[ReadingMama1214]

It's left to right. PEMDAS (parenthesis, exponents, multiply, divide, add, subtract)

 

"PEMDAS is an acronym for the words parenthesis, exponents, multiplication, division, addition, subtraction. For any expression, all exponents should be simplified first, followed by multiplication and division from left to right and finally addition and subtraction from left to right"

[lindsey]

It's left to right. PEMDAS (parenthesis, exponents, multiply, divide, add, subtract)

 

"PEMDAS is an acronym for the words parenthesis, exponents, multiplication, division, addition, subtraction. For any expression, all exponents should be simplified first, followed by multiplication and division from left to right and finally addition and subtraction from left to right"

 

But which comes first? In the example problems (I edited), some of them seem weirdly difficult for the place we're in (red book, early one). Sorry, I am not explaining it well. :/ I just don't get it.  9 - 8 + 8 - ( ) = 0 The blank is 7?

Edited September 9, 2016 by lindsey

[maize]

With subtraction and addition, you go left to right. They're at the same level in order of operations, and operations at the same level always go left to right.

 

These are the levels:

 

Parentheses

 

Exponents

 

Division and multiplication

 

Subtraction and addition

 

I reversed the orders of those last two from their PEMDAS standard to emphasize that multiplication and addition DO NOT come before division and subtraction respectively. Things lumped together at the same level go left to right.

Edited September 9, 2016 by maize

[SilverMoon]

All of those should be worked left to right.

 

A better acronym is PEMA.

 

Parentheses

Exponents

Multiplication/division

Addition/subtraction

 

If you are down to all addition and subtraction then you are to go left to right across them. They are are the reverse of each other and go together.

 

Same with multiplication and division. They are reverse operations and go together, worked left to right.

[Critterfixer]

The way I teach my boys is to think about the size of the fish in a pool.

Parenthesis are big fish. You get them out of the water first.

Then go get the exponents.

But then you have multiplication and division fish. Those are reverse operations, so they are the same size of fish. Which should you catch first? The one you see first. Work them left to right until you fish them out.

Then you have addition and subtraction fish. They are also reverse operations, so again, same size of fish. Fish them out left to right.

Pond is fished.

[EKS]

You add or subtract from left to right in the order that you encounter it.

 

But a better way to think about it is that anything being subtracted is actually a negative number and you are really adding everything.  Then you can do it in any order.

[lindsey]

Oh man. I just told him the opposite.

 

Okay, so for the one we are adding a -7?!

[maize]

5+7-5+(-7)=0

 

Yes

[lindsey]

He just does not really get negative numbers yet so I am skipping that. Lol Thank you all so much!!

[regentrude]

but since addition is commutative, it does not really mater whether you go left to right or right to left.

6-2+5 is the same thing as 5-2+6.

 

 

5 + 7 - 5 + ( ) = 0

You can do left to right, yo can shuffle the terms as you want - in addition (and subtraction is just the addition of the negative of the quantity), order does not matter.

This is not an "order of operations" problem since there is only one kind of operation here, addition.

 

You can first add all the positive terms and then subtract everything. or you can group it to pairs that add to zero and start with 5-5 and then do +7. It's all the same.

Edited September 9, 2016 by regentrude

[maize]

but since addition is commutative, it does not really mater whether you go left to right or right to left.

6-2+5 is the same thing as 5-2+6.

 

 

5 + 7 - 5 + ( ) = 0

You can do left to right, yo can shuffle the terms as you want - in addition (and subtraction is just the addition of the negative of the quantity), order does not matter.

This is not an "order of operations" problem since there is only one kind of operation here, addition.

 

You can first add all the positive terms and then subtract everything. or you can group it to pairs that add to zero and start with 5-5 and then do +7. It's all the same.

This is true, as long as people understand that a - sign needs to stay attached to its number. A common mistake is doing something like this:

 

4-2+2

=4-4

=0

 

Until a person can grasp subtraction as addition of a negative number, the left to right rule is necessary.

[maize]

OP, my kids had fun learning about negative numbers by playing games--we made giant numberlines out of chalk in the sidewalk that extended in both directions of zero and made up games that had them going up and down the numberline.

[lindsey]

but since addition is commutative, it does not really mater whether you go left to right or right to left.

6-2+5 is the same thing as 5-2+6.

 

 

5 + 7 - 5 + ( ) = 0

You can do left to right, yo can shuffle the terms as you want - in addition (and subtraction is just the addition of the negative of the quantity), order does not matter.

This is not an "order of operations" problem since there is only one kind of operation here, addition.

 

You can first add all the positive terms and then subtract everything. or you can group it to pairs that add to zero and start with 5-5 and then do +7. It's all the same.

 

That's not the right-to-left I mean. If he wants to add first, he's doing 5 + 2, 7...-6. Which isn't the same at all. Especially if the blank spot for an answer is on the left side ( )  = 6 - 2 + 5, he doesn't know where to start. 

Edited September 9, 2016 by lindsey

[lindsey]

This is true, as long as people understand that a - sign needs to stay attached to its number. A common mistake is doing something like this:

 

4-2+2

=4-4

=0

 

Until a person can grasp subtraction as addition of a negative number, the left to right rule is necessary.

 

I would say 4-2 is 2 + 2 is 4. Right? If that's not right I need something other than Miquon, lol.

[maize]

I would say 4-2 is 2 + 2 is 4. Right? If that's not right I need something other than Miquon, lol.

Yes you are right.

 

What regentrude is saying is that the same problem could be re-aranged as, for example, 4+2-2, or 2+(-2)+4 to achieve the same result. It all works out as long as the - sign stays attached to the 2 i.e. if you don't think of - as a subtraction operator sitting all by itself. Subtracting 2 is the same as adding a (-2).

[Paige]

I would say 4-2 is 2 + 2 is 4. Right? If that's not right I need something other than Miquon, lol.

 

Right, but we could do -2+2 first, then 4+0=4. Still 4.

 

If your DS is having a hard time, show him that his way and your way have different results. If his way was just as good, the answers would be the same. Maybe changing it to a word problem with cookies or something would help him understand. 

 

Then, you can show him that his way works if you keep the negative with the 2, as it should be drilled into his head- the sign stays with the number! He may not understand it completely now, but if you show him casually every time it comes up (if he inappropriately adds something without the negative or similar- not every day!), the concept will be familiar and easier to grasp when you get to it. 

[Arcadia]

He just does not really get negative numbers yet so I am skipping that

Since it is add and subtract, use number lines to explain the problems you listed in your first post and see if that helps.

[lindsey]

That is definitely not the way I remember learning so it will take some getting used to!! I feel like we need to slow down and go backward a bit now, blah. I don't like being confused by first grade math...not a confidence boost, at all. ;) 

[ondreeuh]

That is definitely not the way I remember learning so it will take some getting used to!! I feel like we need to slow down and go backward a bit now, blah. I don't like being confused by first grade math...not a confidence boost, at all. ;)

 

Being able to do math in your regular life is not necessarily preparation for teaching 1st grade math, as you have found out! I would suggest looking at another math program that has more explicit instructions for either you as the parent or directly to the child, so that you have a model of a good way to explain these concepts to your kid without confusing him. Trust me, it's much better to start off with a clear lesson than to circle around it, trying different things.

 

Personally I love Math in Focus because the text includes all of the teaching tools you  need - photos of manipulatives, photos of children with speech-bubbles that allow them to "explain" to the student their thought process, example problems that start out with blanks so the child learns a model for how to solve. Here's a sample page from 1B: http://www.christianbook.com/Christian/Books/product_slideshow?sku=549309&actual_sku=549309&slide=22

 

1st grade is pretty early for negative numbers, so I wouldn't stress if that is too abstract. Order of Operations is actually first taught in 5A of Math in Focus. If you really want to stay with Miquon, I would skip this section and move on to something more concrete.

[maize]

Order of operations and negative numbers are not ordinarily taught in first grade. Miquon does not follow a typical sequence.

 

I think it is fine to skip these, also fine to switch to a program with more explicit teaching if you are more comfortable with that.

Edited September 9, 2016 by maize

[wendyroo]

Nevermind. I need to figure out what I'm asking, unfortunately can't delete. LOL!

 

 

6 - 2 + 5 = ( )

 

I don't understand what order to use. Add first? Left to right? 

 

4 - 2 + 7 = ( )

 

Same here. I feel super dumb so be gentle. ::shuffle:: My husband says left to right. My kid wants to add first. I'm just super confused. :p

 

5 + 7 - 5 + ( ) = 0

 

Implying parentheses? Or do you have to add first? Because then this one contradicts it: 

 

2 - 3 + ( ) = 0 Adding first, it's...-1? 

 

Same page, 9 - 8 + 8 - ( ) = 0. Left to right it's 9 in the blank. But are we supposed to add first and then subtract? 

 

Helppp. The more I think about it the more confused I get. 

 

 

 

I agree with regentrude that viewing these as "order of operations" problems is not a helpful framework.  One of my main goals in first grade math is teaching a child to exploit the commutative property of addition to facilitate adding and subtracting groups of numbers.

 

In a problem such as 3 + 1 + 7 - 1 = ? , I would view adding and subtracting dogmatically left to right as a sign of weak conceptual skills.  A strong math student who is comfortable manipulating numbers would quickly add the 3 and the 7 and subtract the 1 from the 1 and reframe the problem as 10 + 0 = 10.

 

As for your examples, the one I bolded is incorrect.  2 - 3 is -1, but the answer would be 1 because -1 + 1 = 0.

 

There are a lot of curricula that offer strong, thorough, conceptual math with more explicit teaching than Miquon.  Singapore Primary Math is excellent, but was too many books for me to juggle.  I've never used Math in Focus (also Singapore), but that is another great option.  We use Math Mammoth and I am incredibly pleased with the depth of instruction.

 

Wendy

[SilverMoon]

Ooooooh! First grade. I missed the memo. I'd just tell the kid to work them left to right just like we do for reading and leave it at that. Unless it's one of those quirky, mathy-bent kids that want more anyway.